SILT TRANSPORT BY THIN FlLM FLOW Thesis for the Degree of M. S. MICHEC-éfiafié STATE UNEVERSETY TEREF-{QE H883 PQDMORE 1959 'Jw-tu-ul. li'um.-y~m.m-‘aa«~,y "' t‘ ‘r. 1 e' ‘1' L [51." 5 ii '1’ Michigan Smtc University I THESIS ABSTRACT SILT TRANSPORT BY THIN FILM FLOW By Terence Hugh Podmore Advances in soil conservation and erosion control depend upon the knowledge of the mechanics of the processes involved. Considerable research has been done in the last 20 years on splash erosion, and on the transport of eroded material by Open channel flow. Little work has been done on the processes by which eroded material is transported from its place of detachment to a body of water moving with sufficient velocity to prevent sedimentation. This work was performed to investigate the transport capabilities of uniformly flowing films of water simulat- ing overland flow on a watershed during the runoff process. The variables considered were: slope, flow rate, surface roughness, distance the eroded material was transported before deposition occurred, and the proportion of material deposited as a function of particle size. Individual drops of water containing suspended silt particles were applied to the surface of the flowing film of water to simulate the introduction of raindrop— detached material into the overland flow process. Because the quantity of silt involved was small, a Coulter Counter Terence Hugh Podmore was employed to perform particle size analysis on the deposited material. An analysis of particle size versus amount deposited at specific points down slope from the point of introduc- tion revealed a peak deposition distance in each case which decreased with increasing surface roughness. A minimum retention was observed for a particle size of approximately eight microns under all conditions tested. Several velocity profiles were assumed using conventional transport theories in an attempt to mathematically model the phenomena. Approved ;; .W MajorrProfessor Approved an! a/ M Department Chairman" SILT TRANSPORT BY THIN FILM FLOW By Terence Hugh Podmore A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1969 ACKNOWLEDGMENTS I wish to extend my sincere thanks to Dr. George E. Merva for his endless patience and guidance during this study. His help and suggestions during the research were especially valuable. It has been a privilege to work with him. My thanks go to the other members of my committee, Professor Ernest H. Kidder and Professor Earl A. Erickson, for their help and co—operation. Special appreciation is extended to Professor Theodore I. Hedrick for the use of the Coulter Counter, and for his understanding during the course of its use. I would like to thank my parents, Mr. and Mrs. Arthur Podmore, for constant encouragement during the whole course of my education. Also, to my parents-in-law, Mr. and Mrs. Carl M. Lipscomb, for raising such a wonderful daughter, and for providing a home—from—home in America. This thesis is dedicated to my wife, Carol Ann, without whose constant love and sense of humor, this work would have been given up for lost. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . V LIST OF FIGURES . . . . . . . . . . . . Vi LIST OF SYMBOLS . . . . . . . . . . . . viii INTRODUCTION . . . . . . . . . . . . . 1 LITERATURE SURVEY . . . . . . . . . . . A RATIONALE AND OBJECTIVES . . . . . . . . . l3 EXPERIMENTAL AND THEORETICAL CONSIDERATIONS. . . 14 Theoretical Models. . . . . . . . . . 1A Initial Considerations . . . . . . . . 27 Choice of Eroded Material . . . . . . . 33 Design of Equipment . . . . . . 35 Construction of the Bed Plates. . . . . . Al Instrumentation. . . . . . . . . . . A“ TEST PROCEDURES . . . . . . . . . . . . “7 Flow Test Procedure . . . . . . . . . A7 Sample Analysis. . . . . . . . . . . SO DATA ANALYSIS. . . . . . . . . . . . . 5“ DISCUSSION OF RESULTS . . . . . . . . . . 71 SUMMARY AND CONCLUSIONS . . . . . . . . . 80 Summary . . . . . . . . . . . . . 80 Conclusions . . . . . . . . . . . . 81 RECOMMENDATIONS . . . . . . . . . . . . 82 Further Improvements on the Present Study . . 82 Recommendations for Further Study. . . . . 83 iii REFERENCES. . . . . . . . . . . . . . 85 APPENDICES. . . . . . . . . . . . . . 89 Appendix A. Calibration and Use of the Coulter Counter . . . . . . 90 Appendix B. Preliminary Length of Bed Slope Calculation. . . . . . . . 