ABSTRACT HYDRAULICS 0F SPATIAL PIPE FLOW by Wan Wang Hu The tile main of a soil profile drainage system should have sufficient capacity, yet not be oversized. The adequacy of its design is indicated in part by the position of the water surface profile in the conduit. In general, the pipe size increases with increased dis- charge. The position of the water surface depends on the several factors of discharge, tile diameter, tile roughness and slope. Dis- charge depends largely on precipitation and hydraulic conductivity of soil. The purpose of efficient design is twofold: First, to maintain a free water surface in the main tile so that pressurized flow will not result. Second, to avoid the uneconomical use of large size dia- meter pipes for small discharge. The discharge carried by the tile main generally increases as the distance downstream from the inlet end of the main increases. The flow inside of the main increases by a constant quantity ATQ from each lateral. The flow manifests a complex non-uniform profile. On steep slopes or with large inflows, supercritical flow and waves at lateral junctions may develop. Past studies on variable discharge systems considered only water surface profiles within rectangular cross sections. This dis- sertation explores procedures for calculating the water surface pro- file in circular cross sections as influenced by channel slope and increased discharge. General equations for calculating flow depths are derived from the momentum theory. Experimental observations on water depths at junctions of laterals as well as flow in the main have been care- fully undertaken. A scale model was used to examine the validity of the theoretical analysis. In all instances, close agreement was observed between theory and experiment. The effects of surge waves was investigated analytically and experimentally. Only theoretical work has been done on the unsteady flow condition. Recommendations, based on the results of theoretical and experimental evidences, are made for the selection of main tile sizes under twenty four different field conditions. Approved m Major érofessor A C . 7d. 7% PF“ ”60/ Deparfmefl/ a/r/Mfl We £4. a: we 6 HYDRAULICS OF SPATIAL PIPE FLOW BY Wan Wang Hu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1966 ACKNOWLEDGMENTS The author wishes to acknowledge the professional and moral support of Professor Ernest H. Kidder, who has so unself- ishly given his time and skill to directing this research. The author also expresses sincere thanks to him for the patient supervision of an interrupted graduate program. The author wishes to express his appreciation to Dr. Merle L. Esmay, Dr. Robert F. MacCauley and Dr. Charles P. Wells for their guidances during the development of the thesis. W. W. Hu ii TABLE OF CONTENTS Page ABSTMCT O O 0 O O O O O O O O O O I O O O 1 ACKNOWLEWMNTS O O O O O I O O O O O O O O O 1 1 LIST OF TABLES . . . . . . . . . . . . . . . iv LIST OF FIGURES . . . . . . . . . . . . . . . v I. INTRODUCTION . . . . . . . . . . . . . . 1 II. REVIEW OF LITERATURES . . . . . . . . . . . 2 III . DESIGN OF EXPERIMENT . . . . . . . . . . ' . 5 3.1 Design Data . . . . . . . . . . . . 6 3.2 Equipment . . . . . . . . . . . . . 8 3.3 SimilitUde O O O O O O O O O O O O O 18 IV. METHODOLOGY AND DERIVATION OF EQUATION . . . . . 23 4.1 Notation . . . . . . . . . . . . . 23 4. 2 Analysis . . . . . . . . . . . . 25 4. 3 Determination of Critical Depth . . . . . . 31 V. UNSTEADY FLOW CONDITION . . . . . . . . . . 38 5.1 General Consideration . . . . . . . . . 38 5.2 Theoretical Derivation . . . . . . . . . 39 5.3 Presentation of Data . . . . . . . . . 40 VI . SURGE WAVE O O O I O 0 O O O O O O 0 0 43 6.1 General Consideration . . . . . . . . 43 6. 2 Presentation of Surge Wave Data . . . . . . 46 VII. PRESENTATION OF PROFILE DATA . . . . . . . . 61 VIII. CORGI-”Slow O O O O O O O O O O O O O O 63 uFEuNCES O O O O O O O O O O O O O O O O 64 APPENDIX 0 O O O O O O O O O O O O O O O O 6 7 LIST OF TABLES values of K for various Model and Prototype Sizes as Computed by Eqs. (3.3.9) and (3.3.10) . . . Values of Critical Depth dc and Position xc for Various Slopes, Discharges and Diameters . . . . Combination of Pipe Length and Sizes under Various Conditions of Flow for an Overall Length of Drain- age of 1320 Feet . . . . . . . . . . . . Relationships between d, A, R.and 2r for various Pipe Diameters . . . . . . . . . . . . . Theoretical and Experimental Profile Data for various Conditions . . . . . . . . . . iv Page 22 37 62 68 FIGURE 2a 2b 10 11 12 13 14 15' 16a 16b 17 18 LIST OF FIGURES Gridiron Type Tile Drainage System . . . . . Layout of Main and Lateral Tile System for Laboratory S tudy O O O O O O O O O I O O O O O 0 Cross Sections.ArA and B-B in Fig. 2a . . . . Head Tank in Operation . . . . . . . . . Side Tank in Operation . . . . . . . . . Elevation of Equipment . . . . . . . Equipment during Operation . . . . . . Lateral Inflows . . . . . . . Main Conduit Plow at Maximum Condition . . . . Flow in Main . . . . . . . . . Geometrical Elements of A Flow Cross Section . Plow at Junction . . . . . . . . . . . Neighboring Sections Upstream and Downstream of A. Critical section 0 O O O O O O O 0 Velocity, Depth, Slope and Rate of Lateral Inflow Relationship Curves for Pipe Diameter of 8 Inches Characteristic Curve for .AQ = 0.1050 cfs . . . . Surge Wave at Junction of.A Lateral and.Main . Condition before Merging of Lateral Inflow . Condition after Merging of Lateral Inflow . . . Junction Wave at Maximum Condition . . . . . Junction Waves under Various Conditions . . V Page 11 12 13 13 14 15 16 17 25 26 30 32 41 42 43 44 45 48 49 INTRODUCTION In the field of Drainage Engineering, the Yarnell-Woodward formula V = l38Rfi S"z ‘which was developed from extensive flow studies in full sized tile mains has been accepted for tile main design for over 35 years. Since the entire flow in this study entered the main at its upper end, recognition was not given to the disturbance of the flow by the injection of .AQ's from tile laterals as would occur in a complete farm field drainage system. A study was initiated in the Agricultural Engineering Department at Michigan State University in 1960 with the.following objectives: 1. To compute the water surface profiles in the main from derived theoretical equations with various combinations of flow, slape and tile diameter. 2. To select the most economical tile size combinations based on the theoretically derived profiles. 3. To verify the theoretical analysis by experiments on models. 4. To investigate the supercritical and subcritical flow and waves at lateral junctions in the main. II REVIEW OF LITERATURES This dissertation is concerned with "spatial flow" in a closed conduit. A constant increment of discharge AQ is added to this conduit at constant sixty-six foot intervals of distance. Negligible research has been reported on problems of spatial flow in closed circular conduits. Yarnell and Woodward (1920) worked intensively on the flow in drain tile. Full scale models were used for experimental inves- tigations, but the theoretical analysis was based on the assumptions of uniform flow. These investigators checked the Chezy's uniform flow formula, tested the roughness coefficient of Kutter's uniform flow formula, and found that the velocity of flow is proportional to the square root of conduit slope and the two-thirds power of the mean hydraulic radius. They also disproved the belief that the velocity of flow in a pipe flowing one-half full was the same with the one flowing full as given by Chezy's formula. For non-uniform and unsteady flow, Beij (1934) discovered that whereas the point of critical depth was located at the outlet of a gently sloping channel, this point moved upstream for increas- ing channel slopes. Keulegan (1944) derived an equation of motion for a rectangular channel with a continuously increasing flow. Surface profiles were calculated on the assumption that the rate of change of discharge with respect to the travel distance was a posi- tive constant. Conservation of momentum was used to analyze the flow. Iwagaki (1954) derived the general equation of motion for the unsteady flow subject to spatial variation of discharge in open channels. An exact analytical solution of spatial flow is not available to date. All approaches to the problem depend on a number of simplifying assump- tions. For the study of waves, classical theories concerning the simpler problem of periodic waves contained much of the informations required. Bousinesq, Rayliegh, Stokes, and Korteweg had contributed to these theories and concluded that "the curvature of wave is assumed to increase linearly from the channel bed to the curved flow surface." Horton (1938) analyzed quantitatively the channel waves chiefly sub- jected to momentum control. Scott (1944) observed surge waves for several miles. Scott also conducted a series of experiments in a small laboratory flume on solitary wave and reported the detailed behavior of it. A study of Open channel junctions was reported by Saint Anthony Fall Hydraulic Laboratory of University of Minnesota (1950), in which an intensive investigation of junction waves was observed. It was found that the backwater effects caused by junction inflows increased the water depth in upstream parts of the channel. Sandover (1957), experimenting in a model channel one meter deep and six hundred meters long, succeeded in measuring with reasonable accu- racy some of the salient features, such as wave heights and lengths of undular surge wave trains. 4 Despite all developments, a satisfactory general solution of the wave problem has not been obtained. Practical hydraulicians, therefore, have come to regard the various conditions of waves as a number of isolated cases, each requiring its own uperical treat- ment . III DESIGN OF EXPERIMENT When the land topography is gentle, a field that is indepen- dent might have a size of forty acres with dimensions of 1320 feet by 1320 feet. Three principal types of lateral subdrainage layouts in common use are the Random, Herringbone and Gridiron systems. The Gridiron system is economical since it can be designed for complete profile drainage of the field and few junctions of laterals to main are involved. It is especially advantageous in fields which have relatively uniform land slapes. It has the field layout shown in Pig. 1 in partial form for a forty-acre field. parallel laterals / I \ H— 66' 66' ‘— 1320 ft —> to outlet 1320 ft. main tile Figure l. Gridiron Type Tile Drainage System In Fig. 1, each of the twenty parallel underground laterals, spaced at sixty-six feet intervals, serves to collect the gravitational water from a two-acre area. A.tile main collects the lateral discharges and carries it to the outlet. Since a discharge increment AQ is added at intervals of sixty-six feet, the flow inside the tile main can not be uniform. Theoretically, all of the laterals would discharge the same increment AQ into the main. On steep slopes or with large inflows, supercritical flow and surge waves may develop in the main. The position of the water surface profile developed in the main should be known and used as a guide in selecting proper sizes for the tile main. Most investigations of spatial flow have been conducted in rectangular channel sections. .An experimental investigation was essen- tial for the determination of qualitative information for a circular channel section. The experhmental study was developed to investigate l) transitional flow from subcritical to supercritical and 2) surge waves at lateral junctions. The experimental study verified the theoretical derivation in this dissertation. 3.1 Design Data The several variables that must be considered in analyzing the water surface profile are briefly described below: 1. Roughness: The Manning's roughness "n" was considered a constant of 0.011 for smooth clay or concrete tile. 2. Size of Tile: Lateral tiles were four inches diameter. Prototype main tiles used were four, five, six, eight and ten inches diameter. 3. Drainage Coefficient: The drainage coefficient C is the the depth of water in inches to be removed.from.the drain- age area in twenty four hours. Correlating the drainage coefficient with rainfall is difficult since the distri- bution of rainfall during the crop growing season and the rainfall intensity must be considered along with evapora- tion and hydraulic conductivity of soils. Selection of the drainage coefficient is primarily based on experience and judgement. The rate of drainage selected should result in minimum crop damage. This research used three-, five-, seven-, and ten-eighths of an inch as the drainage coefficients of laterals, each serving a two-acre area in Fig. l were calculated from the equation .aQ = 0.042CA * and tabulated below: Drainage Coefficient Corresponding Discharge per Area of Two Acres 0 AQ 3/8 inches 0.0315 cfs 5/8 inches 0.0525 cfs 7/8 inches 0.0735 cfs 10/8 inches 0.1050 cfs * See reference: U. 8. Soil Conservation Service (1953) "Farm Planners' Handbook" 4. Slope of Tile: Topography is the major factor influencing the slopes of tile.1ines. In this study, the slopes of laterals were assumed to be small, less than a fall of 1 ft per 1000 ft, so that high velocity or supercritical flow would not occur. Seven slopes of main tiles were studies to cover most field conditions. They were: 0.0005, 0.0010, 0.0025, 0.005, 0.010, 0.025 and 0.05 feet per foot of main. 3.2 Equipment Sketches and photographs of the equipment used are shown in Figs. 2--8. The following paragraphs describe briefly the various components of the equipment and how they were used. Fig. 2 shows the general layout of the experimental set-up. l. 3. The main tank dimensions were 2.5 ft by 1.5 ft by 1.5 ft (see Fig.3). A gravel screen was used to tranquilize the inflowing water. The side walls were made of transparent plastic sheets. Two lateral tanks supplied the lateral inflow. Each tank had 1) dimensions of 1.5 ft cubic and 2) transparent side walls and gravel screens. All junctions and edges are tightly sealed with rubber gaskets and glue to prevent leakage. The main conduit shown in Fig. 2a was made of lucite pipe sections of the following sizes: 2.5 inches inside diameter, 4 feet long; 3 inches inside diameter, 4.5 feet long; 4 inches inside diameter, 4.5 feet long. 6. The main conduit was laid on an adjustable slope for experi- ‘ments on slope variation. The two lateral lucite pipes shown in Fig. 2a had the following dimensions: 2 inches inside diameter, 3 feet long; 3 inches inside diameter, 3 feet long. Both lateral pipes were tightly connected to the main pipe. The Manning's roughness "n" for all lucite pipes were tested. It was a constant value of 0.009. All pipe junctions were smoothly constructed to provide a straight bottom line. The junctions of pipes and tanks were sealed with soft rubber so that they could be tilted without leakage. An adjustable hardwood bed slope was used to support the main pipe as shown in Pig. 5. It could be adjusted to staximum slope of 0.05 ft per ft. To increase the slope, the lateral tanks were elevated by inserting blocks under the tank bottom. The lateral flow velocities were always low. The main tank water was supplied by pump and controlled by valves. Lateral tanks were supplied by hoses connected to water faucets. A white paper covered blackboard was installed vertically on the left side of the main, opposite the lateral tanks as shown in Pig. 6. The blackboard was set strictly parallel to the main pipe. A flood light was set at the right side of the main so that the light could project the flow profile on the white paper. .A precise point gage was set to slide on the top edge of the board to mea- sure the depth of profile projections. The point gage could be 10. 