100 Appendix C. Data . . . . . . . . . . 103 iv Table LIST OF TABLES Slope Data from Site 1 SlOpe Data from Site 2 Comparison of Degree of Detachability and Transportability . . . . . Sample Coulter Counter Data. Analysis of Data of Table A Page 28 3O 33 52 53 LIST OF FIGURES Figure Page 1. Diagram of flow conditions . . . . . . l7 2. Photograph of Site 1 . . . . . . . . 29 3. Photograph of Site 2 . . . . . . . . 31 A. Graph of velocity of flow . . . . . . 38 5. Photograph of equipment . . . . . . . 39 6. Diagram of apparatus used to produce thin film flow . . . . . . . . . A0 7. Graph of typical flow profile . . . . . A2 8. Photograph of Coulter Counter . . . . . A6 9. Typical deposition curve. . . . . . . 57 lO. Graphs of theoretical models . . . . . 58 ll. Comparison of two tests (AD-grade) . . . 59 12. Comparison of two tests (BO-grade) . . . 6O 13. Comparison of two tests (glass bed) . . . 6l lA. Comparison of runs (1% slope, low flow). . 2 15. Comparison of runs (1% slope, medium flow). 63 16. Comparison of runs (3% slope, low flow). . 6A 17. Comparison of runs (3% slope, medium flow). 65 18. Comparison of runs (5% slope, low flow). . 66 19. Comparison of runs (5% slope, medium flow). 67 20. Comparison of slopes (glass bed and low flow) . . . . . 68 vi Figure Page 21. Comparison of slopes (80—grade bed and low flow). . . . . . . . . . . 69 22. Comparison of lepes (AO— —grade bed and low flow). . . . . . . . . . 7O 23. Graph of total particle retention (glass bed) . . . . . . . . . . 76 2A. Graph of total particle retention (80-grade bed) . . . . . . . . . 77 25. Graph of total particle retention (AO—grade bed) . . . . . . . . . 78 26. Diagram of Coulter Counter . . . . . . 92 Vii A* 0.. 0| :7 CM H.) LIST OF SYMBOLS Amplification Constant Constant Constant Lift Coefficient Coefficient of Resistance Density of water Equivalent spherical diameter (cm.) Density of Silt (gm./cm.3) Particle diameter (cm.) Depth of Flow (cm.) Mean depth of Flow (cm.) Dimensionless Film Thickness Function of 2) Acceleration due to gravity (980 cm./sec. Coulter Counter Calibration Constant Aperture Current Stoke's Law Constant Constant as subscript, Maximum Full particle count Particle half count viii n Particle oversize count 0 P Percentage slope r Particle radius (cm.) R Constant t Time (seconds) tL Threshold value (Coulter Counter) u Flow velocity in x—direction (cm./sec.) 3 Mean Flow Velocity (cm./sec.) uS Surface velocity (cm./sec.) u+ Dimensionless velocity u* Friction velocity (cm./sec.) v Velocity (cm./sec.) vL Volume of particle (cm.3) vS Terminal velocity of silt (cm./sec.) vSX Component of vS in x-direction (cm./sec.) vSy Component of vS in y-direction (cm./sec.) vt Critical Threshold Velocity (ft./sec.) x Distance along axial coordinate (cm.) xi (Where i = integer) Particle count f Mean particle count X Critical Distance (cm.) y Distance along vertical coordinate (cm.) I Shear stress (gm./cm. sec.2) v Kinematic Viscosity (cm.2/sec.) u Viscosity (gm./sm. sec.) 9 Angle (Degrees) ix INTRODUCTION The author became interested in soil erosion while working for his Bachelor's degree. A study of the litera— ture available showed a gap in information related to the erosion process. Ellison (19A7), Meyer (1958, 1965), Rose (1960), and Hudson (1963) have investigated the splash erosion process. The transport of eroded material by streams and rivers has had special attention from Einstein (196A), Kalinske (l9A7), and various other workers. Conventional concepts of erosion have suggested that the process begins with the detachment of soil particles caused by the splash impact of falling raindrops. The detachment is followed by sheet erosion in which the detached material is removed by rainfall running off the watershed in the form of a uniform sheet. Although the latter concept has had considerable acceptance, it has been shown to be incorrect (Schwab gg_al., 1966). The flow of water as a sheet occurs for only a short distance before forming into micro-rills. The formation of micro-rills is the first stage in the concentration of flowing water. The micro—rills join to form rills which in turn form gullies. Rill erosion is characterized by the movement of soil material in suspension and by bed drag. Conventionally, rill erosion occurs when the rill is large enough to be well defined and easily seen. Gully erosion is an advanced stage of rill formation where scour of the channel bed occurs due to the excess energy in the flowing water. Gullies are a major hazard to agriculture since they remove soil, create water channels, and continue to enlarge in- definitely unless action is taken. For a more complete understanding of erosion mechanics it was considered necessary to investigate the interrela- tionship between splash erosion detachment and transport of eroded material by streams and rivers. The transportation mechanics of the intermediate stage linking these two phases of the erosion process was to be the subject of this study, together with the factors which influence the process. Following a literature survey, it was decided that a study of the transportation capacities of thin films of flowing water would contribute valuable information concerning the soil erosion process. The runoff process would be simu- lated to determine its role in the transportation of eroded material from the point of detachment to a stream of water having sufficient velocity to prevent settling out of eroded material. If a film of flowing water could be simulated and its transportation characteristics determined in the study, one could then determine the description of the rill con- stituting an erosion threat since the eroded material must reach water moving with sufficient velocity to maintain its suspension and prevent deposition in the micro-rills as sediment. Thus a critical distance of transport could be found for suspended material in thin film flow. LITERATURE SURVEY The literature survey began with the work of W. D. Ellison, an early investigator in the scientific study of soil erosion by water. Ellison (l9A6) defines soil erosion as "a process of detachment and transportation of soil materials by erosive agents." In his l9A7 publication he amplifies the definition as follows: This definition describes the erosion process as consisting of two principal sequential events. In the first event soil particles are torn loose (detached) from their moorings in the soil mass and made available for transport. In the second event, detached soil materials are transported. We cannot combine these two processes and express them as a single quantitive result, because they cannot be expressed in like units. Ellison (l9A7) indicates that the erosive capacity of an eroding agent is divided into (a) a detaching capacity and (b) a transporting capacity. In this study only the transporting capacity is considered. Ellison‘s work on splash erosion was thoroughly reviewed in six articles in Agricultural Engineering (l9A7). Widespread investigation into the erosive nature of rainfall and water drcp splash subsequently took place. Hudson (196A) reviewed the development of rainfall simulators including thread droppers, nozzle droppers, and spray simulators. Of these the spray simulator has been A given the most attention. One of the most successful devices is the Rainfall Simulator which was developed by Meyer (1958). The Rainfall Simulator has almost become a standard for soil and water loss evaluations. Using a rainfall simulator similar to that of Meyer, Rose (1960) investigated some aspects of soil detachment including the relationships between rate of soil detach- ment, rainfall momentum, and rainfall kinetic energy. Palmer (1965) measured the force of water drop impact under varying conditions and Mutchler (1967) investigated the parameters for describing raindrop splash. The above works have been cited to indicate the extent of investigation revealing the present state of knowledge concerning splash erosion. However, Ellison (l9A7) makes it clear that both detachment and transporta- tion must occur in sequence before significant erosion results. Detachment under rainfall action alone merely produces soil movement in random directions in a restricted area with no net soil loss. The problem of soil particle transportation by water has been largely investigated by civil engineers dealing with "sediment load" in rivers and streams. In the litera- ture on this subject, the suspended material is referred to as "sediment.” owever, according to Webster's Seventh New Collegiate Dictionary (1961 Edition) "sediment" is defined as: "The matter that settles to the bottom of a liquid." Thus, the use of the term "sediment