10 moved to any horizontal position and could be read to one- hundredth of an inch. The rate of flow was controlled by the valve openings. These ‘were protested by direct measurements and found to be accurate and reliable. For shallow flow depths, dye (Potassium Permanganate, KMnO4) ‘was injected into the flow to color the water. ll “mamom ow #05 33am 33333 now Eoumzm odE. H833 one 5m: mo 50%: "on 0.»:me 3&3 80E flamenco m a. V J . luff“! _ _ MI! _ D. _ E. _ _ 0mm :v and. am ..V_W :\|+|‘L 4V |+l I 3' J ,1 Section B-B ...__ 8n_.12I1_._ 8n u| 3! 1-5' '4\ CT) “' 3" I.D. T J Gravel Screen to be connected to the main pipe of 3"I.D. Figure 2b: Cross Sections A-A and B-B in Fig. 2a 13 I v .Q - “a - ; Figure 4: Side Tank in Operation “ode om ou #05 Reagan mo Saugoam untuynow we 3.00.3 0573:“ x» 10130.0 04 1.13 Payton—man visa...» nonz/ am am mm _ 99% Tau 122,6 «+23 » puss... 21> 15 (b) Figure 6: Equipment during Operation 16 (3) AQ = 0.0735 cfs (b) so = 0.1050 cfs Figure 7: Lateral Inflows 17 Figure 8: Main Channel Flow at Maximum Condition AQ = 0.1050 cfs S = 0.05 Q = 2.100 cfs wave . 18 3.3 Similitude The problem under consideration was analyzed in two parts. size and discharge. the parameters. Part one was the flow profile with a channel section of constant Part two was the flow depths just upstream and downstream from a junction where the lateral discharge produced a In this section, Buckingham's 1r- method was used to analyze Ihg gnalygig f2; ghannel sections of constant sige and discharge The following list of parameters was considered to be significant in the dimensional analysis of the problem under consideration: Symbol Ad AI. Y Entity difference of flow depths of two flow sections slope of the conduit distance between the two flow sections average velocity of the two flow sections average hydraulic depths of two flow sections density of water dynamic viscosity of water unit weight of water MLT Dimension L LO L LT The difference of two flow depths,.ed, could then be expressed as a function of all other variables in this form: Ad=¢. (3. AL, V. mfg/BY) 19 All these seven variables may be completely described by the three fundamental dimensions of MLT system. Hence there are 7 - 3 = 4 dimensionless 1T- terms: Ad = ¢,( 'rr., 1r, , 1r, , ’17.) ------------ (3.3.2) By choosing f, V and D as the repeating primary variables and assign- ing a negative unit exponent for each non-repeating variable, the four 1f- terms are formed as follows: b. ’TT. = ya'v Dc‘ Y'1 11.2 = fa; vb; Del/('1 ------------- (3.3.3) 1r, = faavb’ 13°33"1 1r, = ga‘vb‘n ”ail Substituting the MLT dimensions, one obtains: 0 -3 a. on 13' cl -7. '2 " ’lr,=M°L°r =(ML ) (LT ) (L) (ML T ) -------- (3.3.4) By equating corresponding values of exponents on both sides of Eq. (3.3.4), one obtains the values of a. , b, , and c. to be: a, = 1, b. = 2 and c, = -1. This calculation shows that 41; = yv‘lnv = Froude Number NF ------------- (3.3.53) Following the same process, the other three fl'terms are found: «r, = VDf/f = Reynolds Number NR w; = 3'1 ------------- (3.3.5b) 11" = D/ AL Therefore, the difference of two flow depths 45d can be expressed as ad = 4H N}; , NR , D/AL, s") ------------- (3.3.6) 20 Eq. (3.3.6) shows 4d as a function of Reynolds Number, Froude Number, slope and the depth-length ratio. 2. Flow wave at the junction The variable, lateral inflow AQ, was added to the conditions existing under case 1. There would be eight variables and five dimensionless 7f terms. 4Q has the dimension LST.‘. Proceeding as in case 1, one found: ad = 4>1( NF , NR , s" , D/AL, VDz/AQ) ----------- (3.3.7) The fifth fl'term could be analyzed further. Since the conti- nuity holds Q = VA = NAQ, where N is the number of laterals, it follows that .V_D‘ =N_VP.1 = NVD‘ =32: =32 ----------- (3.3.8) aQ NAQ VA A T Substituting Eq. (3.3.8) into Eq. (3.3.7), Ad becomes a function of Reynolds Number, Froude Number, slope, the depth-length ratio and the depth-width ratio. Geometric similarity could have been easily achieved in the design of the experiment, but the attainment of dynamic similarity required the simultaneous equalities of two dimensionless parameters N? and NR. For the experiment, it was difficult to construct precise equipment required to match the two dynamic similarities. However, the discharge of the main and the laterals of this problem were usu- ally small and the author used the following procedures to overcome the difficulty: (1) For investigation of open-channel flow as in case 1, Manning's formula was used for similarity. Thus by equating Manning's 21 velocities for model and prototype, one obtains the following equation: 2 *é a Qm Am Vm Dm Dm “m Dm /3 ._ = = “72—4— : 0.818(-— ------------ (3.3.9) Qp AP VP DP DP “p DP (2) For investigation of wave motion and profile as in case 2. Froude Number was used for similarity. By equating Froude Number for model and prototype, one obtains the following equation: '/z_ Q A v 2 5/2 m m m Dm Dm (Imn) — ------------ (303010) Qp Ap Vp D If it was assumed that the discharge in the model was directly proportional to the discharge in the prototype, i.e., Qm = K Qp , then one could compute the values of K by Eqs. (3.3.9) and (3.3.10). These values are shown in Table l. 22 .Ewpmmfipmgfi 263 mo on: any 90% man Simavém “consumapum>ca scam no «a: one son as Am.m.m3 .am “manuaum Hoa.o saH.o mam.o mem.o coo.a Aoa.m.mv Hao.o mma.o ms~.o um:.o mam.o .. Am.m.mw m:o.o mmo.o asfl.o me~.o mm:.o AoH.m.mV mmo.o Hmo.o mma.o 0H~.o mam.o Am.m.mv Hmo.o :mo.o NHH.o eaa.o mom.o AoH.m.mV =m.~ Hmo.o emo.o mso.o mNH.o mmm.o Am.m.mv .3553 =oa =m =m zm =3 asses mcoanmsvm gan—Md 099395 nod.m.mv new Am.m.mV man 509% 3939.3 mm monwm RS355 new Homo: 3033, now 2 .«0 mosau> 3.. 0.3.3. Symbol A.L AQ IV METHODOLOGY AND DERIVATION OF EQUATIONS 4.1 Notation Definition flow depth hydraulic depth cross sectional flow area free surface width of flow slape of channel hydraulic radius angle of channel inclination length of channel distance between two flow sections discharge in main conduit lateral discharge or increment of discharge velocity of flow discharge per unit surface area ratio of D/R distance along channel measured from the initial inlet end of the conduit specific energy 23 Unit ft ft ft ft ft/ft ft ft ft cfs cfs fps cfs/ftz ft ft 24 coefficient of resistance infinitisimal increment of distance dynamic viscosity kinematic viscosity unit weight of water density of water Manning's roughness of channel numbers of laterals frictional force shear stress Froude Number Froude Number at n-th section Reynolds Number radius of pipe wave celerity wave height pressure force momentum force weight of water body wetted perimeter ft lb-sec/ft‘ fta /sec lbs/ft' lb-sect/ft‘ ft fps ft lb 1b lb ft 25 k.2 Analysis l \j ’ / d' ‘W “I __4m-£E____ G '—- —__1__ ~— ‘g L ——em T 61) ab Figure 9: Flow in Main Forces, including pressure, gravitation, friction and ‘momentum are involved and control the flow profile in the main tile. momentum theory was used for analysis. The general momentum equation is: Pp. - r" + w sinO - T = rm -------------- (4.2.1) where FF is the pressure force, W is the weight of the water body between sections (:) and (:) in Fig. 9, I’is the frictional force and R. the momentum force. 2. Pressure force Pp For the flow cross section shown in Fig. 10: 26 Figure 10: Geometrical Elements of A Flow Cross Section V 27 the equation of circle is X = i [213’ - y: ---------------------- (402e2) The pressure force is defined as the product of the flow area A, the unit weight of water Y and the height of the centroid of A, thus, y=d 2 1.3/1. Fp = yf (d-y)dA = Y(d-r)A + _Y(2rd-d) -------- (4.2.3) =0 3 where d z 1 A = j 2xdy = [(d-r) 2rd-d - 133151224. —7|’r"] o r 2 = 4:01) ---------------------- (4.2.4) Component of gravitational force W sinG The gravitational force is equal to the unit weight of water times the volume of the water body and its component along the direction of flow is W sinG: W sing YAL A sine YA L sinG [ (d-r) / 2rd-dz - r'sin” Ligl + %1rr"] ...................... (4.2.5) where A.L is the distance between two neighboring cross sections. The depth d is the average depth of the water body. Since .AL and (d, -dz) were taken small, d could be assumed equal to the end depth. Thus d for the cross sections N and N+l was taken equal to dun. 28 Frictional force 'I Based on the assmption that AL was small and the flow was uniform within the two cross sections, the Chezy's formula shows that 1. I. = R8 and S = v =—_L' ---------- 40206 I " e e ‘cTi' an ‘ ’ where I; is the shear stress, R is the hydraulic radius, Se is the slope of the energy line and C is the Chezy's constant. Frictional force T equals the shear stress multiplied by the rubbing surface area: 2 1 = ‘QAL P = YR GTE-{E AL P """"" (4'2'7) where P is the wetted perimeter. Since R.=.A/P and C‘= 8g/f where f is the resistance coefficient in Chezy's formula and g is the gravitational acceleration, then 3 I. T = L‘%Q_ ._. M .......... (4,2,3) 0 AR BgAR Substituting Manning's roughness n for f, one obtains .i = n" _ (0.011)‘ _ 0.0000548 _______ (4 2 9) 88 (1.480%:W (1.486)‘R"' R"? ° ' and 1 0.0000548 ‘L T = TQ ---------- (4.2.10) where n was assumed to have a constant value of 0.011 for smooth clay pipes. 6. 29 Momentum force Fm The momentum force is equal to the product of the mass and the change in flow velocities. Thus, Fm = gQ(V2 - v1) = fez. - TEE) ------------ (41.11) where A can be computed from Eq. (4.2.4). General equations A. For calculating the two section depths in a conduit with a given constant discharge, Eq. (4.2.1) was applied. After substituting all values of forces and simplifying, this equa- tion reduced to the following form: 2 '9' + (dz' r)Az +-§- (2rdz- d:)% - 4L sine Az 3A; 2 2 0.000054/Bj 4L = _Q_ + ((1.- r)... + Z (my-<13)" 3 3A 3 AtR, ' ------------- (4.2012) With one of the two depths known, the second depth could be calculated from Eq. (4.2.12). The controlling depth is the critical depth, and computation of the profile should begin at the critical section. Computation of critical depth is in the following section. For calculation of the two adjacent depths just upstream and downstream at the lateral junction, Eq. (4.2.12) needs modification. At each junction where lateral discharge .AQ flowed into the main as shown in Fig. 11, A L was only four inches and hence negligible. 30 _. T " “t "' Q + eQ .94 ‘*|L‘.AI.= 4" Figure 11: Flow at Junction When the discharge was varied fron.Q to Q+aQ and .aL neglected, Eq. (4.2.12) became: I A - .2. .“4 8A. + (d, r)A, + 3 (2rd. d.) ‘I. = .iQfiL + (d,-r)A,_ +§ (2rd,- at)" ---- (4.2.13) 31 4.3. Detenmination of Critical Depth The critical depth is defined as the flow depth at which the flow energy assumes its least value. This depth can be computed from the given flow condition. In an open channel of subcritical slope with a spatial discharge, the critical depth occurs at the channel outlet. Critical depth moves upstream as the slope in- creases. Since critical depth is controlling, computation of the water surface profile requires that the magnitude and position of .the critical depth be determined. 1. The criterion for critical depth Since flow is down grade toward the outlet end of the tile main, its upper end could be considered closed and the lower end open. Continuity equation shows that VA = 1440 or V]: = qx --------- (4.3.1) where V is the average velocity of flow in tile, N is the number of laterals which carry each a discharge 0Q into the main, D is the hydraulic depth which equals to A/T, T is the flow width of free surface (Fig. 10), x is the distance of the flow section from the inlet end of the main (Fig. 12) and q is the discharge per unit surface area or equals to Q/Tx. The flow is tranquil for small values of x or N and critical depth occurs at the outlet section. If the flow increases so that supercritical flow is realized at the open end of the channel, a critical flow section results at a distance xc from the inlet end. This critical section.must possess a Froude Number of unity. 2. 32 - .As shown in Fig. 12, let x. and x, be the positions of upstream and downstream neighboring sections, each section is an infinitisimal distance 6 from the critical section. Section (:) is then subcritical and section (:) is supercritical. The inequalities are then F'<.l and F,> l, Fn being the Froude number of n-th section. . Between the two sections, the water surface exhibits either discontinuous or continuous conditions at the critical section. The discontinuous condition is a negative hydraulic jump which is known to be impossible. The continuous case is then the only physically valid condition which yields a finite value of dd/dx. inlet end of the pipe a ““1 4? ‘1 dc +2 "" V __. X. .___.