load" and other related terms is incorrect. A more appropriate description would be "suspended material load" or, in the context of soil erosion, "eroded material load." These terms will be used when applicable. Sediment transporta- tion, which has widespread use in present literature, is more accurately described as "the transport of suspended, eroded material." Whether or not this material becomes sediment is the subject of this research. The investigators of suspended material transporta- tion are concerned with the prevention of channel erosion or silting. To avoid silting a minimum velocity approach is used. Chow (1959) outlines this approach for non- erodible channels where the maximum permissible velocity-- that is, the maximum velocity which will not cause erosion-- can be ignored. Chow (1959) states that minimum permissible velocities for given suspended particle diameters are very uncertain. He adds that a mean velocity of 2 to 3 feet per second can be used safely in most cases when the per- centage of silt present in the channel is small. For erodible channels a maximum permissible velocity is used since scour of the channel will occur. Values of water velocity for channels of varying compositions are given. The process of suspended material movement in channels is outlined by Schwab, et al. (1966): Sediment in streams is transported by suspension, by saltation, and by bed load movement. Although many theoretical and empirical relationships have been developed between the suspended material transport capacity of the stream, it is not possible to predict suspended material loads with any degree of accuracy. . . . . . . Variables affecting suspended material movement include velocity of flow, turbulence, size distribution, diameter, cohesiveness, and specific gravity of transported materials, channel roughness, obstructions to flow, and the avail- ability of materials for movement. The suspended material fraction is defined by Schwab, et_al. (1966) as that material which remains in suspension in flow— ing water for a considerable period of time without contact with the stream bed. The phenomenon of "saltation" mentioned previously is most commonly associated with movement of soil particles in air. However, it is also present in stream transport of eroded material according to Schwab, et_al. (1966). He states: Sediment movement by saltation occurs where the particles skip or bounce along the stream bed. The height of the bounce, expressed in mathe— matical form, is directly proportional to the ratio of particle density to fluid density. Particles in water rise only a few particle diameters for most practical conditions. In comparison to total suspended material transported saltation is considered relatively unimportant. Einstein (196A) describes saltation in a similar manner, but adds: Saltation of the kind taking place in the air is impossible in water, as Kalinske (l9A2) has shown very convincingly. . . . Saltation is unimportant as a separate mode of particle motion in water, but may be a part of the bed-load movement, where the rolling and sliding particles sometimes jump at small distances. -P y r: a. Bed-load is defined (Schwab, et al., 1966; Einstein, 196A, pp. 17-37; and Raudkivi, 1967, p. A5) as suspended material that moves in almost continuous contact with the stream bed, being rolled or pushed along the bottom by the force of the water. Bed load is generally considered to be onecfl‘the major factors of suspended material movement in streams. Bed load is difficult to determine experimentally and empirical formulae have been developed to express it. None of the many empirical formulae developed to give the rate of the bed load movement have been entirely satis- factory. Laboratory studies (Mavis, 1935) have shown that the critical threshold velocity required to initiate move- ment of particles in the bottom of a stream is expressed by an empirical equation of the form, 1 . Vt TO— I (C13 - C1) where threshold velocity (ft./sec.) C. II t r = particle radius (cm.) Q dS = density of silt particles (gm./cm.”) d = density of water (gm./cm.3) (This is limited to unigranular materials ranging in diameter from 0.35 to 5.7 mm. and in specific gravity from 1.83 to 2.6A). Einstein (196A) gives an excellent account of the present state of sedimentation. He defines his concept of "Dual Control of Sediment Transport": Every sediment particle which passes a particular cross section of the stream must satisfy two conditions: 1.) It must have been eroded from somewhere in the watershed above the cross section; 2.) It must be transported by the flow from the place of erosion to the cross section. Each of these two conditions may limit the sedi— ment rate at the cross section, depending on the relative magnitude of the two controls; the availability of the material in the watershed; and the transporting ability of the stream. In most streams the finer part of the load, i.e. the part which the flow can easily carry in large quantities, is limited by its availability in the watershed. This part of the load is designated as the 'wash load.‘ The coarser part of the load, i.e. the part which is more difficult to move by flowing water, is limited in its rate by the transporting ability of the flow between the source and the section. This part of the load is designated as 'bed-material load.‘ Einstein (196A) also indicates the effect of particle settling velocity: When a sediment grain moves through water, it experiences considerable resistence which is a function of the Reynolds number of this movement. When the particle moves downward, a settling velocity will be reached at which the resistence equals the weight of the grain in water. For laminar and turbulent flow, the settling velocities for spherical grains have been shown to be as follows: Laminar flow v = 3 (d8 — d) gr2 5 9 U Turbulent flow vS = /(dS — d) g %3 r Where vS = settling velocity, cm./sec. dS = density of silt, gm./cm.3 d = density of water, gm./c~m.3 r = particle radius, cm. g = acceleration due to gravity, or 980 cm/sec.2 u = viscosity of fluid, gm./cm. sec. Cr = coefficient of resistence, depending on Reynolds number, with a value of about 0.5 for a large range of Reynolds numbers above critical. Einstein (196A) further outlines a procedure for determining the suspended material load as a function of the bed load composition and the flow. This is not applicable for the present work since it does not take account of the effects of the boundary layer. A thorough analysis of laminar and turbulent boundary layer theory is given by Schlichting (1968). Reference will be made to this topic 0 in the theoretical con ide_ations. U The most recent comprehensive work available on suspended material transport is the publication of Raudkivi (1967). Here most of the various formulae in ) use are compar.d and contrasted. Work on threshold of (‘1‘ particle ransport is also discussed. This has been very useful for this study and will be dealt with in greater detail later. The literature reviewed gave an indication of the present state of knowledge on the two most researched ll aspects of erosion; detachment by water drOp impact, and transport phenomena in large water masses. The conventional theories of suspended material transportation consider much greater depths and quantities of flowing water as opposed to the thin films used in this approach. Hence these theories were considered to be largely inapplicable, although note was taken of the methods used. An account of the theory and practice in the descrip— tion of thin film flow has been compiled by Fulford (196A). He discusses laminar and turbulent flow together with interactions of the liquid with the walls of the channel and the surrounding fluid. The effect of boundary layers is discussed. The latter effect is considered to void the theories of suspended material transportation at present in use for streams and rivers as applied to thin film flow. Fulford (196A) cites the "universal velocity equationg'cm'Nikuradse (l9A2) which will be introduced and used later. Fulford (196A) also presents an analysis of the Navier-Stokes equations for smooth, laminar, two-dimensional film flow which describes the velocity distribution in terms of a semi—parabolic equation. 