(2) AJ x‘ 29 Figure 12: Neighboring Sections Upstream and Downstream of a Critical Section. Eguations for ddldx with a finite value Keulegan (1944) derived an equation of motion for rectangular channel from the theory of conservation of energy: ‘3 L3 = 3‘s'%’ - gal;— - q-g ----------------- (4.3.2) 33 where f. is Blasius coefficient of resistance defined by For a circular conduit, the flow depth d may be replaced by its equivalence in term of the hydraulic depth D. For the friction term, it suffices to multiply f, by the ratio m=D/R for the transformation from a rectangular channel to circular conduit. Eq. (4.3.2) is then: t dD f V V V '31.! = 8(9' 3;) ' 335“ «:5 """"" ““3"” The original derivation assumed uniform velocity at cross sections. For accuracy, the term VdV/dx should be mmltiplied by the energy correction factor o“which is near unity, to account for non-uniform velocity distribution. An approximation was introduced by assuming as to be equal to unity. It was found from the continuity equation (4.3.1) that dD dV VD _ d v — + D — — ----------- 0 ° _ qx an _ q (4 3 5) Let Eq. (4.3.5) be multiplied by V/D, to obtain dV v as» v.5; = ,3 - m; ----------- (4.3.6) Eq. (4.3.6) can be substituted into Eq. (4.3.4), which then becomes: 1 v _ dD v _ d mf v‘ — - .... s- —p - —L_ D ----------- QB dx D 3( d2) 20 q% (4'3°7) and s -2qV - if?! +gDS - dD _ = ----------- 4.3.8 dx ED _ v, < > At the critical section, the value of gD approaches V since its Froude Number must equal to unity. This means that the numerator 34 on the right side of Eq. (4.3.8) must approach zero to give dD/dx a finite value. Accordingly, I. 8DS -flf‘zl - 2qV = O """""" (4.3.9) replacing gD by V1, one obtains s - 8.1131: 2.3. ---------- (4.3.10) Since Vl = gD and VD = qx, it follows that V = qu and V = (qu9b ---------- (4.3.11) Eliminating V in Eq. (4.3.10), one obtains x = 8C? ---------- (4.3.12) (3 - m£./2)’g This criterion has led to the location of the critical depth. Since the free outlet end of the pipe was lower than the inlet end, S was considered positive. When S was greater than the value of mf./2, x had a positive value, and if S was decreased, but still maintained larger than mf./2, the critical depth moved towards the free end of the conduit. To obtain the maximum slope for which the critical depth was at the free end of conduit, f. was denoted as the resistance coefficient at the end of conduit. Since there were twenty laterals, the total discharge was 20(AxQ). The value of x = L was 1320 ft. Eq. (4.3.12) then led to the following: s = mf./2 + (8q‘/gL)y3 ---------- (4.3.13) From the condition gD = V,‘ = (Q/Af' and the fact that D = A/T where T was the width of the free water surface, it has followed 35 .zthat for the critical condition: a 3 Q Is = Ac / Tc ----------- (4.3.14) from geometry, T = zfiar - d) ----------- (4.3.15) The largest diameter of the outlet end pipe for this research was 10 inches and the maximum discharge was 20(AQ) = 20(0.1050) cfs. It was assumed that the viscosity 1' of water at 70‘F is a constant value of 1.05 x 10" ft'lsec. Substituting these values into Eq. (4.3.14), one obtains 1’. / r. = 0.137 when Eqs. (4.2.4) and (4.3.15) were used, the value of the critical depth dc was found by trial to be 6.42 inches. The corresponding data for the critical section were: critical area Ac = 0.3699 ftz critical wetted perimeter Pc = 1.55 ft critical hydraulic depth Dc = 0.2389 ft critical velocity Vb = 5.68 fps Dy Blassiu's law of resistance, it was concluded that r. = masons/,1)” = 0.00296 also, mf./2 s Df./2R = Af./2TR = 0.00286, furthermore, by Eq. (4.3.1) 3:2 3 VA 3 5.68:0.3699g 0.001987 Tr? 9.61 12 x 1320 (1:: Therefore, by Eq. (4.3.13), the value of the critical slope for the extrema condition of this problem was 31-31. 931%. 3c 2 + (8L ) _ 0.003765 3. 36 This value of Sc was a demarcation between subcritical flow and supercritical flow. Flatter slopes resulted in a critical depth at the free outlet of the channel and its critical section movedupstream when the slope was greater than 0.003765. Computation A. For slopes flatter than 0.003765, the critical depths were calculated from Eq. (4.3.14) by trial. It was observed that the critical section for those conditions occured at the outlet end. B. For slopes steeper than 0.003765, the critical depths could be calculated by the following procedures: a. 'Estimate the approximate size of pipe to be used in certain intervals of lateral inflows. .A discharge N40 and the corresponding hydraulic elements were roughly obtained. b. Where the flow was turbulent, the coefficient of resis- tance f| from Moody's diagram was found with the hydrau- lic elements given by step a.. c. The position of critical depth was found from Eq.(4.3.12). d. A.careful experiment was run to simulate the prototype at critical section. The model flow depth was measured. e._ By the technique of similitude which was stated in previous section "DESIGN OF EXPERIMENT", the model critical depth was converted to the prototype critical depth. values of critical depths and their positions are listed in Table 2 for several values of discharge, slope and pipe diameter. 37 Table 2. values of Critical Depths dc and Positions xc for Various Slopes, Discharges and Diameters xc (ft) dc 2r Lateral Slope Discharge From From Outlet Inlet in in S AQ cfs 0.0315 4.62 10 0.0525 5.27 10 °'°°°5 0.0735 0 132° 5.77 10 0.1050 6.42 10 0.0315 4.62 10 0.0525 5.27 10 0'0010 0.0735 0 1320 5.77‘ 10 0.1050 6.42 10 0.0315 4.62 10 0.0525 5.27 10 0'0025 0.0735 0 132° 5.77 10 0.1050 6.42 10 0.0315 282.75 1037.25 4.10 8 0 0050 0.0525 240.00 1080.00 4.40 8 ’ 0.0735 168.30 1151.70 4.48 8 0.1050 100.00 1220.00 4.50 8 0.0315 370.00 950.00 3.86 6 0.0100 0.0525 316.00 1004.00 4.04 6 0.0735 160.00 1160.00 4.21 8 0.0315 543.50 776.50 2.74 5 0.0250 0.0525 483.80 836.20 2.60 5 0.0735 360.00 960.00 2.97 6 0 0500 0.0315 680.75 639.25 2.41 4 ' ,0.0525 291.35 1028.65 4.27 5 UNSTEADY FLOW CONDITION 5.1 General Consideration The purpose of this section was to analyze mathematically the velocity-depth relationship and the variation of water surface profile under the unsteady flow condition. The experimental inves- tigation for this phase usually required a very large scale model. Since there was an increment of lateral discharge into the main at a sixty-six foot interval, general analysis for non-uniform lateral inflows was difficult. However, an assumption that the lateral inflows were uniform and continuous permitted a simplication in the analysis and led to adequate results. With this assumption, a lateral inflow of AQ = 0.1050 cfs occurring every sixty six feet was considered as q = 0.1050/66 = 0.0016 cfs per foot of main. For laminar flow, the Reynolds Number NR = VDA) must be less than 2000. By this criteria, a four-inch diameter main tile must possess a velocity of less than 0.06 fps for laminar flow at 70°F. When the diameter was larger, the velocity for laminar flow was still less. Since the velocities in drain tiles were usually greater than 0.06 fps, laminar flow was seldom experienced and only turbulent flow has been considered herein. 38 39 5.2 Theoretical Derivation Steady flow motion was expressed by Eq. (4.3.4) which is repeated here for ready reference: dV dD mf.v‘ v V3; =8(S--d-;)--—2-b—- Q‘fi' --------- (4.3.4) The equation of motion for unsteady flow has the same form except that the term dV/dt should be added to the left side of Eq.(4.3.4). The equation then becomes: 1 2! 91- -32-}311, 3L _________ V dx + dt ‘ 3(5 dx> 20 q 0 (5°2'1) >The friction term, mf.V1/2D may be expressed in terms of 13 , f , R, n and g as follows: m3" = to - ___&_“1 V2 - 0 00174v‘/R“’3 --------- (5 2 2) 5D 3’ R 2.24 R” where the value 0.011 was used for n. Thus, 1. dV dV dD V V viii-+0? + g—(E- = 38 - 0.00174—y: " q-D- """"" (5-2-3) R When the slope is steep, flow is nearly uniform and the left side of Eq. (5.2.3) could be assumed to be zero. Therefore, Z _ V_. - .Y ......... gS .. 0.00174 R55 qD (5.2.4) and v __dx _ 11% [a s)‘ 02245.] at - W n+/(n + ' R... """"" ‘5'”) Eq. (5.2.5) shows the velocity-depth and also the x-t relationships. 40 5.3 Presentation of Data As a numerical example, the following conditions were assumed: diameter of pipe 2r = 8 inches total length of pipe x = 66 feet Manning's roughness n = 0.011 slope of pipe S = 0.050, 0.025 and 0.010 lateral discharge .40 = 0.1050 and 0.0735 cfs. For a given hydraulic depth D, Eqs. (4.2.4) and (4.3.15) led to the value of flow depth d which in turn could be used to compute the value of hydraulic radius R*. Eq. (4.3.1) yielded the value of q. With these data, Eq. (5.2.5) could be used to calculate the velocity V. Fig. 13 shows the relationship between velocity and hydraulic depth for various values of lateral discharges .60 and slopes S. It was observed that for a given hydraulic depth D, the flatter the slope S, and the larger the llQ, the slower was the velocity V. Eq. (5.2.5) also expresses the relationship between the pipe length x and the time of flow t. Using the same conditions given above, the "characteristic" curve C, which defines the boundary between steady and unsteady regions could be established. This curve is shown in Fig. 14. * Appendix Table 4 shows the relationships between d, A and R for various diameters of pipes ranging from four-inch to ten-inch. 41 1.2 _ 3 - - [I [17/ ./ ,I I ' .1050 cfs ! - ’. J AQ = 0 I, e AQ = 0.1050 cfs ' ,1 $1 1 0 AQ = 0.1050 cfs—71v. I” 3 ‘ ’ 40 = 0.0735 cfs . L .1 AQ = 0.0735 cfs . ’ r 40 = 0.0735 cfs _ / [Ill ' II 0 8 // [I] e ” ' I // ,Il - I Depth D L // [I] ‘ (inches) //'/// 0.6L - . ,l’ . ///, “/1 .447 //M . .-,/ //// .,/ 0 21. / I 4’,’ 8 =0.050 A7/’ 7’ S=0025 ----- /’ 3-0.010 ----- . 1 1 1 A 1 1 n 0 1 2 3 Velocity (feet per second) Figure 13: Velocity, Depth, Slope and Rate of Lateral Inflow Relationship Curves for Pipe Diameter of 8 Inches 42 30 I I I I r I 20 P Steady ‘ Time t (sec.) - 10 ” Unsteady - 0 1 1 1 l I 1 Flow Path x (feet) Figure 14: Characteristic Curve for AQ = 0.1050 cfs VI SURGE WAVES 6.1 General Consideration Fig. 15 shows schematically the wave conditions existing at the junction of a lateral and the main. In order to analyze this surge wave, it was necessary to make several assumptions as follows: 1. Conservation of energy existed. 2. Kinetic energy correction factor a was equal to unity. 3. The frictional force for this small distance, between upstream and downstream of the lateral, which equals to the lateral diameter four inches, could be neglected. Wall of Main Conduit Hydraulic_Energv Line C72g l \ / Lateral 11 Zr - CD Figure 15: Surge Wave at Junction of A Lateral and Main 43 44 Based on the above assumptions, the equation defining the surge wave was: I. ‘2. Mi- =D+h+ '33‘3‘379 ------------ (6.1.1) where h was the wave height above the normal flow depth. The wave celerity C was found from Eq. (6.1.1): 7. C = jam ............ (6.1.2) 20 + h Experiments showed that the surge height h was generally small compared to the flow hydraulic depth D except for the largest lateral discharge .80 = 0.1050 cfs, which was not usual in practical field situations. Thus it was possible to neglect h in computation in order to simplify the analysis. As shown in Figs.l6a and 16b, a surge, when arriving at a conduit junction, splits into several surges entering the connecting conduit. Since there was no surge at conduit II and III before Conduit I V. h. A. Conduit II 1 Conduit 111 V, V3 h! --.P —o- h: A: A3 Figure 16a: Condition before Merging of Lateral Inflow 45 Conduit I V. h. C. Conduit II I Conduit III 4. c 4——- v, h v, ——+- c, Figure 16b: Condition after Merging of Lateral Inflow ‘merging (see Fig. 16a), the wave height h1 = h, = 0, and the velocity difference V3 - V1 in the conduit before merging was zero. When the lateral inflow reached the junction, its flow height was reduced be- cause the flow area was expanded. A surge of height h then traveled through conduits II and III with celerities C, and C, respectively (see Fig. 16b). In the meantime, a reflected wave traveled along conduit I at a celerity equal to C,as shown in Fig. 16b. From the above condition and Eqs. (6.1.1) and (6.1.2), it could be shown that h. - h = c,(v; - V.)/g h. = C,V./g for conduit 1 ......... (6ele3) h = C,V;/g for conduit II h = 03V, /g for conduit III The continuity requires that A'V4 = Asz + A’v’ --------- (6.1.4) 46 Solving Eqs. (6.1.3) and (6.1.4) simultaneously for h, one obtains: 2 h.A. ' = ---------- .1.5 h (A. + A! + 443‘ C. (6 ) C. Cz C, where all C values were gD. To examine the validity of the various assumptions made in analyzing the surge wave, a number of experiments with various con- ditions were performed. Typical experimental set-ups are shown in Fig. 17. 6.2 Presentation of Surge Wave Data The results of theoretical calculations and those of ex= perimental investigations of the surge waves are summarized in the curves of Fig. 18. The flow conditions are indicated below each curve. Both theoretical and experimental curves were superimposed for comparison. The term "horizontal distance across lateral" means a horizontal measurement of the diameter of the lateral by consider» ing that the upper edge of junction of the lateral to the main as zero inch. Examination of the various curves shown in Fig. 18 led to the following conclusions: 1. The theoretical analysis were generally in good agree= ment with experimental observations. ‘2. When the flow slope became steeper and the flow rate larger, the theoretical and experimental data showed a greater deviation. 47 3. Since the deviations between theory and experiments were generally small, the proposed theoretical analysis could be used for predicting the wave profiles. 48 (a) Q = 2.100 cfs (b) Q = 1.050 cfs Figure 17: Junction Wave at Maximum Condition AQ = 0.1050 cfs S = 0.05 49 --*--— Experbmental 1 - - o- — - Theoretical 5n _ .. 4" _ l 0 1" 2" 3" i" Horizontal Distance Across Lateral (a) 396' from outlet, 8" pipe, S = 0.005, £0 = 0.0315 cfs Q1 = 0.4410 cfs, Qz = 0.4725 cfs 5n _ - 4" F u I l I o 1" 2" 53" ll." Horizontal Distance Across Lateral (b) 594' from outlet, 6" pipe, S = 0.005, AQ = 0.0315 cfs Q1 = 0-3455 cfs, 02 = 0.3780 cfs Figure 18: Junction Waves under various Conditions 50 -—-¥--- Experimental — - o- — - Theoretical r l I I r 5" __ _ 0‘ ‘ - / \ ‘0 o’ ‘\\ h r ' \b 4n _ "‘ 1 I J I filr 0 l" 2" 3" 4" Horizontal Distance Across Lateral (c) 264' from outlet, 8" pipe, 8 = 0.005, 40 = 0.0525 cfs Q1 = 0.8400 cfs, Q2 = 0.8925 cfs I! 4 I I l l TIL 1 l I 1 I o 1" 2" 3" 4" Horizontal Distance Across Lateral (d) 1188' from outlet, 5" pipe, 8 = 0.005, A0 = 0.0525 cfs Q1 = 0.1050 Cffl, Q2 = 0.1575 Cf! Figure 18: (continued) 51 ——w—— Experimental Theoretical .__o._ __ _ 6" _ _ 5n _, - l I 1 J L o 1" 2" . 3" 4" Horizontal Distance Across Lateral 8" pipe, S = 0.005, AQ = 0.0735 cfs 02 = 1.0290 cfs (e) 462' from outlet, Q1 = 0.9555 cfs, 5"... .- l 0 (f) 726' from outlet, 01 = 0.6615 cfs, Figure 18: 1" Horizontal Distance Across Lateral Q2 2" 6" pipe, S = 0.005, (continued) AQ = 0.0735 cfs 52 --4F--— Experflmental - - 0- - - Theoretical 7" I I T [ I h 9“. --~ m“ — 5:: I J 1 l 1 0 1n 2:: 3n 4:: Horizontal Distance Across Lateral (s) 528' from outlet, 8" pipe, 3 = 0.005, 40 = 0 1050 cfs Q1 = 1.2500 cfs, 02 = 1.3650 cfs l l l 1 1 0 1" 2" 3" 4" Horizontal Distance Across Lateral (h) 1122' from outlet, 6" pipe, 8 = 0.005, AQ = 0.1050 cfs Q1 = 0.3150 cfs, Q2 = 0.4200 cfs Figure 18: (continued) 53 * ' Experimental " -°"‘ " — Theoretical 5" I 1 I f I F- q u __ '— .. h 4 .K \ ‘5 ‘ w - a 3:: I o 1:. 2". 3:. 4:. Horizontal Distance Across Lateral (i) 462' from outlet, 6" pipe, S = 0.010, 40 = 0.0315 cfs I I l l r h n- .1 3n - - (J) 792' from.outlet, Q1 = 0.4095 cfs, J I I I I 0 Figure 18: 1" Q2 2" Horizontal Distance Across Lateral 5" pipe. 3" 4" 8 = 0.010, = 0.4410 Cfl (continued) AQ = 0.0315 cfs 54 ___¥_———— Experimental ——-e--—-- Theoretical I V F Y ' 4:: ,_ - h _ - 3" r _ 11' 11.. 2:. .4 4 Horizontal Distance Across Lateral (k) 660' from outlet, 6" pipe, S = 0.010, .AQ = 0.0525 cfs Q1 = 0.5250 cfs, 02 = 0.5775 cfs 1‘" I T T ‘ 1 l 2" I l - 0 1" 2'“ 3'" 4"“ " Horizontal Distance Across Lateral (l) 1188' from outlet, 4" pipe, 8 = 0.010, .40 = 0.0525 cfs Q1 = 0.1050 cfs, Q2 = 0.1575 cfs Figure 18: (continued) 55 —"— Experimental - ‘0’ — - Theoretical 4" J I I I I o 1" 2" 3" 4" Horizontal Distance Across Lateral (m) 462' from outlet, 8" pipe, S = 0.010, 5I1_ - K 4" .. an I I I I 1 0 I" 2" 3" 4" Horizontal Distance Across Lateral AQ = 0.0735 cfs (n) 726' from outlet, 6" pipe, 8 = 0.010, Q1 = 0.6515 CfB, Q2 = 0.7350 cfs Figure 18: (continued) 56 -—*—'— Experimental _ —o- - - Theoretical 3" - _ 2" .