2 u = % (sin 6) (Dy - § ) where the surface velocity is l2 [0% sin 0 CD |\) C and the mean velocity is Ll 3V 8111 6 hence , uS = 1.5u A full theoretical analysis applied to the present study is given in a later section. Meyer and Monke (1965) investigated the mechanics of soil erosion by the combined action of rainfall and overland flow. Commercial glass beds were used to simulate a soil bed, the smallest particle used having a diameter of 58 microns. Rainfall and shallow depths of flowing surface water could be applied simultaneoulsy. Slope steepness, slope length, and particle Size were the variables studied. It was found that runoff erosion increased rapidly with increasing slope steepness and length. Smaller particle sizes were more erosive at most slope steepness and lengths, but the larger sizes were more erosive at small steepness and lengths. Rainfall plus runoff, as compared with runoff alone, increased the erosion of the smaller particle sizes but decreased the erosion of the larger sizes. The study was among the first to simulate the process of soil erosion as a whole in the laboratory. RATIONALE AND OBJECTIVES The literature survey has indicated an area of deficient information concerning the erosion process, that is, the mechanics of eroded material transportation from the point of detachment to water moving with suffi— cient velocity to maintain the eroded particles in sus- pension. In an effort to contribute information to this area the study reported on in this thesis has as its objective to investigate the variables which may affect the transport of eroded material by thin film flow. These variables were assumed to be: 1. Degree of slope 2. Flow rate 3. Surface roughness A. Length of slope 5. Particle size. The first step was to formulate a mathematical model of the flow conditions. The second step was the investigation of the variables given above to attempt to establish their effect on the transport. The final step was to determine the validity of the mathematical models. 13 EXPERIMENTAL AND THEORETICAL CONSIDERATIONS Theoretical Models Stoke's law of settling is used in this study. Baver (1956) states Stoke's law as follows: < ll mum and gives the assumptions necessary for this formula to apply. These are: l. The particles must be large in comparison to liquid molecules so that Brownian movement will not affect the fall. This is true for all soil particles except colloidal clays (Baver, 1956, p. 17). 2. The extent of the liquid must be great in com- parison with the size of the particles. The fall of the particles must not be affected by the proximity of the wall of the vessel or adjacent particles. This condition was con- sidered when the experiment reported on in this theSis was designed. The particles must be rigid and smooth. This condition is difficult to fulfill with soil particles. It is highly probable that the particles are not completely smooth over their entire surface. It is fairly well established that the particles are not spherical but are irregularly shaped with a large number of plate- shaped particles present in the clay fractions. Since variously shaped particles fall with dif- ferent velocities, the term "equivalent or effective radius" is used to overcome this dif- ficulty in Stoke's law. "Equivalent or effective radius" is defined as the radius of a sphere of the same material which would fall with the same velocity as the particle in question. There must be no slipping between the particles and the liquid. This requirement is easily ful- filled in the case of soils because of the water hull around the particles. The velocity of fall must not exceed a certain critical value so that the viscosity of the liquid remains the only resistance to the fall of the particle. Particles larger than silt cannot be separated accurately by Stoke's law. 16 From the above considerations: a. Colloidal clays are excluded because of effects due to Brownian movement. b. The clay fraction is excluded due to the plate- like nature of the particles. c. The sand fraction cannot be separated by Stoke's Law. Therefore the silt fraction was considered to conform to the predictions of Stoke's law. Further reasons for choosing the silt fraction are given later. Stoke's law is used with all velocity profile models to give expressions for distance of particle transport. The procedure used is given as follows: The velocity profile model is of the form u = NW The velocity of the particle is given from Stoke's Law as \olm v = s The reference frame used is shown in Figure 1. Consider the vertical velocity from Stoke's Law in the x-y frame of reference. 1? Figure 1. Diagram of flow conditions used in theoretical analysis. Note coordinate system used. Velocity profile is some function of depth. 