— l 0 1'" 2'" 3"—_4’“—_J Horizontal Distance Across Lateral (o) 462' from outlet, 5" pipe, S = 0.025, AQ = 0.0315 cfs 2:1_ I I . l l o 1" 2" 3" 4" Horizontal Distance Across lateral (P) 1122' from outlet, 4" pipe, 8 = 0.025, AQ = 0.0315 cfs 01 = 0.0935 cfs, 02 = 0.1260 cfs Figure 18: (continued), 57 '——*——-7- Experimental - — e— — —- Theoretical I ‘0-— “1"" fi" 1* 4'" Horizontal Distance Across Lateral (‘1) 330' from outlet, 6" pipe, 8 = 0.025, AQ = 0.0525 cfs 01 = 0.7875 cfs, Q2 = 0.8400 cfs 5 l l T l I P- - ,n-—'--o\ \ h 4'” \\ -« 3" L I I I I o 1" 2" 3" 4" Horizontal Distance Across Lateral (t) 660' from outlet, 5" pipe, S = 0.025, AQ = 0.0525 cfs Q1 = 0.5250 cfs, Q2 = 0.5775 cfs Figure 18: (continued) 58 ——"—" Experimental ._ .. -o- — — Theoretical 3" D 0 1n '2" .3" if Horizontal Distance Across .Lateral (s) '528' from outlet, 6" pipe, S = 0.025, 40 = 0.0735 cfs Q1 = 0.8820 cfs, 02 = 0.9555 cfs 5" ' I l l l I I I I 0 1" 2" 3" 4" Horizontal Distance Across Lateral 3:: v, (t) 924' from outlet, 5" pipe, 8 = 0.025, AQ = 0.0735 cfs Q1 = 0.4410 CfB, Q2 = 0.5415 cfs Figure 18: (continued) 59 --**-- Experimental --o---— Theoretical 5" I I l 1 I 3" I I J I I 0 1" 2" 3" 4" Horizontal Distance.Across Lateral (u) 396' from outlet, 5" pipe, S = 0.05, .60 = 0.0315 cfs 01 = 0.4410 cfs, Q2 = 0.4725 cfs 3" l l l j I 1:11 I 1 I I 1 o 1" 2" 3" 4" Horizontal Distance.Across Lateral (v), 1122' from outlet, 4" pipe, S = 0.05, 4Q = 0.0315 cfs Q1 = 0.0945 cfs, 02 = 0.1260 cfs Figure 18: (continued) 60 «———+————— Experimental —.-o_.-._ Theoretical 5"— - 4.1 ' I' I I 1 0 1" 2" 3" 4" Horizontal Distance Across Lateral (w) 462' from outlet, 5" pipe, 8 = 0.05, .AQ 0.0525 cfs Q1 = 0.6825 cfs, Q2 = 0.7350 cfs 3" _ o 1" 2" 3" 4" Horizontal Distance Across Lateral (x) 660' from outlet, 5" pipe, 8 = 0.05, 30 = 0.0525 cfs Q1 = 0.5250 cfs, Q2 = 0.5775 cfs Figure 18: (continued) VII PRESENINTION OF PROFILE DATA Table 3 summarizes the most economical combinations of the main tile sizes under various conditions for an overall length of drain of 1320 feet. The several conditions investigated includ- ed the slope which varied from 0.0005 to 0.05 ft/ft, lateral dis- charge varying from 0.0315 cfs to 0.1050 cfs, and pipe diameter ranging from four to ten inches. A complete set of profile data, comparing theory and experiment are given in.Appendix in Table 5.1 to 5.24. 61 62 Table 3: Combination of Pipe Length and Sizes under various Conditions of Flow for en Overall Length of Drain- age of 1320 Feet j— Length of Pipes in Feet Slope Lateral Discharge Diameter in Inches 5 AQ cfs 10" 8" 6" 5n 4" 0.0315 745 575 0 O 0 0.0525 810 510 0 0 0 0.0005 0.0735 960 360 0 0 0 0.1050 1170 150 0 0 0 0.0315 370 650 200 100 0 0 0010 0.0525 440 640 240 0 0 ' , 0.0735 700 520 100 0 0 0.1050 960 360 0 0 0 0.0315 100 530 270 200 220 0 0025 0.0525 230 460 460 170 0 ' 0.0735 360 460 500 0 0 0.1050 490 530 300 0 0 0.0315 0 420 340 260 300 0 0050 0.0525 0 560 330 430 0 ° 0.0735 0 690 270 360 0 0.1050 0 820 500 O 0 7 0.0315 0 150 470 330 370 0.0100 0.0525 0 300 350 340 230 0.0735 0 560 390 370 0 0.0315 0 0 300 400 620 0.0250 0.0525 0 0 430 420 470 0.0735 0 0 560 460 300 0.0315 0 0 O 630 690 0.0500 0.0525 0 0 ‘ 0 830 490 VIII CONCLUSIONS The flow profile under a given condition may be adequately pre- dicted from Eqs. (4.2.12) and (4.2.13). For constant pipe size and lateral discharge, the critical depth moves upstream in the main as the slope increases. For constant slope and constant pipe size, the critical depth moves upstream as the discharge in the main increases. A change of pipe size influences the position of critical depth only slightly. The roughness or the coefficient of friction of the pipe exerts a major influence on the flow profile as seen in Eqs. (4.2.12) and (4.2.13). As a result of momentum conservation, the upstream depth at a junction inflow would always be greater than the downstream depth. For slopes or discharges other than the twenty-four profiles presented, an approximate design of pipe size combinations could be accomplished by interpolation. Accurate design should include all steps and considerations of this dissertation. The twenty-four water surface profiles should prove a valuable tool for the design of drainage main tiles with lateral inflows. It should stimulate further experimental research in a large model. 63 REFERENCES Beij, K. Hilding 1934 Flow in Roof Gutters. Research Journal, National Bureau of Standard, 12. Chow, V. T. 1959 Open Channel Hydraulics. McCraw Hill Book Company. Dressler, R. F. 1949 Mathematical Solution of the Problem of Roll-Waves in Inclined Open Channels. Communications on Pure and Applied Mathematics, New York University, Vol. II. Frevert, Schwab, Edminster and Barnes 1955 Soil and Water Conservation Engineering. John-Wiley Book Company. Cladding, R. D. . 1950 Channel Design Factors. Engineering News Record, Feb. 16. Green, G. 1937 On the Motion of waves in a Variable Canal of Small Depth and Width. Transactions Cambridge Philosophical Society, Vol. VI. Hall, L. S. g 1943 Open Channel Flow at High Velocities. Transaction, ASCE, Vol. 108. Horton, R. 1938 Channel waves Subject Chiefly to Momentum Control. U. S. Soil Conservation Service, SCS-TP-l6, May. Honk, Ivan E. 1918 Calculation of Flow in Open Channels. Miami Conservancy District Technical Reports, Part IV. Ippen,.A. T. 1949 Mechanics of Supercritical Flow. Proceedings, ASCE, November. Ippen, A, T. and Dawson, J. H. 1949 Design of Channel Contraction. Proceedings, ASCE. 65 Israelsen, O. W. 1956 Irrigation Principles and Practices -- 2nd Edition. John-Wiley & Sons, Inc. Iwagaki, C. 1954 On the Unsteady Flow in Open Channels with Uniform Lateral Flow -- Hydraulic Studies on the Run-Off of Rain Water. 1st Report, Journal of JSCE., Vol. 39, No. 11. Izzard, C. F. 1944 The Surface Profile of Overland Flow. Transaction, AGU, Part VI. Jurney, W. H. 1946 Surge Tank Analysis. U. S. Bureau of Reclamation Technical Memorandum 632. Knapp, R. T. 1949 Design of Channel Curves for Supercritical Flow. Proceedings ASCE, November. Kirpich, P. 2. 1948 Dimensionless Constants for Hydraulic Elements of Open-Channel Cross Sections. Civil Engineering, Vol. 18, October. Keulegan, G. H. 1944 Spatially variable Discharge Over a Sloping Plane. Transactions AGU, Part VI. Keulegan, G. H. and Patterson, G. W. 1943. Effect of Turbulence and Channel Slope on Translation Waves. Research Paper RP1544, Journal of Research of National Bureau of Standards, Vol. 30, June Powell, R. W. ~ 1950 Resistance to Flow in Rough Channels. Transactions, AGU, V01. 31, No.4. Powell, R. W. 1949 Resistance to Flow in Smooth Channels. Transactions, Rouse, Hunter 1957 Elementary Mechanics of Fluids. John-Wiley & Sons, Inc.. Ramser, C. E. 1950 Flow of Water in Drainage Channels. Technical Bulletin, USDA. SCS-TP-62. 66 Saint Anthony Fall Hydraulic Laboratory 1950 Study of Open-Channel Junctions. University of Minnesota, Project Report No. 24, Part V. Sandover, and Zienkiewicz 1957 Experiments on Surge Waves. Water Power Journal, London, Vol. 9, No. 11. The Undular Surge Waves. I.A.H.R., 7th Congress, Lisbon. Scobey, F. C. 1939 The Flow of Water in Irrigation and Similar Canals. USDA Technical Bulletin. Scott, R. p 1944 Report on Waves. Report of British Association for the Advancement of Science. Swain, F. 1951 Determination of Flows in Interconnected Estuarine Channels Produced by the Combined Effects of Tidal Fluctuations and Gravity Flows. Transactions.AGU, Vol. 32, No. 5. Thomas, H. A. 1940 The Propagation of Waves in Steep Prismatic Conduits. Proceedigns of Hydraulic Conference, University of Iowa Studies in Engineering, Bulletin 20. U. S. Soil Conservation Service 1953 Farm Planners' Handbook. Upper Mississippi Region III. Uchida, R. A. 1952 On the Analysis of the Flood Wave in Reservoir by the Method of Characteristics. Proceedings, Second Japanese National Congress for Applied Mechanics. Von Seggern, M. E. 1949 Integrating the Equation of Non-uniform Flow. Proceedings, ASCE, January. Weir, C. 1950 Land Drainage. California Agricultural Experimental Station, Circular 391. Woodward, S. M. and Posey, C. J. 1941 Hydraulics of Steady Flow in Open Channels. John-Wiley & Sons, Inc.. Yarnell, D. L. and Woodward, S. M. 1920 The Flow of Water in Drain Tile. Bulletin No. 854, USDA 1926 Yarnell-Woodward Tile Drain Formula. The Flow of Water Through Culverts. Bulletin No. 1, University of Iowa. APPENDIX 67 68 Table 4: Relationships between d, A, R and Zr for Various Pipe Diameters. for 10" Pipe for 8" Pipe for 6" Pipe for 5" Pipe for 4" Pipe c~¢~c~c~c~ uw$~uan>ri This table is calculated from Eqs. (4.2.3) and (4.2.4). 69 Table 4.1: Relationships between d, A, R and Zr for a '10" Pipe. d A R” (d-r)A + %(2rd-d‘)3" :2: (16)“ (28)” (151:)3 4.500 0.375 0.238055 0.19425 0.0375357 6.2233 0.244931 0.19716 0.0396184 3:3316 0.251875 0.20000 0.0417414 3.2800 0.258819 0.20283 0.0438555 3:2383 0.265763 0.20558 0.0459952 3:2267 0.272707 0.20833 0.0482291 3.4250 0.279653 0.21092 0.0505403 3.2333 0.286597 0.21342 0.0529458 3.2216 0.293542 0.21592 0.0553768 3:2g00 0.300486 0.21833 0.0577987 3.2283 0.307361 0.22075 0.0602614 3:2266 0.314306 0.22300 0.0629077 324350 0.321181 0.22525 0.0656108 3223:: 0.327986- 0.22733 0.0682343 3:2316 0.334861 0.22942 0.0710587 3.2300 0.341666 0.23133 0.0738108 3.5383 0.348472 0.23308 0.0766659 3.5267 0.355308 0.23483 0.0797058 3.3250 0.361944 0.23658 0.0825987 3.5g33 0.368611 0.23833 0.0856466 3:5216 0.375277 0.24008 0.0887766 70 Table 4.1: (continued) 4 A 2‘5 (sq-)1 + gum-8*)“ inch feet (ft) (ftf’S (ft)3 6.60 0.5500 0.381875 0.24158 0.0918882 3.5283 0.388472 0.24308 0.0951576 3::266 0.394931 0.24413 0.0984926 3.5350 0.401388 0.24583 0.1016604 6:?233 0.407777 0.24683 0.1050000 6.5316 0.414166 0.24775 0.1086259 6.6300 0.420416 0.24866 0.1154766 6.2383 0.426597 0.24958 0.1191293 6:2266 0.432708 0.25050 0.1197840 6.2250 0.438750 0.25142 0.1227458 71 Table 4.2: Relationships between d, A, R and Zr for an 8" Pipe. .1 A 11‘“ (d-r)A + gum-6")“ 22:1: (£t)‘ (ftf’s (ft)‘ 3.28 0.2733 0.13476 0.0767 0.0153821 6:2:00 0.13911 0.0783 0.0163412 3:2:67 0.14351 0.0800 0.0172682 6:;g33 0.14791 0.0818 0.0182198 3.3300 0.15236 0.0835 0.0192313 g.g:67 0.15676 0.0855 0.0202733 6:3133 0.16120 0.0869 0.0213503 3:3200 0.16564 0.0885 0.0224213 3:3267 0.17009 0.0901 0.0235230 32333: 0.17453 0.0917 0.0246914 6:g200 0.17897 0.0932 0.0258499 6.3267 0.18342 0.0948 0.0270754 6.3533 0.18787 0.0962 0.0283317 3:3600 0.19231 0.0977 0.0295817 3:3267 0.19671 0.0991 0.0308670 323333- 0.20115 0.1004 0.0321822 3:3:00 0.20556 0.1018 0.0335580 3:3:67 0.20991 0.1030 0.0349510 313933 0.21431 0.1043 0.0363263 3:2300 0.21867 0.1056 0.0378005 3.2367 0.22303 0.1065 0.0392275 72 Table 4.2: (continued) d A 855 (d-r)A +.§(2rd-d‘f%- 2:: (67;)2 (ft)% (ft), 4.96 ‘ 0.4133 0.22730 0.1076 0.0407813 3.2200 0.23164 0.1087 0.0423148 3.4267 0.23591 0.1097 0.0438618 3.2333 0.24018 0.1108 0.0454518 3.2200 0.24440 0.1117 0.0470331 3.2267 0.24862 0.1127 0.0487154 3.2533 0.25275 0.1139 0.0503961 3.2§00 0.25689 0.1144 0.0521040 3.2267 0.26098 0.1150 0.0538172 3.2333 0.26507 0.1156 0.0555755 3.4300 0.26907 0.1161 0.0573370 3.2267 ~8627302 0.1167 0.0591477 3.2333 0.27693 0.1173 0.0609739 g:g300 0.28080 0.1178 0.0628333 3.2367 0.28462 0.1183 0.0647277 3.5133 0.28840 0.1186 0.0666300 g.§:oo 0.29213 0.1189 0.0685715 3.2367 0.29578 0.1190 0.0705327 322g33 0.29938 0.1191 0.0725195 8.2200 0.30289 0.1193 0.0745261 3.3267 0.30635 0.1192 0.0765656 73 Table 4.2: (continued) a A 8‘6 (d-r)A +.§(2rd-d‘f‘ 2:: (ft)1 (id's (it? 6.64 0.5533 0.30973 0.1191 0.0786133 3.;goo 0.31302 0.1190 0.0806875 3.3267 0.31622 0.1187 0.0827661 3.3733 0.31937 0.1183 0.0849015 3.2300 0.32240 0 1178 0.0870399 0.2867 0.32533 0.1174 0.0891835 0.5333 0.32817 0.1167 0.0913722 3.6300 0.33089 0.1159 0.0935684 3.2867 0.33351 0.1150 0.0957894 0.2233 0.33600 0.1140 0.0980217 0.2300 0.33831 0.1129 0.1002630 3.2367 0.34052 0.1116 0.1025277 3.2g33 0.34253 0.1099 0.1048025 0.2200 0.34440 0.1082 0.1071005 3.2267 0.34600 0.1060 0.1093936 0.2533 0.34747 0.1034 0.1117011 3.2200 0.34849 0.0999 0.1140343 3.2267 0.34906 0.0917 0.1163533 74 Table 4.3: Relationships between d, A, R and Zr for a 6" Pipe. d A 11% (d- r)A + %(2rd-d‘i/‘ inch feet (661‘ (fc)"’ (£03 3.06 0.255 0.10068 0.0635 0.0109117 3.260 0.10312 0.0645 0.0114270 3.225 0.10567 0.0656 0.0119351 3.370 0.10817 0.0665 0.0124782 3.335 0.11065 0.0675 0.0130252 3.330 0.11315 0.0684 0.0135770 3.385 0.11563 0.0694 0.0141575 3.230 0.11808 0.0702 0.0147413 3.335 0.12055 0.0711 0.0153427 3.330 0.12300 0.0719 0.0159420 3.335 0.12545 0.0726 0.0165645 3.310 0.12788 0.0733 0.0172087 3.335 0.13030 0.0740 0.0178518 3.84 0.320 0.13270 0.0748 0.0185050 3.?25 0.13510 0.0755 0.0191756 3.330 0.13748 0.0762 0.0198622 323:5 0.14000 0.0768 0.0205762 4.08 0.340 0.14218 0.0774 0.0212554 3.325 0.14450 0.0779 0.0220054 3.§g0 0.14680 0.0784 0.0227073 3.325 0.14910 0.0787 0.0234333 75 Table 4.3: (continued) d A 83’ (d-r)A + %(2rd-d‘f‘ 32:: (ft): at)” (ft)! 4.32 0.360 0.15135 0.0791 0.0241883 3.335 0.15358 0.0795 0.0249593 32330 0.15578 0.0799 0.0257210 3:335 0.15795 0.0803 0.0265032 3:330 0.16010 0.0806 0.0272973 3:335 0.16223 0.0808 0.0281084 3:330 0.16433 0.0810 0.0289325 3:335 0.16638 0.0811 0.0297573 4.80 0.400. 0.16840 0.0812 0.0305933 3:335 0.17034 0.0813 0.0314355 3:330 0.17233 0.0812 0.0322962 4.98 0.415 0.17423 0.0811 0.0331609 33330 0.17608 0.0810 0.0340366 3:335 0.17788 0.0808 0.0349253 3:330 0.17965 0.0806 0.0358196 31335 0.18135 0.0803 0.0367168 3:330 0.18300 0 0799 0.0375905 32335 0.18460 0.0795 0.0385448 32330 0.18613 0.0790 0.0394760 3:335 0.18760 0.0784 0.0404133 32330 0.18900 0.0777 0.0413534 76 Table 4.3: (continued) d A R“ (d-r)A + -§-(2rd-d‘)’l‘ inch feet (ftj‘ (ftfh (ft) 5.58 0.465 0.19030 0.0770 0.0422988 3.230 0.19155 0.0760 0.0432563 3.435 0.19263 0.0749 0.0442151 3.430 0.19373 0.0737 0.0451858 3.285 0.19463 0.0723 0.0461519 3.230 0.19540 0.0705 0.0471246 3.235 0.19603 0.0681 0.0481092 32336 0.19635 0.0625 0.0490880 77 Table 4.4: Relationships between d, A, R and 2: for a 5" Pipe. d A a” (d-r)A + 3;.(21-6-6‘)“ 2:: (ft)z (ft)4/’ (ft), 2.25 0.1875 0.0595125 0.0446 0.0046919 3.1316 0.0612328 0.0455 0.0049523 3.3358 0.0629687 0.0464 0.0052177 3.2300 0.0647049 0.0473 0.0054819 3.2341. 0.0664410 0.0482 0.0057494 3.3883 0.0681771 0.0490 0.0060286 3:;i25' 0.0699132 0.0498 0.0063175 3:3267 0.0716493 0.0506 0.0066182 3.3308 0.0733854 0.0514 0.0069221 3.2250 0.0751215 0.0522 0.0072248 3.2391 0.0768403 0.0529 0.0075327 323333 0.0785764 0.0537 0.0078635 3.3375 0.0802951 0.0544 0.0082014 3:3216 0.0819965 0.0551 0.0085293 3.3258 0.0837152 0.0558 0.0088823 3.g300 0.0854167 0.0564 0.0092264 ”3.2241 0.0871181 0.0569 0.0095831 3:;283 0.0888021 0.0575 0.0099632 3.2225 0.0904861 0.0581 0.0i03248 3.3267 0.0921528 0.0586 0.0107058 3.3308 0.0938194 0.0592 0.0110971 78 Table 4.4: (continued) d A 11% (d-r)A + gum-8‘)“ 2:: (ft)2 4 (fly/3 (ft)3 3.30 0.2750 0.0954687 0.0597 0.0114860 3.2791 0.0971181 0.0602 0.0118997 3.3233 0.0987326 0.0607 0.0122991 3.2375 0.1003472 0.0611 0.0127076 3.3316 0.1019444 0.0614 0.0131250 3.3358 0.1035417 0.0617 0.0135657 3.3300 0.1051042 0.0620 0.0139973 3.3341 0.1066492 0.0624 0.0144346 3.;383 0.1081771 0.0627 0.0148912 3.3725 0.1096875 0.0630 0.0153432 3:3267 0.1111806 0.0632 0.0153432 3:3;08 0.1126562 0.0634 0.0162670 3.3350 0.1141146 0.0635 0.0167452 3.3291 0.1155382 0.0636 0.0172148 3.gg33 0.1169444 0.0637 0.0177044 3:?375 0.1183160 0.0637 0.0181869 3.;217 0.1196701 0.0637 0.0186893 3:;258 0.1209896 0.0636 0.0191919 323366 0.1222743 0.0635 0.0196974 32:341 0.1235234 0.0634 0.0196974 3:3g83 0.1247569 0.0632 0.0207293 79 Table 4.4: (continued) d A 27* (d-r)A +.§(2rd-d‘f” inch 1 95 3 feet (ft) (ft) (ft) 4.35 0.3625 0.1259375 0.0630 0.0212411 3.3267 0.1270833 0.0627 0.0217746 3:2;08 0.1281944 0.0624 0.0223086 3.3350 0.1292535 0.0619 0.0228443 3.3391 0.1302778' 0.0614 0.0233857 3.3233 0.1312500 0.0609 0.0239314 3.3275 0.1321528 0.0603 0.0244786 3:;316 0.1330208 0.0597 0.0250459 3:;358 0.1338021 0.0587 0.0255871 3.2300 0.1345312 0.0578 0.0261480 3:2341 0.1351562 0.0567 0.0267076 3.2383 0.1356944 0.0553 0.0272748 3.2125 0.1361285 0.0534 0.0278404 3.2367 0.1363542 0.0490 0.0284071 80 Table 4.5: Relationships between d, A, R.and 2: for a 4" Pipe. 4 A a”? (d-r)A.+ §(2rd-d‘i‘ 22:: (it)1 (ft;)""a (ft); 1.04 0.0867 0.018033 0.0187 0.00064053 0.3300 0.019011 0.0195 0.00070302 0.0933 0.020000 0.0203 0.00076774 0.0367 0.021000 0.0212 0.00083821 0.?300 0.022022 0.0219 0.00090954 0.3333 0.023044 0.0227 0.00098622 32:367 0.024077 0.0235- 0.00106360 gziioo 0.025111 0.0243 0.00114446 0Zii33 0.026166 0.0251 0.00122498 3::267 0.027222 0.0259 0.00131813 0.:200 0.028288 0.0266 0.00141036 0.?333 0.029355 0.0274 0.00150574 3::367 0.030433 0.0281 0.00160704 323300 0.031511 0.0289 0.00170381 02:233 0.032599 0.0296 0.00180879 3::267 0.033688 0.0304 0.00192282 02:200 0.034777 0.0311 0.00204276 0.1233 0.035871 0.0317 0.00215853 0.1267 0.036977 0.0325 0.00227751 0.2g00 0.038088 0.0331 0.00240392 3.2233 0.039188 , 0.0339 0.00253425 81 Table 4.5: (continued) d A R“3 (d-r)A + .§.(2rd-d‘ )1." :22: (131:)1 (fly-3 (ft)3 1.88 0.1567 0.040300 0.0345 0.0026688 0.2200 0.041411 0.0351 0.0028027 0.3233 0.042533 0.0358 0.0029404 3.2267 0.043633 0.0364 0.0030864 3.3700 0.044744 0.0370 0.0032313 3.2333 0.045855 0.0376 0.0033844 3.1;67 0.046966 0.0382 0.0035414 3..300 0.048077 0.0388 0.0036977 3::233 0.049177 0.0393 0.0038585 g.i§67 0.050288 0.0398 0.0040228 32:300 0.051388 0.0404 0.0041948 3.3533 0.052477 0.0409 0.0043689 3.3367 0.053577 0.0414 0.0045408 3.2300 0.054666 0.0419 0.0047176 3.3333 0.055755 0.0423 0.0049034 3.3367 0.056833 0.0427 0.0050977 3.3.00 0.057911 0.0431 0.0052893 3.3233 0.058977 0.0435 0.0054827 3.2267 0.060044 0.0440 0.0056815 3.3200 0.061100 0.0443 0.0058791 0.3333 0.062155 0.0447 0.0060894 82 Table 4.5: (continued) d A 35‘ (d-r)A +‘§(2rd-d‘§a 32:: (ft)1 at)“a (151:)3 2.72 0.2267 0.063188 0.0452 0.0062995 3.3300 0.064222 0.0454 0.0065130 3.3333 0.065244 0.0456 0.0067272 3.3367 0.066266 0.0459 0.0069469 3.3200 0.067266 0.0461 0.0071671 3.3333 0.068255 0.0463 0.0073935 *3.;267 0.069233 0.0466 0.0076217 3.3300 0.070200 0.0467 0.0078542 3.2333 0.071155 0.0489 0.0080910 3.3367 0.072100 0.0471 0.0083288 3.3300 0.073033 0.0472 0.0085714 3.3333 0.073944 0.0472 0.0087502 3.3367 0.074844 0.0473 0.0090649 3.330. 0.075722 0.0473‘ 0.0093158 3.3333 0.076588 0.0473 0.0095707 3.3367 40.077433 0.0473 0.0098267 3.3300 0.078255 0.0472 0.0100859 3.3333 0.079055 0.0471 0.0103458 3.3367 0.079844 0.0469 0.0106127 3.3300 0.080600 0.0467 0.0108800 3.3333 0.081333 0.0466 0.0111479 { 83 Table 4.5: (continued) d A 11* (d-r)A + gum-8‘)“ 2:: (it? (ft)~§ (ft), 3.56 0.2967 0.082044 0.0463 0.0114215 3.3300 0.082722 0.0460 ‘ 0.0116961 3.3333 0.083377 0.0456 0.0119737 3.2367 0.084000 0.0452 0.0122527 3.3100 0.084577 0.0448 0.0125329 3.3133 0.085133 0.0443 0.0128160 3.3167 0.085633 0.0436 0.0131003 3.3200 0.086100 0.0429 0.0133876 3.3333 0.086500 0.0420 0.0136742 3.3367 0.086844 0.0410 0.0139626 3.3300 0.087122 0.0396 0.0142543 3.3g33 0.087266 0.0364 0.0145442 84 Table 5. Theoretical and Experimental Profile Data for Various Conditions. 5. 1 A.Q = 0.0315 cfs n = 0.011 S = 0.0005 5. 2 .A Q = 0.0525 cfs n = 0.011 S = 0.0005 5. 3 A,Q = 0.0735 cfs n = 0.011 S = 0.0005 5. 4 A Q = 0.1050 CfS n = 0.011 S = 0.0005 5. 5 A.Q = 0.0315 cfs n = 0.011 S = 0.0010 5. 6 .A Q = 0.0525 cfs n = 0.011 S = 0.0010 5. 7 A_Q = 0.0735 cfs n = 0.011 S = 0.0010 5. 8 A.Q = 0.1050 cfs n = 0.011 S = 0.0010 5. 9 A.Q = 0.0315 cfs n = 0.011 S = 0.0025 5.10 A.Q = 0.0525 cfs n = 0.011 S = 0.0025 5.11 A.Q = 0.0735 cfs n = 0.011 S = 0.0025 5.12 .A Q = 0.1050 cfs n = 0.011 S = 0.0025 5.13 A.Q = 0.0315 cfs n = 0.011 S = 0.0050 5.14 A.Q = 0.0525 cfs n = 0.011 S = 0.0050 5.15 .A Q = 0.0735 cfs n = 0.011 S = 0.0050 5.16 .A Q = 0.1050 cfs n = 0.011 S = 0.0050 5.17 .A Q = 0.0315 cfs n = 0.011 S = 0.0100 5.18 A Q = 0.0525 CfS n = 0.01]. S = 0.0100 5.19 A.Q = 0.0735 cfs n = 0.011 S = 0.0100 5.20 .A Q = 0.0315 cfs n = 0.011 S = 0.0250 5.21 .A Q = 0.0525 cfs n = 0.011 S = 0.0250 5.22 ‘A Q = 0.0735 cfs n = 0.011 S = 0.0250 5.23 A Q = 0.0315 cfs n = 0.011 S = 0.0500 5.24 A.Q = 0.0525 cfs n = 0.011 S = 0.0500 This table is an extensive set of theoretical profile data for various conditions as computed from Eqs. (4.2.12) and (4.2.13). Spot checks were made experimentally in an effort to evaluate the validity of the theoretical computations. These experimental values are also included and indicate that, in general, there was good agreement between theory and experiment. 85 Table 5.1: Theoretical and Experimental Profile Data for the Condition: 4Q = 0.0315 Cf! n = 0.011 S = 0.0005 Distance from Calculated Experilnntal Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 4.620 0.6300 10 2.55 4.800 0.6300 10 6.00 5.000 0.6300 10 10.15 5.200 0.6300 10 14.82 5.400 0.6300 10 26.34 5.600 0.6300 10 1%36.00 5.800 0.6300 10 50.00 6.000 0.6300 10 66.00 6.170 6.2 0.6300 10 66.00 6.320 6.5 0.5985 10 76.75 6.400 0.5985 10 110.00 6.600 0.5985 10 132.00 6.700 6.7 0.5985 10 132.00 6.810 6.9 0.5670 10 160.00 6.900 0.5670 10 198.00 7.000 0.5670 10 198.00 7.090 0.5355 10 210.95 7.100 0.5355 10 236.45 7.130 0.5355 10 264.00 7.150 7.2 0.5355 10 264.00 7.230 7.3 0.5040 10 286.00 7.220 0.5040 10 308.00 7.220 0.5040 10 330.00 7.220 0.5040 10 330.00 7.290 0.4725 10 374.04 7.250 0.4725 10 396.00 7.230 0.4725 10 396.00 7.290 0.4410 10 424.25 7.250 0.4410 10 442.00 7.230 0.4410 10 450.52 7.210 0.4410 10 462.00 7.190 7.2 0.4410 10 462.00 7.250 7.3 0.4095 10 478.12 7.210 0.4095 10 506.00 7.150 0.4095 10 528.00 7.110 0.4095 10 528.00 7.180 0.3780 10 554.00 7.100 0.3780 10 568.95 7.040 0.3780 10 594.00 6.980 0.3780 10 594.00 7.010 0.3465 10 614.00 6.990 0.3465 10 Table 5.1: (continued) 86 Distance from. Calculated Experimental Diacharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 628.00 6.950 0.3465 10 634.90 6.930 0.3465 10 654.95 6.870 0.3465 10 660.00 6.860 0.3465 10 660.00 6.910 0.3150 10 676.00 6.850 0.3150 10 690.00 6.800 0.3150 10 726.00 6.720 6.8 0.3150 10 726.00 6.770. 6.9 0.2835 10 744.58 6.690 6.7 0.2835 10 744.58 7.210 7.3 0.2835 10 770.00 7.160 7.3 0.2835 8 792.00 7.120 7.3 0.2835 8 792.00 7.180 7.5 0.2520 8 814.00 7.120 0.2520 8 828.00 7.080 0.2520 8 842.94 7.040 0.2520 8 858.00 7.000 0.2520 8 858.00 7.055 0.2205 8 872.15 7.000 0.2205 8 884.15 6.960 0.2205 8 894.82 6.920 0.2205 8 908.16 6.880 0.2205 8 920.00 6.840 0.2205 8 924.00 6.830 0.2205 8 924.00 6.880 0.1890 8 935.35 6.830 0.1890 8 942.72 6.800 0.1890 8 952.95 6.760 0.1890 8 962.00 6.720 0.1890 8 972.12 6.680 0.1890 8 982.94 6.640 0.1890 8 990.00 6.610 6.6 0.1890 8 990.00 6.650 6.7 0.1575 8 1000.55 6.600 0.1575 8 1010.00 6.560 0.1575 8 1018.38 6.520 0.1575 8 1026.82 6.480 0.1575 8 1036;00 6.440 0.1575 8 1044.00 6.400 0.1575 8 1056.00 6.350 0.1575 8 1056.00 6.390 0.1260 8 1070.00 6.320 0.1260 8 87 Table 5.1: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 1084.15 6.240 0.1260 8 1100.15 6.160 0.1260 8 1116.74 6.080 0.1260 8 1122.00 6.060 6.0 0.1260 8 1122.00 6.090 6.1 0.0945 8 1138.55 6.000 0.0945 8 1154.00 5.920 0.0945 8 1168.50 5.840 0.0945 8 1184.00 5.760 0.0945 8 1188.00 5.740 0.0945 8 1188.00 5.770 0.0630 8 1216.00 5.600 0.0630 8 1230.35 5.520 0.0630 8 1244.84 5.440 0.0630 8 1254.00 5.390 5.5 0.0630 8 1254.00 5.410 5.6 0.0315 8 1262.00 5.360 0.0315 8 1276.00 5.280 0.0315 8 1288.58 5.200 0.0315 8 1302.95 5.120 0.0315 8 1316.24 5.040 0.0315 8 1320.00 5.020 0.0315 8 Table 5.2: Theoretical and Experimental Profile Data for the condition: 88 4Q = 0.0525 cfs n = 0.011 S = 0.0005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 5.270 5.3 1.0500 10 2.60 5.425 1.0500 10 8.00 5.690 1.0500 10 11.20 5.760 1.0500 10 15.20 5.920 1.0500 10 18.60 6.000 1.0500 10 40.00 6.300 1.0500 10 66.00 6.635 6.6 1.0500 10 66.00 6.790 6.8 0.9975 10 76.00 6.865 0.9975 10 104.00 7.000 0.9975 10 132.00 7.150 0.9975 10 132.00 7.265 0.9450 10 162.00 7.310 0.9450 10 198.00 7.380 7.4 0.9450 10 198.00 7.480 7.5 0.8925 10 234.00 7.515 0.8925 10 264.00 7.560 0.8925 10 264.00 7.630 0.8400 10 298.00 7.670 0.8400 10 330.00 7.710 0.8400 10 330.00 7.800 0.7875 10 360.00 7.795 0.7875 10 396.00 7.790 7.8 0.7875 10 396.00 7.880 7.9 0.7350 10 428.00 7.875 0.7350 10 462.00 7.865 0.7350 10 462.00 7.900 0.6825 10 490.00 7.875 0.6825 10 528.00 7.840 7.9 0.6825 10 528.00 7.880 7.9 0.6300 10 560.00 7.825 0.6300 10 594.00 7.775 0.6300 10 594.00 7.850 0.5775 10 628.00 7.730 0.5775 10 660.00 7.700 0.5775 10 660.00 7.800 0.5250 10 692.00 7.700 0.5250 10 726.00 7.610 7.6 0.5250 10 726.00 7.670 7.7 0.4725 10 758.00 7.625 0.4725 10 792.00 7.590 0.4725 10 792.00 7.670 0.4200 10 89 Table 5.2: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 810.00 7.600 0.4200 10 810.00 7.900 0.4200 8 830.00 7.780 0.4200 8 858.00 7.610 0.4200 8 858.00 7.660 0.3675 8 890.00 7.530 0.3675 8 924.00 7.400 7.4 0.3675 8 924.00 7.490 7 5 0.3150 8 960.00 7.300 0.3150 8 990.00 7.130 0.3150 8 990.00 7.200 0.2625 8 1022.00 ~7.050 0.2625 8 1056.00 6.900 0.2625 8 1056.00 6.925 0.2100 8 1090.00 6.750 0.2100 8 1122.00 6.580 6:6 0.2100 8 1122.00 6.590 6.6 0.1575 8 1150.00 6.450 0.1575 8 1188.00 6.255 0.1575 8 1188.00 6.325 0.1050 8 1220.00 6.120 0.1050 8 1254.00 5.900 0.1050 8 1254.00 5.960 0.0525 8 1293.00 5.690 0.0525 8 1320.00 5.500 0.0525 8 Table 5.3: Theoretical and Experimental Profile Data for the condition: AQ = 0.0735 cfs 90 n = 0.011 S = 0.0005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (ind Depth (in) (cfs) (in) 0.00 5.770 5.8 1.4700 10 3.85 5.820 1.4700 10 8.20 6.190 1.4700 10 14.00 6.350 1.4700 10 26.10 6.510 1.4700 10 36.00 6.140 1.4700 10 66.00 6.940 7.0 1.4700 10 66.00 7.190 7.2 1.3965 10 100.00 7.390 1.3965 10 132.00 7.580 1.3965 10 132.00 7.790 1.3230 10 162.00 7.920 1.3230 10 198.00 8.080 1.3230 10 198.00 8.210 1.2495 10 230.00 8.270 1.2495 10 264.00 8.300 1.2495 10 264.00 8.420 1.1760 10 298.00 8.450 1.1760 10 330.00 8.500 8.5 1.1760 10 330.00 8.590 8.6 1.1025 10 360.00 8.580 1.1025 10 396.00 8.570 1.1025 10 396.00 8.660 1.0290 10 428.00 8.620 1.0290 10 462.00 8.580 1.0290 10 462.00 8.650 0.9555 10 490.00 8.610 0.9555 10 528.00 8.570 0.9555 10 528.00 8.650 0.8820 10 560.00 8.550 0.8820 10 594.00 8.470 0.8820 10 594.00 8.530 0.8085 10 628.00 8.440 0.8085 10 660.00 8.370 8.4 0.8085 10 660.00 8.470 8.6 0.7350 10 692.00 8.370 0.7350 10 726.00 8.275 0.7350 10 726.00 8.360 0.6615 10 758.00 8.250 0.6615 10 792.00 8.140 8.1 0.6615 10 792.00 8.230' 8.3 0.5880 10 820.00 8.130 0.5880 10 91 Table 5.3: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (ft) (cfs) (in) 858.00 8.000 0.5880 10 858.00 8.120 0.5145 10 890.00 7.970 0.5145 10 924.00 7.790 7.8 0.5145 10 924.00 7.840 7.8 0.4410 10 960.00 7.600 7.6 0.4410 10 960.00 7.890 7.9 0.4410 '8~ 990.00 7.530 0.4410 8 990.00 7.560 0.3675 8 1022.00 7.405 0.3675 8 1056.00 7.230 0.3675 8 1056.00 7.290 0.2940 8 1090.00 7.140 0.2940 8 1122.00 7.000 0.2940 8 1122.00 7.080 0.2205 8 1156.00 7.990 0.2205 8 1188.00 6.880 6.9 0.2205 8 1188.00 7.000 7.0 0.1470 8 1220.00 6.860 0.1470 8 1254.00 6.700 0.1470 8 1254.00 6.800 0.0735 8 1288.00 6.470 0.0735 8 1320.00 6.170 0.0735 8 Table 5.4: Theoretical and Experimental Profile Data for the Condition: 92 4Q = 0.1050 CfS n = 0.011 S = 0.0005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 6.420 6.4 2.1000 10 4.00 6.600 2.1000 10 6.30 6.700 2.1000 10 9.80 6.800 2.1000 10 13.00 6.900 2.1000 10 22.00 7.200 2.1000 10 42.00 7.330 2.1000 10 53.90 7.410 2.1000 10 66.00 7.500 7.5 2.1000 10 .66.00 7.770 7.7 1.9950 10 100.00 7.880 1.9950 10 132.00 8.000 1.9950 10 132.00 8.250 1.8900 10 162.00 8.340 1.8900 10 198.00 8.490 1.8900 10 198.00 8.750 1.7850 10 230.00 8.820 1.7850 10 264.00 8.900 1.7850 10 264.00 9.140 1.6800 10 298.00 9.180 1.6800 10 330.00 9.190 1.6800 10 330.00 9.400 1.5750 10 360.00 9.400 1.5750 10 396.00 9.430 9.2 1.5750 10 396.00 9.570 9.6 1.4700 10 428.00 9.600 1.4700 10 462.00 9.610 1.4700 10 462.00 9.700 1.3650 10 490.00 9.700 1.3650 10 528.00 9.690 1.3650 10 528.00 9.800 1.2600 10 560.00 9.740 1.2600 10 594.00 9.660 9.7 1.2600 10 594.00 9.870 9.9 1.1550 10 628.00 9.670 1.1550 10 660.00 9.570 1.1550 10 660.00 9.630 1.0500 10 692.00 9.520 1.0500 10 726.00 9.420 1.0500 10 726.00 9.510 0.9450 10 758.00 9.400 0.9450 10 792.00 9.290 9.3 0.9450 10 792.00 9.350 9.5 0.8400 10 93 Table 5.4: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 820.00 9.240 0.8400 10 858.00 9.080 0.8400 10 858.00 9.170 0.7350 10 890.00 9.000 0.7350 10 924.00 8.820 8.8 0.7350 10 924.00 8.880 9.0 0.6300 10 960.00 8.650 0.6300 10 990.00 8.450 0.6300 10 990.00 8.525 0.5250 10 1022.00 8.350 0.5250 10 1056.00 8.175 0.5250 10 1056.00 8.245 0.4200 10 1090.00 8.040 0.4200 10 1122.00 7.840 0.4200 10 1122.00 7.940 0.3150 10 1146.00 7.750 0.3150 10 1170.00 7.570 7.6 0.3150 10 1170.00 7.930 8.1 0.3150 8 1188.00 8.840 0.3150 8 1188.00 7.890 0.2100 8 1220.00 7.710 0.2100 8 1254.00 7.520 0.2100 8 1254.00 7.590 0.1050 8 1288.00 7.180 0.1050 8 1320.00 6.800 0.1050 8 94 Table 5.5: Theoretical and Experimental Profile Data for the Condition: A0 = 0.0315 cfs n = 0.011 S = 0.001 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 4.620 4.6 0.6300 10 3.00 4.800 0.6300 10 5.30 4.900 0.6300 10 7.50 5.000 0.6300 10 11.72 5.100 0.6300 10 14.95 5.200 0.6300 10 20.28 5.400 0.6300 10 40.15 5.600 0.6300 10 62.50 5.800 0.6300 10 66.00 5.820 5.8 0.6300 10 66.00 5.990 6.1 0.5985 10 83.00 6.040 0.5985 10 110.85 6.100 0.5985 10 132.00 6.140 0.5985 10 132.00 6.250 0.5670 10 181.15 6.230 0.5670 10 198.00 6.220 0.5670 10 198.00 6.330 0.5355 10 214.25 6.300 0.5355 10 222.00 6.280 0.5355 10 238.74 6.240 0.5355 10 256.84 6.200 0.5355 10 264.00 6.190 6.2 0.5355 10 w264.00 6.305 6.4 0.5040 10 288.12 6.230 0.5040 10 296.00 6.200 0.5040 10 330.00 6.100 0.5040 10 330.00 6.200 0.4725 10 354.50 6.100 0.4725 10 370.00 6.060 0.4725 10 370.00 6.390 0.4725 8 396.00 6.440 6.5 0.4725 8 396.00 6.570 6.6 0;4410 8 424.55 6.550 0.4410 8 457.25 6.530 0.4410 8 462.00 6.528 0.4410 8 462.00 6.645 0.4095 8 474.25 6.600 0.4095 8 486.85 6.560 0.4095 8 504.94 6.520 0.4095 8 528.00 6.470 6.5 0.4095 8 528.00 6.580 6.6 0.3780 8 Table 5.5: (continued) 95 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 533.90 6.560 0.3780 8 548.00 6.500 0.3780 8 564.25 6.440 0.3780 8 584.00 6.380 0.3780 8 594.00 6.350 6.4 0.3780 8 594.00 6.440 6.5 0.3465 8 602.05 6.400 0.3465 8 618.42 6.320 0.3465 8 636.00 6.240 0.3465 8 654.82 6.160 0.3465 8 660.00 6.140 0.3465 8 660.00 6.240 0.3150 8 672.00 6.160 0.3150 8 686.00 6.080 0.3150 8 700.45 6.000 0.3150 8 715.50 5.920 0.3150 8 726.75 5.860 5.9 0.3150 8 726.75 5.960 6.1 0.2835 8 732.00 5.920 0.2835 8 747.15 5.840 0.2835 8 765.14 5.760 0.2835 8 770.00 5.680 0.2835 8 783.00 5.600 0.2835 8 792.00 5.550 0.2835 8 792.00 5.650 0.2520 8 798.55 5.600 0.2520 8 810.80 5.520 0.2520 8 822.82 5.440 0.2520 8 834.00 5.360 0.2520 8 846.48 5.280 0.2520 8 858.00 5.210 5.2 0.2520_r 8 858.00 5.310 5.3 0.2205 8 872.14 5.200 0.2205 8 882.35 5.120 0.2205 8 894.00 5.040 0.2205 8 904.55 4.960 0.2205 8 918.00 4.880 0.2205 8 924.00 4.840 0.2205 8 924.00 4.940 0.1890 8 932.75 4.880 0.1890 8 940.55 4.800 0.1890 8 952.00 4.720 0.1890 8 962.05 43640 0.1890 8 96 Table 5.5: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 973.82 4.560 0.1890 8 984.85 4.480 0.1890 8 990.00 4.450 4.4 0.1890 8 990.00 4.560 4.7 0.1575 8 998.92 4.480 0.1575 8 1008.02 4.400 0.1575 8 1020.00 4.310 4.4 0.1575 8 1020.00 4.670 4.7 0.1575 6 1030.00 4.620 0.1575 6 1042.35 4.560 0.1575 6 1056.00 4.500 0.1575 6 1056.00 4.640 0.1260 6 1066.12 4.560 0.1260 6 1074.20 4.500 0.1260 6 1082.00 4.440 0.1260 6 1100.00 4.320 0.1260 6 1118.10 4.200 0.1260 6 1122.00 4.180 4.2 0.1260 6 1122.00 4.310 4.4 0.0945 6 1133.28 4.200 0.0945 6 1146.48 4.080 0.0945 6 1160.55 3.960 0.0945 6 1176.50 3.840 0.0945 6 1188.00 3.750 0.0945 6 1188.00 3.860 0.0630 6 1196.30 3.780 0.0630 6 1208.75 3.660 0.0630 6 1220.00 3.550 3.7 0.0630 6 1220.00 3.750 3.9 0.0630 5 1230.00 3.650 0.0630 5 1242.15 3.550 0.0630 5 1254.00 3.450 0.0630 5 1254.00 3.560 0.0315 5 1264.00 3.450 0.0315 5 1272.18 3.350 0.0315 5 1290.46 3.150 0.0315 5 1310.00 2.950 0.0315 5 1320.00 2.850 0.0315 5 Table 5.6: Theoretical and Experimental Profile Data for the Condition: 97 AQ = 0.0525 cfs n = 0.011 S = 0.001 VDistance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 5.270 5.3 1.0500 10 4.00 5.400 1.0500 10 8.00 5.540 1.0500 10 13.00 5.650 1.0500 10 20.00 5.770 1.0500 10 40.00 6.000 1.0500 10 60.00 6.170 1.0500 10 66.00 6.220 6.0 0.9975 10 66.00 6.485 6.5 0.9975 10 100.00 6.500 0.9975 10 132.00 6.600 0.9975 10 132.00 6.770 0.9975 10 164.00 6.810 0.9975 10 198.00 6.860 0.9975 10 198.00 6.950 0.8925 10 230.00 6.930 0.8925 10 264.00 6.925 7.0 0.8925 10 264.00 7.040 7.1 0.8400 10 296.00 6.980 0.8400 10 330.00 6.900 0.8400 10 330.00 7.020 0.7875 10 362.00 6.985 0.7875 10 396.00 6.930 0.7875 10 396.00 7.070 0.7350 10 420.00 7.000 0.7350 10 440.00 6.925 7.0 0.7350 10 440.00 7.300 7.5 0.7350 8 462.00 7.300 0.7350 8 462.00 7.380 0.6825 8 496.00 7.370 0.6825 8 528.00 7.370 0.6825 8 528.00 7.440 0.6300 8 560.00 7.325 0.6300 8 594.00 7.200 7.2 0.6300 8 594.00 7.280 7.3 0.5775 8 628.00 7.150 0.5775 8 660.00 7.050 0.5775 8 660.00 7.100 0.5250 8 692.00 6.980 0.5250 8 726.00 6.830 0.5250 8 726.00 6.860 0.4725 8 98 Table 5.6: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 760.00 6.650 0.4725 8 792.00 6.470 0.4725 8 792.00 6.540 0.4200 8 822.00 6.300 0.4200 8 858.00 6.020 6.0 0.4200 8 858.00 6.120 6.2 0.3675 8 890.00 5.920 0.3675 8 924.00 5.710 0.3675 8 924.00 5.800 0.3150 8 960.00 5.570 0.3150 8 990.00 5.365 0.3150 8 990.00 5.465 0.2625 8 1022.00 5.220 0.2625 8 1056.00 5.000 0.2625 8 1056.00 5.100 0.2100 8 1080.00 4.980 5.0 0.2100 8 1080.00 5.410 5.5 0.2100 6 1100.00 5.275 0.2100 6 1122.00 5.120 0.2100 6 1122.00 5.210 0.1575 6 1154.00 4.960 0.1575 6 1188.00 4.700 0.1575 6 1188.00 4.800 0.1050 6 1220.00 4.550 0.1050 6 1236.00 4.410 0.1050' 6 1254.00 4.275 0.1050 6 1254.00 4.365 0.0525 6 1284.00 4.040 0.0525 6 41320.00 3.170 0.0525 6 Table 5.7: Theoretical and Experimental Profile Data for the Condition: 4Q = 0.0735 cfs 99 n = 0.011 S a 0.001 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 5.770 5.8 1.4700 10 5.80 5.820 1.4700 10 14.45 6.060 1.4700 10 18.00 6.130 1.4700 10 24.00 6.210 1.4700 10 33.00 6.290 1.4700 10 40.00 6.330 1.4700 10 50.00 6.400 1.4700 10 66.00 6.500 6.5 1.4700 10 66.00 6.690 6.7 1.3965 10 100.00 6.790 1.3965 10 132.00 6.890 1.3965 10 132.00 7.080 1.3230 10 164.00 7.130 1.3230 10 198.00 7.200 1.3230 10 198.00 7.330 1.2495 10 230.00 7.350 1.2495 10 264.00 7.390 1.2495 10 264.00 7.470 1.1760 10 296.00 7.460 1.1760 10 330.00 7.470 7.5 1.1760 10 330.00 7.570 7.6 1.1025 10 362.00 7.560 1.1025 10 396.00 7.565 1.1025 10 396.00 7.635 1.0290 10 430.00 7.600 1.0290 10 462.00 7.600 1.0290 10 462.00 7.700 0.9555 10 496.00 7.650 0.9555 10 528.00 7.610 0.9555 10 528.00 7.700 0.8820 10 560.00 7.620 0.8820 10 594.00 7.545 7.6 0.8820 10 594.00 7.610 7.7 0.8085 10 628.00 7.500 0.8085 10 660.00 7.400 0.8085 10 660.00 7.510 0.8085 10 700.00 7.300 7.3 0.7350 10 700.00 7.600 7.8 0.7350 8 726.00 7.660 0.7350 8 726.00 7.730 0.6615 8 100 Table 5.7: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 760.00 7.630 0.6615 8 792.00 7.520 0.6615 8 792.00 7.600 0.5880 8 822.00 7.410 0.5880 8 858.00 7.200 0.5880 8 858.00 7.300 0.5145 8 890.00 7.020 7.1 0.5145 8 924.00 6.725 6.5 0.5145 8 924.00 6.776 0.4410 8 960.00 6.380 0.4410 8 990.00 6.050 0.4410 8 990.00 6.110 0.3675 8 1022.00 5.920 0.3675 8 1056.00 5.700 0.3675 8 1056.00 5.800 0.2940 8 1080.00 5.610 0.2940 8 1100.00 5.470 0.2940 8 1122.00 5.300 0.2940 8 1122.00 5.335 0.2205 8 1154.00 5.100 0.2205 8 1188.00 4.825 0.2205 8 1188.00 4.910 0.1470 8 1220.00 4.760 4.8 0.1470 8 1220.00 5.060 5.1 0.1470 6 1236.00 4.970 0.1470 6 1254.00 4.860 0.1470 6 1254.00 4.960 0.0735 6 1284.00 4.680 0.0735 6 1320.00 4.335 0.0735 6 101 Table 5.8: Theoretical and Experimental Profile Data for the Condition: 50 = 0.1050 cfs n = 0.011 S = 0.001 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 6.420 2.1000, 10 4.00 6.460 2.1000 10 9.00 6.530 2.1000 10 14.50 6.590 2.1000 10 27.00 6.710 2.1000 10 40.00 6.800 2.1900 10 50.00 6.830 2.1000 10 66.00 6.900 7.0 2.1000 10 66.00 7.020 7.2 1.9950 10 100.00 7.100 1.9950 10 132.00 7.160 1.9950 10 132.00 7.290 1.8900 10 164.00 7.370 1.8900 10 198.00 7.440 1.8900 10 198.00 7.560 1.7850 10 230.00 7.600 1.7850 10 264.00 7.630 7.6 1.7850 10 264.00 7.700 7.7 1.6800 10 296.00 7.730 1.6800 10 330.00 7.770 1.6800 10 330.00 7.850 1.5750 10 362.00 7.830 1.5750 10 396.00 7.835 1.5750 10 396.00 7.921 1.4700 10 430.00 7.770 1.4700 10 462.00 7.850 1.4700 10 462.00 7.830 1.3650 10 496.00 7.900 1.3650 10 528.00 7.865 7.8 1.3650 10 528.00 7.840 7.8 1.2600 10 560.00 7.920 1.2600 10 594.00 7:900 1.2600 10 594.00 7.860 1.1550 10 628.00 7.950 1.1550 10 660.00 7.900 1.1550 10 660.00 7.850 1.0500 10 692.00 7.950 1.0500 10 726.00 7.900 7.9 1.0500 10 726.00 7.920 7.9 0.9450 10 760.00 7.850 0.9450 10 792.00 7.780 0.9450 10 792.00 7.870 0.8400 10 102 Table 5.8: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 822.00 7.740 0.8400 10 858.00 7.590 0.8400 10 858.00 7.700 0.7350 10 .890.00 7.490 0.7350 10 924.00 7.225 7.2 0.7350 10 924.00 7.335 7.4 0.6300 10 960.00 6.960 7.0 0.6300 10 960.00 7.410 7.5 0.6300 8 990.00 7.400 0.6300 8 990.00 7.525 0.5250 8 1022.00 7.370 0.5250 8 1056.00 7.190 7.2 0.5250 8 1056.00 7.250 7.3 0.4200 8 1086.00 6.920 0.4200 8 1100.00 6.650 0.4200 8 1122.00 6.360 0.4200 8 1122.00 6.435 0.3150 8 1154.00 6.044 0.3150 8 1188.00 5.600 5.6 0.3150 8 1188.00 5.725 5.8 0.2100 8 1220.00 5.470 0.2100 8 1236.00 5.340 0.2100 8 1254.00 5.210 0.2100 8 1254.00 5.265 0.1050 8 1284.00 4.950 0.1050 8 . 1320.00 4.550 0.1050 8 Table 5.9: Theoretical and Experbmental Profile Data for the Condition: 103 .50 = 0.0315 cfs n = 0.011 S = 0.025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 4.620 0.6300 10 5.00 4.700 0.6300 10 11.00 4.760 0.6300 10 13.50 4.800 0.6300 10 23.50 4.850 0.6300 10 29.50 4.900 0.6300 10 66.00 4.950 5.0 0.6300 10 66.00 5.280 5.3 0.5985 10 72.00 5.200 0.5985 10 92.00 5.000 0.5985 10 100.00 4.940 5.0 0.5985 10.. 100.00 4.740 4.6 0.5985 8 101.00 4.800 0.5985 8 102.00 4.880 0.5985 8 107.50 5.040 0.5985 8 116.50 5.200 0.5985 8 132.00 5.360 0.5985 8 132.00 5.695 0.5670 8 149.50 5.600 0.5670 8 170.20 5.520 0.5670 8 198.00 5.450 5.5 0.5670 8 198.00 5.735 5.8 0.5355 8 203.50 5.680 0.5355 8 212.50 5.600 0.5355 8 233.50 5.440 0.5355 8 264.00 5.290 0.5355 8 264.00 5.570 0.5040 8 276.00 5.440 0.5040 8 294.50 5.280 0.5040 8 300.00 5.240 0.5040 8 330.00 5.120 0.5040 8 330.00 5.410 0.4725 8 340.50 5.280 0.4725 8 357.50 5.120 0.4725 8 376.00 4.960 0.4725 8 396.00 4.880 5.0 0.4725 8 396.00 5.180 5.2 0.4410 8 407.00 5.040 0.4410 8 422.50 4.880 0.4410 8 443.50 4.720 0.4410 8 462.00 4.640 0.4410 8 462.00 4.960 0.4095 8 4 Table 5.9: (continued) 104 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 474.50 4.800 0.4095 8 489.00 4.640 0.4095 8 499.00 4.560 0.4095 8 528.00 4.410 4.4 0.4095 8 528.00 4.750 4.8 0.3780 8 541.13 4.560 0.3780 8 556.22 4.400 0.3780 8 580.78 4.240 0.3780 8 594.00 4.190 0.3780 8 594.00 4.550 0.3465 8 603.72 4.400 0.3465 8 616.33 4.240 0.3465 8 630.00 4.110 4.0 0.3465 8 630.00 3.840 3.7 0.3465 6 632.03 4.080 0.3465 6 635.54 4.200 0.3465 6 638.94 4.320 0.3465 6 644.85 4.440 0.3465 6 651.75 4.560 0.3465 6 660.00 4.650 0.3465 6 660.00 4.030 0.3150 6 670.38 4.980 0.3150 6 685.74 4.920 0.3150 6 703.35 4.860 0.3150 6 726.00 4.800 4.8 0.3150 6 726.00 5.090 5.1 0.2835 6 731.25 5.040 0.2835 6 736.67 4.980 0.2835 6 748.84 4.860 0.2835 6 762.59 4.740 0.2835 6 778.86 4.620 0.2835 6 792.00 4.500 0.2835 6 792.00 4.830 0.2520 6 798.38 4.740 0.2520 6 806.47 4.620 0.2520 6 816.67 4.500 0.2520 6 827.64 4.380 0.2520 6 840.36 4.260 0.2520 6 858.00 4.130 4.1 0.2520 6 858.00 4.455 4.5 0.2205 6 866.44 4.320 0.2205 6 874.53 4.200 0.2205 6 Table 5.9: (continued) 105 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 885.25 4.040 0.2205 6 900.00 3.840 4.0 0.2205 6 900.00 3.880 4.0 0.2205 5 909.33 4.000 0.2205 5 924.00 4.100 0.2205 5 924.00 4.495 0.1890 5 948.87 4.300 0.1890 5 980.49 4.100 0.1890 5 990.00 4.050 4.1 0.1890 5 990.00 4.370 4.4 0.1575 5 1001.03 4.200 0.1575 5 1015.70 4.000 0.1575 5 1031.65 3.800 0.1575 5 1050.56 3.600 0.1575 5 1056.00 3.550 0.1575 5 1056.00 3.890 0.1260 5 1066.00 3.700 0.1260 5 1077.35 3.500 0.1260 5 1090.00 3.300 0.1260 5 1100.00 3.150 3.2 0.1260 5 1100.00 3.260 3.5 0.1260 4 1110.00 3.360 0.1260 4 1122.00 3.440 0.0945 4 1122.00 3.860 0.0945 4 1130.76 3.760 0.0945 4 1142.45 3.600 0.0945 4 1162.77 3.360 0.0945 4 1188.00 3.120 3.1 0.0945 4 1188.00 3.470 3.5 0.0630 4 1200.00 3.200 0.0630 4 12%0.00 2.960 0.0630 4 12 2.31 2.720 0.0630 4 1238.00 2.480 0.0630 4 1254.00 2.280 0.0630 4 1254.00 2.680 0.0315 4 1266.00 2.360 0.0315 4 1278.91 2.040 0.0315 4 1292.89 1.720 0.0315 4 1320.00 1.400 0.0315 4 106 Table 5.10: Theoretical and Experimental Profile Data for the Condition: AQ = 0.0525 cfs n = 0.011 S = 0.0025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 5.270 1.0500 10 7.50 5.335 1.0500 10 18.80 5.430 1.0500 10 26.00 5.480 1.0500 10 30.20 5.500 1.0500 10 66.00 5.500 1.0500 10 66.00 5.880 0.9975 10 100.00 5.880 0.9975 10 132.00 5.880 6.0 0.9975 10 132.00 6.210 6.3 0.9450 10 150.00 6.075 0.9450 10 160.00 6.000 0.9450 10 180.00 5.940 0.9450 10 200.00 5.880 0.9450 10 200.00 6.320 0.8925 8 214.00 6.100 6.0 0.8925 8 230.00 5.950 6.0 0.8925 8 234.00 5.800 0.8925 8 246.00 5.920 0.8925 8 264.00 5.980 0.8925 8 264.00 6.390 0.8400 8 270.00 6.320 0.8400 8 298.00 6.120 0.8400 8 313.00 6.069 0.8400 8 330.00 5.990 6.0 0.8400 8 330.00 6.350 6.4 0.7875 8 334.00 6.290 0.7875 8 364.00 5.920 0.7875 8 379.00 5.780 0.7875 28~~ 396.00 5.650 0.7875 8 396.00 5.950 0.7350 8 412.00 5.680 0.7350 8 432.00 5.400 0.7350 8 462.00 5.230 0.7350 8 462.00 5.590 0.6825 8 480.00 53265 0.6825 8 500.00 5.080 0.6825 8 528.00 4.910 5.0 0.6825 8 528.00 5.290 5.3 0.6300 8 541100 5.140 0.6300 8 560.00 4.945 0.6300 8 580.00 4.780 0.6300 8 Table 5.10: (continued) 107 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 594.00 4.690 0.6300 8 594.00 5.150 0.5775 8 610.00 4.980 0.5775 8 634.00 4.820 0.5775 8 660.00 4.680 0.5775 8 660.00 5.230 0.5250 8 670.00 5.060 0.5250 8 690.00 4.865 5.0 0.5250 8 690.00 4.550 4.5 0.5250 6 694.00 4.780 0.5250 6 698.00 4.875 0.5250 6 710.00 5.020 0.5250 6 726.00 5.090 5.1 0.5250 6 726.00 5.490 5.5 0.4725 6 750.00 5.350 0.4725 6 772.00 5.290 0.4725 6 792.00 5.290 0.4725 6 792.00 5.685 0.4200 6 817.00 5.350 0.4200 6 840.00 5.250 0.4200 6 858.00 5.210 0.4200 6 858.00 5.575 0.3675 6 879.00 5.165 0.3675 6 882.00 5.135 0.3675 6 900.00 5.000 0.3675 6 924.00 4.920 5.0 0.3675 6 924.00 5.375 5.4 0.3150 6 950.00 5.000 0.3150 6 971.00 4.820 0.3150 6 990.00 4.750 0.3150 6 990.00 5.200 0.2625 6 1022.50 4.650 0.2625 6 1036.00 4.450 0.2625 6 1056.00 4.245 0.2625 6 1056.00 4.620 0.2100 6 1079.00 4.080 0.2100 6 1102.00 3.800 0.2100 6 1122.00 3.690 3.8 0.2100 6 1122.00 4.090 4.2 0.1575 6 1150.00 3.590 0.1575 6 1150.00 3.250 0.1575 5 1151.00 3.380 0.1575 5 108 Table 5.10: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 1155.00 3.540 0.1575 5 1162.00 3.690 0.1575 5 1170.00 3.750 0.1575 5 1188.00 3.800 0.1575 5 1188.00 4.150 0.1050 5 1210.00 3.610 0.1050 5 1232.00 3.400 0.1050 5 1254.00 3.250 0.1050 5 1254.00 3.610 0.0525 5 1280.00 2.835 0.0525 5 1300.00 2.500 0.0525 5 1320.00 2.100 0.0525 5 109 Table 5.11: Theoretical and Experimental Profile Data for the Condition: AQ = 0.0735 cfs n = 0.011 S = 0.0025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 5.770 5.8 1.4700 10 6.00 5.850 1.4700 10 16.00 5.940 1.4700 10 26.00 5.947 1.4700 10 44.00 6.035 1.4700 10 50.50 6.040 6.0 1.4700 10 66.00 6.040 6.0 1.4700 10 66.00 6.350 6.4 1.3965 10 100.00 6.400 1.3965 10 132.00 6.470 1.3965 10 132.00 6.800 1.3230 10 166.00 6.800 1.3230 10 198.00 7.165 1.3230 10 198.00 6.900 1.2495 10 218.00 6.790 1.2495 10 240.00 6.720 1.2495 10 264.00 6.730 1.2495 10 264.00 7.100 1.1760 10 287.00 6.650 1.1760 10 308.00 6.460 1.1760 10 330.00 6.350 6.4 1.1760 10 330.00 6.700 6.7 1.1025 10 360.00 6.140 6.1 1.1025 10 360.00 5.850 6.0 1.1025 8 365.00 6.180 1.1025 8 374.00 6.335 1.1025 8 384.00 6.400 1.1025 8 396.00 6.400 1.1025 8 396.00 6.700 1.0290 8 420.00 6.260 1.0290 8 440.00 6.090 1.0290 8 462100 5.990 6.1 1.0290 8 462.00 6.400 6.3 0.9555 8 486.00 6.045 0.9555 8 508.00 5.870 0.9555 8 528.00 5.775 0.9555 8 528.00 6.230 0.8820 8 546.00 5.930 0.8820 8 570.00 5.725 0.8820 8 594.00 5.570 0.8820 8 594 . 00 6 . 045 0 38085 8 612.00 5.700 0.8085 8 636.00 5.500 0.8085 8 660.00 5.420 0.8085 8 660.00 5.900 0.7350 8 110 Table 5.11: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 682.00 5.600 0.7350 8 708.00 5.390 0.7350 8 726.00 5.315 0.7350 8 726.00 5.745 0.6615 8 743.00 5.350 0.6615 8 770.00 5.140 0.6615 8 792.00 5.065 5.1 0.6615 8 792.00 5.470 5.5 0.5880 8 820.00 5.050 5.1 0.5880 8 820.00 4.735 4.5 0.5880 6 822.00 4.950 0.5880 6 826.00 5.090 0.5880 6 836.00 5.200 0.5880 6 858.00 5.340 0.5880 6 858.00 5.820 0.5145 6 882.00 5.480 0.5145 6 902.00 5.320 0.5145 6 924.00 5.200 5.2 0.5145 6 924.00 5.620 5.6 0.4410 6 939.00 5.435 0.4410 6 964.00 5.200 0.4410 6 990.00 5.050 0.4410 6 990.00 5.445 0.3675 6 1008.00 5.100 0.3675 6 1032.00 4.900 0.3675 6 1056.00 4.815 0.3675 6 1056.00 5.280 0.2940 6 1073.00 5.000 0.2940 6 1096.00 4.750 0.2940 6 1122.00 4.600 4.6 0.2940 6 1122.00 4.970 5.0 0.2205 6 1130.00 4.745 0.2205 6 1145.00 4.400 0.2205 6 1170.00 4.090 0.2205 6 1188.00 3.920 0.2205 6 1188.00 4.350 0.1470 6 1211.00 3.770 0.1470 6 1234.00 3.500 0.1470 6 1254.00 3.310 0.1470 6 1254.00 3.800 0.0735 6 1276.00 3.200 0.0735 6 1298.00 2.645 0.0735 6 1320.00 2.245 0.0735 6 111 Table 5.12: Theoretical and Experimental Profile Data for the Condition: 4Q = 0.1050 cfs n: 0.011 S = 0.0025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 6.420 2.1000 10 6.00 6.530 2.1000 10 10.00 6.580 2.1000 10 18.00 6.610 2.1000 10 28.00 6.060 2.1000 10 40.00 6.700 2.1000 10 66.00 6.740 6.5 2.1000 10 66.00 7.110 7.2 1.9950 10 100.00 7.145 1.9950 10 132.00 7.170 1.9950 10 132.00 7.500 1.8900 10 166.00 7.500 1.8900 10 198.00 7.500 1.8900 10 198.00 7.750 1.7850 10 220.00 7.380 1.7850 10 240.00 7.170 1.7850 10 250.00 7.090 1.7850 10 264.00 6.990 7.0 1.7850 10 264.00 7.470 7.5 1.6800 10 285.00 7.070 1.6800 10 306.00 6.800 1.6800 10 315.00 6.740 1.6800 10 330.00 6.640 1.6800 10 330.00 7.150 1.5750 10 352.00 6.700 1.5750 10 370.00 6.490 1.5750 10 375.00 6.420 1.5750 10 385.00 6.350 1.5750 10 396.00 6.290 6.3 1.5750 10 396.00 6.830 7.0 1.4700 10 422.00 6.400 1.4700 10 436.00 6.255 1.4700 10 447.00 6.150 1.4700 10 462.00 6.080 1.4700 10 462.00 6.690 1.3650 10 464.80 6.500 1.3650 10 468.00 6.370 1.3650 10 490.00 6.060: 6.0 1.3650 10 490.00 5.720 5.5 1.3650 8 493.80 5.900 1.3650 8 498.00 5.950 1.3650 8 512.00 6.080 1.3650 8 528.00 6.130 1.3650 8 528.00 6.550 1.2600 8 560.00 6.550 1.2600 8 Table 5.12: (continued) 112 Distance from Calculated Experimental Discharge ’ Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 594.00 6.700 1.2600 8 594.00 7.050 1.1550 8 610.00 6.720 1.1550 8 640.00 6.390 1.1550 8 660.00 6.200 6.0 1.1550 8 660.00 6.675 6.8 1.0500 8 684.00 6.250 1.0500 8 710.00 5.970 1.0500 8 726.00 5.860 1.0500 8 726.00 6.350 0.9450 8 748.00 6.000 0.9450 8 776.00 5.700 0.9450 8 792.00 5.600 0.9450 8 792.00 6.150 0.8400 8 815.00 5.820 0.8400 8 838.00 5.600 0.8400 8 858.00 5.500 5.5 0.8400 8 858.00 6.110 6.1 0.7350 8 890.00 5.660 0.7350 8 903.00 5.500 0.7350 8 924.00 5.300 0.7350 8 924.00 5.800 0.6300 8 940.00 5.545 0.6300 8 964.00 5.200 0.6300 8 990.00 5.000 0.6300 8 990.00 5.600 0.5250 8 1005.00 5.400 0.5250 8 1020.00 5.210 5.5 0.5250 8 1020.00 4.875 5.0 0.5250 6 1023.00 5.150 0.5250 6 1030.00 5.300 0.5250 6 1056.00 5.500 0.5250 6 1056.00 5.810 0.4200 6 1098.00 5.220 0.4200 6 1122.00 4.960 0.4200 6 1122.00 5.500 0.3150 6 1170.00 4.590 0.3150 6 1188.00 4.380 4.4 0.3150 6 1188.00 4.810 5.0 0.2100 6 1232.00 3.990 0.2100 6 1254.00 3.700 0.2100 6 1254.00 4.260 0.1050 6 1302.00 3.000 0.1050 6 1320.00 2.730 0.1050 6 Table 5.13: Theoretical and Experimental Profile Data for the Condition: 113 .aQ = 0.0315 cfs n = 0.011 S = 0.005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.140 2.0 0.6300 8 6.00 2.240 0.6300 8 18.50 2.320 0.6300 8 38.25 2.400 0.6300 8 66.00 2.470 2.5 0.6300 8 66.00 2.750 3.0 0.5985 8 72.00 2.800 0.5985 8 84.00 2.880 0.5985 8 108.25 2.960 0.5985 8 132.00 3.010 0.5985 8 132.00 3.340 0.5670 8 153.95 3.420 0.5670 8 180.50 3.500 0.5670 8 198.00 3.530 3.5 0.5670 8 198.00 3.910 4.0 0.5335 8 228.45 3.880 0.5335 8 265.00 3.850 0.5335 8 265.00 4.090 0.5040 8 282.75 4.100 0.5040 8 330.00 4.120 0.5040 8 330.00 4.420 0.4725 8 336.34 4.320 0.4725 8 348.00 4.240 0.4725 8 359.15 4.160 0.4725 8 378.72 4.080 0.4725 8 396.00 4.010 4.0 0.4725 8 396.00 4.340 4.5 0.4410 8 408.86 4.120 0.4410 8 420.00 4.040 4.0 0.4410 8 420.00 3.170 3.5 0.4410 6 422.00 3.760 0.4410 6 424.30 3.840 0.4410 6 428.00 3.920 0.4410 6 436.00 4.080 0.4410 6 446.14 4.240 0.4410 6 462.00 4.360 4.4 0.4410 6 462.00 4.730 4.7 0.4095 6 472.00 4.640 0.4095 6 486.00 4.560 0.4095 6 506.85 4.480 0.4095 6 528.00 4.390 0.4095 6 528.00 4.880 0.3780 6 538.00 4.720 0.3780 6 546.00 4.640 0.3780 6 114 Table 5.13: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 554.00 4.560 0.3780 6 562.50 4.480 0.3780 6 575.55 4.320 0.3780 6 594.00 4.180 4.2 0.3780 6 594.00 4.530 4.6 0.3465 6 600.00 4.480 0.3465 6 606.45 4.320 0.3465 6 624.40 4.160 0.3465 6 640.82 4.000 0.3465 6 660.00 3.900 0.3465 6 660.00 4.340 0.3150 6 664.75 4.240 0.3150 6 678.00 4.080 0.3150 6 696.00 3.920 0.3150 6 718.00 3.760 0.3150 6 726.00 3.710 0.3150 6 726.00 4.080 0.2835 6 732.45 3.920 0.2835 6 742.52 3.780 0.2835 6 760.00 3.560 3.6 0.2835 6 760.00 3.360 3.4 0.2835 5 774.00 3.540 0.2835 5 792.00 3.630 0.2835 5 792.00 4.110 0.2520 5 804.90 4.000 0.2520 5 828.00 3.840 0.2520 5 858.00 3.790 0.2520 5 858.00 4.210 0.2205 5 868.00 4.080 0.2205 5 884.00 3.900 0.2205 5 900.75 3.780 0.2205 5 924.00 3.680 3.7 0.2205 5 924.00 4.020 4.0 0.1890 5 930.15 3.900 0.1890 5 944.00 3.720 0.1890 5 958.80 3.540 0.1890 5 ' 976.25 3.360 0.1890 5 990.00 3.270 0.1890 5 990.00 3.680 0.1575 5 1004.00 3.410 0.1575 5 1120.00 3.190 3.0 0.1575 5 1120.00 3.250 3.2 0.1575 4 1034.00 3.360 0.1575 4 Table 5.13: (continued) 115 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 1056.00 3.370 0.1575 4 1056.00 3.790 0.1260 4 1072.62 3.580 0.1260 4 1 1098.00 3.300 0.1260 4 1122.00 3.020 3.0 0.1260 4 1122.00 3.460 3.5 0.0945 4 1136.00 3.240 0.0945 4 1154.10 2.960 0.0945 4 1170.15 2.780 0.0945 4 1188.00 2.620 2.6 0.0945 4 1188.00 3.140 3.3 0.0630 4 1204.00 2.800 0.0630 4 1223.40 2.480 0.0630 4 1254.00 2.080 0.0630 4 1254.00 2.520 0.0315 4 1264.95 2.320 0.0315 4 1282.38 1.880 0.0315 4 1300.58 1.480 0.0315 4 1320.00 1.200 0.0315 4 116 Table 5.14: Theoretical and Experimental Profile Data for the Condition: .30 = 0.0525 cfs n = 0.011 S = 0.005 Distance from Calculated Experimental Discharge Diameter Outlet Depth (in) (cfs) 0.00 2.800 1.0500 8 4.15 2.870 1.0500 8 14.00 2.990 1.0500 8 44.20 3.140 1.0500 8 66.00 3.200 3.2 1.0500 8 66.00 3.580 3.6 0.9975 8 88.00 3.640 0.9975 8 112.70 3.710 0.9975 8 132.00 3.740 0.9975 8 132.00 4.130 0.9450 8 164.00 4.130 0.9450 8 198.00 4.130 0.9450 8 198.00 4.430 0.8925 8 220.00 4.410 0.8925 8 240.00 4.400 0.8925 8 264.00 4.390 4.5 0.8925 8 264.00 4.680 4.8 0.8400 8 296.05 4.640 0.8400 8 330.00 4.600 0.8400 8 330.00 4.680 0.7875 8 359.80 4.840 0.7875 8 396.00 4.800 0.7875 8 396.00 5.120 0.7350 8 409.80 5.000 0.7350 8 436.00 4.840 0.7350 8 462.00 4.710 0.7350 8 462.00 5.070 0.6825 8 475.90 4.860 0.6825 8 493.90 4.670 0.6825 8 514.00 4.510 0.6825 8 528.00 4.460 4.5 0.6825 8 528.00 4.850 4.8 0.6300 8 534.30 4.660 0.6300 8 547.00 4.500 0.6300 8 560.00 4.380 0.6300 8 560.00 4.050 0.6300 6 563.10 4.090 0.6300 6 571.55 4.200 0.6300 6 583.25 4.290 0.6300 6 594.00 4.340 0.6300 6 594.00 4.650 0.5775. 6 601.00 4.500 0.5775 6 640.00 4.080 0.5775 6 Table 5.14: (continued) 117 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 660.00 3.970 4.0 0.5775 6 660.00 4.450 4.5 0.5250 6 668.00 4.350 0.5250 6 680.00 4.240 0.5250 6 706.00 3.990 0.5250 6 726.00 3.830 0.5250 6 726.00 4.290 0.4725 6 750.00 4.050 0.4725 6 770.00 3.860 0.4725 6 792.00 3.730 4.0 0.4725 6 792.00 4.060 4.5 0.4200 6 815.85 3.820 0.4200 6 840.00 3.630 0.4200 6 858.00 3.500 0.4200 6 858.00 3.760 0.3675 6 867.90 3.580 0.3675 6 878.00 3.460 0.3675 6 890.00 3.360 3.4 0.3675 6 890.00 3.110 3.1 0.3675 5 900.00 3.260 0.3675 5 912.60 3.400 0.3675 5 924.00 3.470 0.3675 5 924.00 3.800 0.3150 5 946.40 3.550 0.3150 5 970.00 3.370 0.3150 5 990.00 3.260 3.3 0.3150 5 990.00 3.730 3.7 0.2650 5 1016.00 3.400 0.2650 5 1039.00 3.190 0.2650 5 1056.00 3.110 0.2650 5 1056.00 3.570 0.2100 5 1088.00 3.230 0.2100 5 1122.00 2.860 0.2100 _ 5 1122.00 3.360 0.1575 5 1155.00 2.890 0.1575 5 1188.00 2.560 2.6 0.1575 5 1188.00 3.240 3.2 0.1050 5 1219.85 2.770 0.1050 5 1254.00 2.280 0.1050 5 1254.00 2.940 0.0525 5 1280.00 2.260 0.0525 5 1302.00 1.740 0.0525 5 1320.00 1.440 0.0525 5 Table 5.15: Theoretical and Experimental Profile Data for the Condition: 118 a0 = 0.0735 cfs n = 0.011 S = 0.005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 3.290 1.4700 8 4.45 3.380 1.4700 8 18.20 3.550 1.4700 8 22.60 3.740 1.4700 8 66.00 3.810 4.0 1.4700 8 66.00 4.180 4.5 1.3965 8 100.00 4.190 1.3965 8 132.00 4.200 1.3965 8 132.00 4.460 1.3230 8 168.20 4.480 1.3230 8 198.00 4.500 1.3230 8 198.00 4.700 1.2495 8 230.00 4.750 1.2495 8 264.00 4.740 4.7 1.2495 8 264.00 5.030 5.0 1.1760 8 294.00 5.000 1.1760 8 330.00 4.970 1.1760 8 330.00 5.310 1.1025 8 360.00 5.280 1.1025 8 396.00 5.260 1.1025 8 396.00 5.580 1.0290 8 430.00 5.430 1.0290 8 462.00 5.300 5.3 1.0290 8 462.00 5.650 5.7 0.9555 8 473.10 5.500 0.9555 8 500.00 5.230 0.9555 8 528.00 4.990 0.9555 8 528.00 5.300 0.8820 8 542.80 5.000 0.8820 8 571.35 4.620 0.8820 8 594.00 4.420 0.8820 8 594.00 4.970 0.8085 8 608.40 4.670 0.8085 8 628.00 4.390 0.8085 8 640.00 4.270 0.8085 8 660.00 4.050 4.0 0.8085 8 660.00 4.570 4.7 0.7350 8 666.60 4.350 0.7350 8 676.00 4.170 0.7350 8 690.00 4.030 0.7350 8 690.00 3.640 0.7350 6 694.10 3.800 0.7350 6 700.00 3.930 0.7350 6 119 Table 5.15: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 715.55 4.110 0.7350 6 726.00 4.170 4.2 0.7350 6 726.00 4.600 4.7 0.6615 6 760.00 4.210 0.6615 6 792.00 3.860 0.6615 6 792.00 4.400 0.5880 6 816.25 3.900 0.5880 6 838.00 3.570 0.5880 6 858.00 3.420 0.5880 6 858.00 4.040 0.5145 6 876.00 3.710 0.5145 6 898.30 3.410 0.5145 6 924.00 3.170 0.5145 6 924.00 3.680 0.4410 6 931.90 3.380 0.4410 6 944.00 3.190 0.4410 6 960.00 3.060 3.0 0.4410 6 960.00 2.750 2.8 0.4410 5 968.30 2.950 0.4410 5 978.75 3.040 0.4410 5 990.00 3.120 0.4410 5 990.00 3.600 0.3675 5 1020.00 3.450 0.3675 5 '1056.00 3.280 0.3675 5 1056.00 3.720 0.2940 5 1088.00 3.330 0.2940 5 1122.00 3.110 0.2940 5 1122.00 3.670 0.2205 5 1156.14 3.300 0.2205 5 1188.00 2.960 3.0 0.2205 5 1188.00 3.530 3.7 0.1470 5 1220.00 2.920 0.1470 5 1254.00 2.370 0.1470 5 1254.00 3.140 0.0735 5 1280.00 2.530 0.0735 5 1302.85 1.980 0.0735 5 1320.00 1.660 0.0735 5 Table 5.16: Theoretical and Experimental Profile Data for the Condition: 120 AQ = 0.1050 cfs n = 0.011 S = 0.005 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 3.630 2.1000 8 7.00 3.800 2.1000 8 20.00 3.960 2.1000 8 40.15 4.120 2.1000 8 66.00 4.220 4.0 2.1000 8 66.00 4.430 4.5 1.9950 8 100.00 4.500 1.9950 8 132.00 4.550 1.9950 8 132.00 4.720 1.8900 8 166.50 4.780 1.8900 8 198.00 4.820 1.8900 8 198.00 5.010 1.7850 8 230.00 5.060 1.7850 8 264.00 5.100 5.0 1.7850 8 264.00 5.360 5.5 1.6800 8 300.00 5.430 1.6800 8 330.00 5.380 1.6800 8 330.00 5.690 1.5750 8 368.00 5.740 1.5750 8 396.00 5.700 1.5750 8 396.00 6.010 1.4700 8 430.00 5.970 1.4700 8 462.00 5.780 1.4700 8 462.00 6.150 1.3650 8 490.00 6.000 1.3650 8 528.00 5.600 5.6 1.3650 8 528.00 6.010 6.0 1.2600 8 548.20 5.920 1.2600 8 571.50 5.740 1.2600 8 594.00 5.470 1.2600 8 594.00 6.000 1.1550 8 611.85 5.540 1.1550 8 637.90 5.140 1.1550 8 660.00 4.880 5.0 1.1550 8 660.00 5.450 5.5 1.0500- 8 711.35 4.840 1.0500 8 726.00 4.780 1.0500 8 726.00 5.180 0.9450 8 755.00 4.800 0.9450 8 776.00 4.580 0.9450 8 792.00 4.450 4.5 0.9450 8 792.00 4.840 5.0 0.8400 8 121 Table 5.16: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 820.00 4.920 5.0 0.8400 8 820.00 4.530 4.5 0.8400 6 824.45 4.680 0.8400 6 830.35 4.780 0.8400 6 846.00 4.910 0.8400 6 858.00 4.940 0.8400 6 858.00 5.270 0.7350 6 885.80 5.080 0.7350 6 911.00 4.840 0.7350 6 924.00 4.680 4.7 0.7350 6 924.00 5.150 5.2 0.6300 6 947.20 4.710 0.6300 6 972.00 4.460 0.6300 6 990.00 4.340 0.6300 6 990.00 4.780 0.5250 6 1016.60 4.470 0.5250 6 1040.00 4.240 0.5250 6 1056.00 4.180 0.5250 6 1056.00 4.560 0.4200 6 1090.00 4.180 0.4200 6 1122.00 3.840 4.0 0.4200 6 1122.00 4.480 4.5 0.3150 6 1156.00 3.940 0.3150 6 1188.00 3.580 0.3150 6 1188.00 4.040 0.2100 6 1220.00 3.480 0.2100 6 1254.00 2.860 0.2100 6 1254.00 3.480 0.1050 6 1280.00 2.760 0.1050 6 1303.45 2.120 0.1050 6 1320.00 1.780 0.1050 6 Table 5.17: Theoretical and Experimental Profile Data for the Condition: 122 4Q = 0.0315 cfs n = 0.011 S = 0.010 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.230 0.6300 8 22.00 2.420 0.6300 8 46.25 2.530 0.6300 8 66.00 2.610 3.0 0.6300 8 66.00 2.940 3.5 0.5985 8 90.24 3.060 0.5985 8 132.00 3.110 0.5985 8 132.00 3.500 0.5670 8 136.82 3.390 0.5670 8 150.00 3.230 3.3 0.5670 6 150.00 2.880 2.9 0.5670 6 178.80 3.070 0.5670 6 200.00 3.130 0.5670 6 200.00 3.410 0.5355 6 230.00 3.410 0.5355 6 264.00 3.420 3.5 0.5355 6 264.00 3.720 3.7 0.5040 6 330.00 3.640 0.5040 6 330.00 3.820 0.4725 6 370.00 3.860 0.4725 6 396.00 3.910 0.4725 6 396.00 4.180 0.4410 6 405.00 4.050 0.4410 6 421.73 3.930 0.4410 6 462.00 3.670 3.7 0.4410 6 462.00 4.020 4.0 0.4095 6 472.20 3.900 0.4095 6 510.00 3.660 0.4095 6 528.00 3.560 0.4095 6 528.00 4.080 0.3780 6 536.74 3.960 0.3780 6 550.70 3.780 0.3780 6 570.00 3.540 0.3780 6 594.00 3.340 0.3780 6 594.00 3.820 0.3465 6 604.34 3.600 0.3465 6 620.00 3.430 3.4 0.3465 6 620.00 3.090 3.1 0.3465 5 628.65 3.390 0.3465 5 640.30 3.480 0.3465 5 660.00 3.570 0.3465 5 660.00 4.030 0.3150 5 668.10 3.900 0.3150 5 685.00 3.750 0.3150 5 Table 5.17: (continued) 123 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 726.00 3.500 0.3150 5 726.00 4.080 0.2835 5 736.00 3.800 0.2835 5 760.00 3.550 0.2835 5 792.00 3.210 3.2 0.2835 5 792.00 3.700 3.7 0.2520 5 800.00 3.600 0.2520 5 836.00 3.200 0.2520 5 858.00 2.960 0.2520 5 858.00 3.520 0.2205 5 866.00 3.400 0.2205 5 904.00 3.050 0.2205 5 924.00 2.830 0.2205 5 924.00 3.340 0.1890 5 932.00 31180 0.1890 5 950.00 2.890 3.0 0.1890 5 950.00 3.080 3.2 0.1890 4 965.00 3.180 0.1890 4 976.50 3.240 0.1890 4 990.00 3.290 0.1890 4 990.00 3.720 0.1575 4 1000.00 3.560 0.1575 4 1016.00 3.400 0.1575 4 1038.00 3.200 0.1575 4 1056.00 3.020 3.0 0.1575 4 1056.00 3.500 3.5 0.1260 4 1066.00 3.300 0.1260 4 1084.00 3.080 0.1260 4 1100.00 2.880 0.1260 4 1122.00 2.540 0.1260 4 1122.00 3.030 0.0945 4 1130.24 2.880 0.0945 4 1160.45 2.400 0.0945 4 1188.00 2.120 2.1 0.0945 4 1188.00 2.630 2.6 0.0630 4 1212.20 2.220 0.0630 4 1236.30 1.960 0.0630 4 1254.00 1.810 0.0630 4 1254.00 2.370 0.0315 4 1284.30 2.720 0.0315 4 1304.00 1.400 0.0315 4 1320.00 1.040 0.0315 4 Table 5.18: Theoretical and Experimental Profile Data for the Condition: IQ = 0.0525 cfs 124 n = 0.011 S = 0.010 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.500 1.0500 8 10.80 2.760 1.0500 8 21.85 2.940 1.0500 8 66.00 3.060 3.0 1.0500 8 66.00 3.350 3.5 0.9975 8 81.45 3.470 0.9975 8 99.55 3.540 0.9975 8 110.80 3.590 0.9975 8 132.00 3.610 0.9450 8 132.00 3.900 0.9450 8 141.15 3.850 0.9450 8 170.00 3.850 0.9450 8 198.00 3.820 0.9450 8 198.00 4.170 0.8925 8 230.00 4.140 0.8925 8 264.00 4.100 0.8925 8 264.00 4.400 0.8400 8 300.00 4.250 4.2 0.8400 8 300.00 3.950 4.0 0.8400 6 316.00 4.040 0.8400 6 330.00 4.040 0.8400 6 330.00 4.430 0.7875 6 362.00 4.470 0.7875 6 396.00 4.300 0.7875 6 396.00 4.750 0.7350 6 417.10 4.490 0.7350 6 440.00 4.270 0.7350 6 462.00 4.140 4.2 0.7350 6 462.00 4.560 4.6 0.6825 6 468.70 4.480 0.6825 6 488.00 4.180 0.6825 6 511.20 4.020 0.6825 6 528.00 3.920 4.0 0.6825 6 528.00 4.430 4.5 0.6300 6 560.00 4.000 0.6300 6 594.00 3.740 0.6300 6 594.00 4.190 0.5775¢~ 6 621.25 3.890 0.5775 6 640.00 3.510 0.5775 6 660.00 3.310 2.9 0.5775 6 660.00 3.810 3.8 0.5250 6 683.85 3.500 0.5250 6 708.75 3.180 0.5250 6 125 Table 5.18: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 726.00 3.050 0.5250 6 726.00 3.520 0.4725 6 750.00 3.450 3.5 0.4725 6 750.00 2.890 3.0 0.4725 5 754.15 2.900 0.4725 5 763.00 3.150 0.4725 5 775.00 3.260 0.4725 5 792.00 3.320 0.4725 5 792.00 3.870 0.4200 5 824.00 3.630 0.4200 5 858.00 3.380 0.4200 5 858.00 3.770 0.3675 5 886.00 3.500 0.3675 5 924.00 3.140 3.2 0.3675 5 924.00 3.580 3.6 0.3150 5 956.00 3.350 0.3150 5 990.00 3.100 0.3150 5 990.00 3.620 0.2625 5 1014.00 3.100 0.2625 5 1038.00 2.750 0.2625 5 1056.00 2.640 0.2625 5 1056.00 3.190 0.2100 5 1070.00 2.910 0.2100 5 1090.00 2.550 2.6 0.2100 5 1090.00 2.700 2.7 0.2100 4 1102.00 2.840 0.2100 4 1122.00 2.960 0.2100 4 1122.00 3.400 0.1575 4 1144.70 2.910 0.1575 4 1166.00 2.600 0.1575 4 1188.00 2.380 2.4 0.1575 4 1188.00 3.080 3.2 0.1050 4 1212.00 2.640 0.1050 4 1238.00 2.250 0.1050 4 1254.00 2.090 0.1050 4 1254.00 3.100 0.0525 4 1278.00 2.240 0.0525 4 1299.00 1.800 0.0525 4 1320.00 1.400 0.0525 4 126 Table 5.19: Theoretical and Experimental Profile Data for the Condition: ‘Q = 0.0735 cfs n = 0.011 S = 0.010 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.720 3.0 1.4700 8 12.90 2.900 1.4700 8 18.85 2.970 1.4700 8 30.00 3.100 1.4700 8 39.35 3.190 1.4700 8 66.00 3.420 3.5 1.4700 8 66.00 3.460 3.7 1.3965 8 99.45 3.880 1.3965 8 117.35 3.980 1.3965 8 132.00 4.000 1.3965 8 132.00 4.210 1.3230 8 160.00 4.210 1.3230 8 198.00 4.220 4.0 1.3230 8 198.00 4.580 4.6 1.2495 8 230.00 4.550 1.2495 8 264.00 4.520 1.2495 8 264.00 4.900 1.1760 8 297.00 4.840 1.1760 8 330.00 4.650 1.1760 8 330.00 4.980 1.1025 8 364.00 4.870 1.1025 8 396.00 4.690 1.1025 8 396.00 5.080 1.0290 8 427.00 4.800 1.0290 8 462.00 4.490 4.5 1.0290 8 462.00 4.920 5.0 0.9555 8 494.55 4.600 0.9555 8 528.00 4.280 0.9555 8 528.00 4.700 0.8820 8 536.45 4.660 0.8820 8 548.20 4.500 0.8820 8 560.00 4.500 4.5 0.8820 8 560.00 4.080 4.0 0.8820 6 564.00 4.230 0.8820 6 '568.50 4.320 0.8820 6 580.50 4.400 0.8820 6 594.00 4.430 0.8820 6 594.00 4.700 0.8085 6 620.45 4.600 0.8085 6 660.00 4.470 4.5 0.8085 6 660.00 4.810 5.0 0.7350 6 677.45 4.500 0.7350 6 127 Table 5.19: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 702.00 4.090 0.7350 6 726.00 3.820 4.0 0.7350 6 726.00 4.230 4.3 0.6615 6 741.15 4.090 0.6615 6 768.35 3.840 0.6615 6 792.00 3.660 0.6615 6 792.00 4.140 0.5880 6 824.00 3.860 0.5880 6 858.00 3.580 0.5880 6 858.00 4.120 0.5145 6 893.95 3.600 0.5145 6 924.00 3.200 3.2 0.5145 6 924.00 3.680 3.7 0.4410 6 950.00 3.340 3.3 0.4410 6 950.00 3.600 3.8 0.4410 5 958.00 3.640 0.4410 5 990.00 3.750 0.4410 5 990.00 4.120 0.3675 5 1023.00 3.800 0.3675 5 1056.00 3.480 0.3675 5 1056.00 3.950 4.0 0.2940 5 1078.00 3.660 0.2940 5 1095.15 3.450 0.2940 5 1122.00 3.290 0.2940 5 1122.00 3.780 0.2205 5 1140.00 3.390 0.2205 5 1168.00 2.910 0.2205 5 1188.00 2.690 0.2205 5 1188.00 3.220 0.1470 5 1220.00 2.800 0.1470 5 1254.00 2.370 0.1470 5 1254.00 3.100 0.0735 5 1273.00 2.650 0.0735 5 1297.10 2.100 0.0735 5 1320.00 1.650 0.0735 5 128 Table 5.20: Theoretical and Experimental Profile Data for the Condition: .40 = 0.0315 cfs n = 0.011 S = 0.025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 0.530 0.6300 6 18.20 0.720 0.6300 6 38.20 0.840 0.6300 6 52.00 0.960 0.6300 6 66.00 1.000 1.0 0.6300 6 66.00 1.250 1.4 0.5985 6 132.00 1.280 0.5985 6 132.00 1.560 0.5670 6 164.45 1.500 0.5670 6 198.00 1.470 0.5670 6 198.00 1.720 0.5355 6 215.55 1.600 0.5355 6 245.75 1.520 0.5355 6 264.00 1.460 1.5 0.5355 6 264.00 1.730 1.7 0.5040 6 276.80 1.520 0.5040 6 300.00 1.270 0.5040 6 300.00 1.020 0.5040 5 308.35 1.130 0.5040 5 318.90 1.220 0.5040 5 330.00 1.300 0.5040 5 330.00 1.530 0.4725 5 340.00 1.580 0.4725 5 367.74 1.630 0.4725 5 396.00 1.590 0.4725 5 396.00 1.970 0.4410 5 462.00 1.990 2.0 0.4410 5 462.00 2.250 2.3 0.4095 5 490.48 2.300 0.4095 5 528.00 2.430 0.4095 5 528.00 2.610 0.3780 5 558.00 2.840 0.3780 5 594.00 3.120 0.3780 5 594.00 3.440 0.3465 5 ”610.60 3.300 0.3465 5 645.15 3.040 0.3465 5 660.00 2.970 3.0 0.3465 5 660.00 3.390 3.4 0.3150 5 686.05 2.980 0.3150 5 700.00 2.820 0.3150 5 726.00 2.870 3.0 0.3150 ‘4~ 726.00 3.320 3.5 0.2835 4 Table 5.20: (continued) 129 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 740.00 3.140 0.2835 4 757.75 2.980 0.2835 4 774.72 2.880 0.2835 4 792.00 2.730 0.2835 4 792.00 3.290 0.2520 4 804.00 3.120 0.2520 4 823.40 2.880 0.2520 4 840.58 2.720 0.2520 4 858.00 2.570 2.6 0.2520 4 858.00 3.150 3.2 0.2205 4 865.94 3.040 0.2205 4 878.00 2.880 0.2205 4 892.00 2.760 0.2205 4 908.24 2.600 0.2205 4 924.00 2.420 0.2205 4 924.00 3.020 0.1890 4 934.92 2.880 0.1890 4 942.74 2.720 0.1890 4 970.00 2.500 0.1890 4 990.00 2.1203 2.1 0.1890 4 990.00 2.690 2.7 0.1575 4 1097.50 2.600 0.1575 4 1012.20 2.400 0.1575 4 1030.68 2.200 0.1575 4 1056.00 1.990 0.1575 4 1056.00 2.670 0.1260 4 1070.00 2.400 0.1260 4 1097.00 2.000 0.1260 4 1122.00 1.660 1.7 0.1260 4 1122.00 2.340 2.5 0.0935 4 1135.32 2.120 0.0935 4 1158.00 1.800 0.0935 4 1188.00 1.430 0.0935 4 1188.00 2.280 0.0630 4 1198.55 1.920 0.0630 4 1210.00 1.800 0.0630 4 1234.00 1.380 0.0630 4 1254.00 1.190 0.0630 4 1254.00 2.190 0.0315 4 1262.80 1.820 0.0315 4 1276.52 1.600 0.0315 4 1284.00 1.320 0.0315 4 1320.00 0.850 0.0315 4 130 Table 5.21: Theoretical and Experimental Profile Data for the Condition: .40 = 0.0525 cfs n = 0.011 S = 0.025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 0.800 1.0500 6 18.00 1.090 1.0500 6 34.00 1.250 1.0500 6 52.00 1.400 1.0500 6 66.00 1.470 1.5 1.0500 6 66.00 1.650 1.7 0.9975 6 100.00 1.680 0.9975 6 132.00 1.710 0.9975 6 132.00 1.900 0.9450 6 162.00 1.870 0.9450 6 198.00 1.830 0.9450 6 198.00 2.040 0.8925 6 222.00 2.000 0.8925 6 246.00 1.950 0.8925 6 264.00 1.800 0.8925 6 264.00 2.260 0.8400 6 280.00 2.130 0.8400 6 299.10 2.040 0.8400 6 320.00 2.000 0.8400 6 330.00 2.000 2.0 0.8400 6 330.00 2.470 2.5 0.7875 6 360.00 2.270 0.7875 6 373.85 2.120 0.7875 6 396.00 2.040 0.7875 6 396.00 2.580 0.7350 6 410.00 2.430 0.7350 6 420.00 2.340 0.7350 6 430.00 2.300 2.3 0.7350 6 430.00 1.940 2.0 0.7350 5 436.00 2.040 0.7350 5 450.00 2.180 0.7350 5 462.00 2.210 0.7350 5 462.00 2.460 0.6825 5 469.25 2.530 0.6825 5 483.80 2.600 0.6825 5 506.15 2.660 0.6825 5 528.00 2.690 2.7 0.6825 5 528.00 3.070 3.1 0.6300 5 549.90 3.180 0.6300 5 572.00 3.260 0.6300 5 594.00 3.300 3.5 0.6300 5 594.00 3.650 3.7 0.5775 5 Table 5.21: (continued) 131 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 624.00 3.230 0.5775 5 660.00 3.810 3.8 0.5775 5 660.00 4.100 4.1 0.5250 5 682.41 3.900 0.5250 5 726.00 3.740 0.5250 5 726.00 3.660 0.4725 5 747.50 4.010 0.4725 5 770.00 3.600 0.4725 5 792.00 3.520 0.4725 5 792.00 3.850 0.4200 5 801.50 3.670 0.4200 5 814.00 3.500 0.4200 5 830.00 3.410 3.5 0.4200 5 830.00 3.150 3.2 0.4200 4 836.35 3.280 0.4200 4 858.00 3.370 0.4200 4 858.00 3.780 0.3675 4 880.00 3.520 0.3675 4 904.00 3.350 0.3675 4 924.00 3.240 0.3675 4 924.00 3.550 0.3150 4 956.00 3.100 0.3150 4 975.00 2.830 0.3150 4 990.00 2.620 2.6 0.3150 4 990.00 3.100 3.5 0.2625 4 1018.00 2.780 0.2625 4 1056.00 2.400 0.2625 4 1056.00 2.990 0.2100 4 1086.00 2.560 0.2100 4 1122.00 2.080 0.2100 4 1122.00 2.740 0.1575 4 1155.00 2.300 0.1575 4 1188.00 1.860 0.1575 4 1188.00 2.540 0.1050 4 1198.00 2.280 0.1050 4 1226.00 1.900 0.1050 4 1254.00 1.520 1.5 0.1050 4 1254.00 2.470 2.5 0.0525 4 1282.00 1.800 0.0525 4 1310.75 1.150 0.0525 4 1320.00 0.980 0.0525 4 132 Table 5.22: Theoretical and Experimental Profile Data for the Condition: .60 = 0.0735 cfs n = 0.011 S = 0.025 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 1.110 1.4700 6 16.00 1.390 1.4700 6 29.10 1.540 1.4700 6 36.80 1.630 1.4700 6 66.00 1.870 2.0 1.4700 6 66.00 2.060 2.0 1.3965 6 100.00 2.090 1.3965 6 132.00 2.100 1.3965 6 132.00 2.320 1.3230 6 162.05 2.340 1.3230 6 198.00 2.550 1.3230 6 198.00 2.580 1.2495 6 229.95 2.550 1.2495 6 264.00 2.540 1.2495 6 264.00 2.820 1.1760 6 280.00 2.800 1.1760 6 301.90 2.780 1.1760 6 330.00 2.760 2.8 1.1760 6 330.00 3.030 3.0 1.1025 6 360.00 2.970 1.1025 6 396.00 2.900 1.1025 6 396.00 3.250 1.0290 6 415.85 2.990 1.0290 6 438.00 2.830 1.0290 6 462.00 2.750 1.0290 6 462.00 3.170 0.9555 6 484.25 2.930 0.9555 6 506.00 2.790 0.9555 6 528.00 2.730 2.8 0.9555 6 528.00 3.300 3.3 0.8820 6 537.15 3.110 0.8820 6 549.35 2.950 0.8820 6 560.00 2.890 2.9 0.8820 6 *560.00 2.630 2.6 0.8820 5 563.50 2.800 0.8820 5 570.00 2.970 0.8820 5 580.00 3.150 0.8820 5 594.00 3.200 0.8820 5 594.00 3.500 0.8085 5 624.00 3.490 0.8085 5 r660.00 3.460 3.5 0.8085 5 660.00 3.680 4.0 0.7350 5 692.00 3.670 0.7350 5 133 Table 5.22: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 726.00 3.660 0.7350 5 726.00 3.890 0.6615 5 737.10 3.920 0.6615 5 770.00 3.970 0.6616 5 792.00 3.970 0.6615 5 792.00 4.380 0.5880 5 830.75 3.850 0.5880 5 858.00 3.170 0.5880 5 858.00 4.200 0.5145 5 871.90 3.970 0.5145 5 890.55 3.660 0.5145 5 924.00 3.300 3.3 0.5145 5 924.00 3.850 4.0 0.4410 5 960.00 2.960 0.4410 5 990.00 2.760 0.4410 5 990.00 3.470 0.3675 5 1000.00 3.280 0.3675 5 1010.00 3.140 0.3675 5 1020.00 3.070 0.3675 5 1020.00 2.770 0.3675 4 1023.00 2.890 0.3675 4 1030.00 2.980 0.3675 4 1043.70 3.080 0.3675 4 1056.00 3.130 0.3675 4 1056.00 3.410 0.2940 4 1088.00 3.340 0.2940 4 1122.00 3.260 0.2940 4 1122.00 3.680 0.2205 4 1141.40 3.330 0.2205 4 1165.00 2.970 0.2205 4 1188.00 2.690 0.2205 4 1188.00 3.120 0.1470 4 1220.00 2.410 0.1470 4 1254.00 1.710 0.1470 4 1254.00 2.970 0.0735 4 1270.00 2.460 0.0735 4 1294.55 1.730 0.0735 4 1320.00 1.110 0.0735 4 Table 5.23: Theoretical and Experimental Profile Data for the Condition: 134 .AQ = 0.0315 cfs n = 0.011 S = 0.05 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.040 0.6300 5 10.10 2.150 0.6300 5 26.15 2.320 0.6300 5 44.40 2.450 0.6300 5 66.00 2.590 3.0 0.6300 5 66.00 2.900 3.5 0.5985 5 89.21 3.010 0.5985 5 110.05 3.090 0.5985 5 132.00 3.110 0.5985 5 132.00 3.470 0.5670 5 160.00 3.490 0.5670 5 198.00 3.410 0.5670 5 198.00 3.780 0.5355 5 211.75 3.690 0.5355 5 225.70 3.620 0.5355 5 242.35 3.600 0.5355 5 264.00 3.550 3.5 0.5355 5 264.00 3.590 3.5 0.5040 5 276.25 3.800 0.5040 5 286.50 3.700 0.5040 5 297.50 3.600 0.5040 5 312.80 3.500 0.5040 5 330.00 3.460 0.5040 5 330.00 3.920 0.4725 5 338.10 3.800 0.4725 5 353.30 3.600 0.4725 5 372.15 3.400 0.4725 5 396.00 3.250 3.3 0.4725 5 396.00 3.740 3.8 0.4410 5 406.15 3.600 0.4410 5 420.15 3.400 0.4410 5 438.54 3.200 0.4410 5 462.00 3.030 0.4410 5 462.00 3.530 0.4095 5 472.90 3.300 0.4095 5 485.55 3.100 0.4095 5 496.40 2.900 0.4095 5 518.00 2.700 0.4095 5 528.00 2.620 0.4095 5 528.00 3.190 0.3780 5 537.24 3.000 0.3780 5 550.25 2.800 0.3780 5 563.35 2.700 0.3780 5 135 Table 5.23: (continued) Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 577.10 2.600 0.3780 5 594.00 2.450 0.3780 5 594.00 2.930 0.3465 5 603.30 2.700 0.3465 5 614.20 2.500 0.3465 5 630.00 2.310 2.0 0.3465 5 630.00 1.840 1.5 0.3465 4 646.65 2.000 0.3465 4 660.00 2.060 0.3465 4 660.00 2.300 0.3150 4 680.75 2.410 0.3150 4 692.45 2.460 0.3150 4 708.00 2.500 0.3150 4 726.00 2.610 0.3150 4 726.00 3.080 0.2835 4 734.00 3.000 0.2835 4 754.75 2.800 0.2835 4 780.00 2.600 0.2835 4 792.00 2.520 0.2835 4 792.00 3.120 0.2520 4 798.35 3.000 0.2520 4 810.00 2.800 0.2520 4 828.00 2.600 0.2520 4 858.00 2.260 0.2520 4 858.00 3.050 0.2205 4 868.00 2.800 0.2205 4 882.24 2.600 0.2205 4 898.80 2.400 0.2205 4 924.00 2.080 0.2205 4 924.00 2.870 0.1890 4 930.60 2.720 0.1890 4 939.35 2.600 0.1890 4 952.00 2.400 0.1890 4 970.00 2.200 0.1890 , 4 990.00 1.910 0.1890 4 990.00 2.720 0.1575 .4 1000.00 2.500 0.1575 4 1012.55 2.260 0.1575 4 1026.50 2.080 0.1575 4 1040.70 1.920 0.1575 4 1056.00 1.710 0.1575 4 1056.00 2.600 0.1260 4 1066.00 2.400 0.1260 4 1076.00 2.200 0.1260 4 Table 5.23: (continued) 136 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 1090.00 2.000 0.1260 4 1105.00 1.800 0.1260 4 1122.00 1.580 1.5 0.1260 4 1122.00 2.520 2.7 0.0945 4 1130.25 2.320 0.0945 4 1138.20 2.200 0.0945 4 1148.45 2.000 0.0945 4 1160.75 1.800 0.0945 4 1172.70 1.600 0.0945 4 1188.00 1.380 0.0945 4 1188.00 2.450 0.0630 4 1202.25 2.000 0.0630 4 1222.50 1.600 0.0630 4 1236.00 1.400 0.0630 4 1254.00 1.200 0.0630 4 1254.00 2.320 0.0315 4 1265.30 2.000 0.0315 4 1278.65 1.600 0.0315 4 1296.60 1.200 0.0315 4 1320.00 0.800 0.0315 4 Table 5.24: Theoretical and Experimental Profile Data for the Condition: 137 AQ = 0.0525 cfs n = 0.011 S = 0.05 Distance from Calculated Experimental Discharge Di _ter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 0.00 2.330 1.0500 5 10.00 2.460 1.0500 5 18.00 2.560 1.0500 5 .29_oo 2.700 1.0500 5 44.80 2.870 1.0500 5 66.00 3.000 3.5 1.0500 5 66.00 3.320 4.0 0.9975 5 86.00 3.380 0.9975 5 103.45 3.430 0.9975 5 132.00 3.460 0.9975 5 132.00 3.750 0.9450 5 138.00 3.800 0.9450 5 170.00 3.850 0.9450 5 198.00 3.900 0.9450 5 198.00 4.140 0.8925 5 230.00 4.100 0.8925 5 264.00 4.060 0.8925 5 264.00 4.320 0.8400 5 291.35 4.270 0.8400 5 330.00 4.200 4.0 0.8400 5 330.00 4.670 4.7 0.7875 5 337.40 4.560 0.7875 5 351.00 4.400 0.7875 5 364.00 4.330 0.7875 5 377.40 4.240 0.7875 5 396.00 4.190 0.7875 5 396.00 4.590 0.7350 5 407.35 4.410 0.7350 5 424.45 4.140 0.7350 5 444.00 3.920 0.7350 5 462.00 3.790 4.0 0.7350 5 462.00 4.260 4.5 0.6825 5 471.10 4.110 0.6825 5 492.00 4.870 0.6825 5 514.90 4.640 0.6825 5 528.00 3.560 0.6825 5 528.00 4.110 0.6300 5 642.00 3.800 0.6300 5 559.00 3.500 0.6300 5 577.50 3.220 0.6300 5 594.00 3.080 0.6300 5 594.00 3.750 0.5775 5 619.00 3.240 0.5775 5 641.95 2.940 0.5775 5 Table 5.24: (continued) 138 Distance from Calculated Experimental Discharge Diameter Outlet (ft) Depth (in) Depth (in) (cfs) (in) 660.00 2.780 3.0 0.5775 5 660.00 3.400 4.0 0.5250 5 666.40 3.240 0.5250 5 684.00 2.940 0.5250 5 706.00 2.690 0.5250 5 726.00 2.590 0.5250 5 726.00 3.160 0.4725 5 735.25 2.680 0.4725 5 776.00 2.210 0.4725 5 792.00 2.800 0.4725 5 792.00 2.630 0.4200 5 803.65 2.300 0.4200 5 812.00 2.160 0.4200 5 830.00 2.100 0.4200 5 830.00 1.470 0.4200 4 834.00 1.570 0.4200 4 840.50 1.650 0.4200 4 849.60 1.730 0.4200 4 858.00 1.750 0.4200 4 858.00 2.040 0.3675 4 866.00 2.160 0.3675 4 884.00 2.280 0.3675 4 903.30 2.350 0.3675 4 924.00 2.350 0.3675 4 924.00 2.650 0.3150 4 950.00 2.650 0.3150 4 990.00 2.660 0.3150 4 990.00 3.400 0.2625 4 1010.00 2.900 0.2625 4 1032.00 2.420 0.2625 4 1056.00 2.040 0.2625 4 1056.00 2.960 0.2100 4 1090.00 2.400 0.2100~ 4 1122.00 1.910 0.2100 4 1122.00 3.010 0.1575 4 1150.00 2.440 0.1575 4 1188.00 1.650 0.1575 4 1188.00 2.950 0.1050 4 1207.00 2.480 0.1050 4 1254.00 1.560 0.1050 4 1254.00 3.010 0.0525 4 1280.00 2.030 0.0525 4 1320.00 1.100 0.0525 4