18 One has SX V = - v cos 0 sy s and for small angles: (6 5 5°) v = Pv = Pkr2 sx s v = —v = -—kr2 sy s where 0 = P = percentage slope. Since the particle is moving in water, perfect coupling is assumed. This is similar to Assumption A for Stoke's Law and is justified by the same statement (Baver, 1956, p. 56). To find the components of velocity of the particle in the x—y frame note that in the x-direction the velocity is 2 u = Pkr + f(y) (1) Where Pkr2 = component due to effects of gravity on particle f(y) = component due to the effects of fluid velocity. 19 In the y-direction one has v = kr2 The velocity components thus obtained can be utilized to determine a Critical Distance for particle deposition as follows: and integrating from D to some depth y one obtains; y - D = -kr2t y = D - kr2t when t = tmax y = 0 therefore t = D max 2 kr Using equation (1) one can write -932— 2 u — dt - Pkr + f(y) and by making use of equation (2) one can obtain, with equation (3) (2) (3) 20 = Pkr2 + f(D - kr2t) 94:: Equation (A) can be integrated to obtain 2 t 2 x = Pkr t + J f(D — kr t)dt 0 When x = X (Critical Distance) t = tmax = _2§ kr therefore D/kr2 2 x = PD + J f(D - kr t)dt O In the experiments reported on in this study < o < Pmax _ 5 - 0.05 and D = 0.28A cm. max The maximum value of the product PD is 0.05 x 0.28A or l.A2 x 10—3 cm. Hence the PD term can be ignored. fore the general expression for X is JD/kr2 X = f(D - kr2t)dt O (A) (5) There- 21 It can be seen that from the above equation that the Critical Distance X is only dependent on the depth D and those factors influencing the Stoke's Law settling when they are introduced by the velocity profile function f(y). The veolicty profiles considered in this study were: 1. A velocity constant with depth with a sharp reduction to zero velocity close to the bed surface. This model approximates to the turbu- lent condition. fl(y) = constant = 5 Therefore “=52,— <7) kr A first order relationship between velocity and depth, as proposed by Newton for laminar flow ignoring boundary layer effects. or us y = 25y D D f2(y) = Therefore 2 JD/KP 2 D (D—kr t)dt = E 2 (8) kr X z a" 2 D O A second order relation between velocity and depth from the solution of the Navier—Stokes equations for smooth, laminar, two-dimensional film flow (Fulford, 196A, p. 156). 2 2 . _ - _ P y f (y) — % Sin 0(Dy—XZ) — EV (Dy--§) 3 and therefore . 2 2 X = s3 JD“? (Dy — ~V—2>dt = E31— (9) 3 v 0 A second order relation between velocity and depth from consideration of the lift force on a particle just above the bed surface. (See, for instance, Streeter, 1958, p. 171.) By equating this lift force to the gravitational force on the particle one has, CLA(dS-d)u2 Lift force = 2 where A = fir Gravitational force = n r3(dS — d)g bolt and equating these forces to give zero net vertical force, 23 2_§r_a u - (10) 30L Equation (10) is assumed valid for r in the range 2.5 to 25 microns, the range of particle radii used in the study. It is assumed that equation (10) applies to the whole film thickness. Thus fu = J?%; y and therefore 2 JD/kr ( 2 )% 2D ( ) x = /—5—8 D-kr t dt = i— 11 4 3CL 3CL 31a»2 0 A third order relationship between velocity and depth was considered so that account could be taken of special conditions suggested by the experimental results. The general equation con— sidered has the form: 3 y = R + A*u + Bu2 + Cu (12) * Where R, A , B, and C are constants. To evaluate these constants boundary conditions must be supplied. The primary boundary condition requires that when y = 0, u = 0 then R = 0. 2A The general equation becomes with the above conditions y = A*u + Bu2 + Cu3 The remaining three boundary conditions necessary are evaluated for specific cases. Equation (12) requires that one use a different approach to find X. Note, _e£-easi-§a =_29_2<_ u ” dt ' dy dt ‘ dy V kr dy so that - kr2 dx = u dy if one uses equation (12) dy = (A* + 2Bu + 3Cu2)du After integrating one obtains o —kr2[x]§ = I u(A* + 2Bu + 3Cu3)du u S 1 A*uS2 2Bus3 3CuS X5=k—§[2 + 3 +T] (13) I" A discontinuous velocity profile utilizing the "universal velocity profile equations" of Nikuradse (19A2) given by Fulford (196A, p. 171). 25 u+ = y+ for 0$y+55 (laminar sub-layer) u+ = —3.05 + 5.0 ln y+ for 5 t > (D - __22__1) _l§ kr (Dg P)1 kr u=—%—y (in) 26 In the buffer layer, 1 5v > 1 30v __.__(D— 1)_'C > (D- 1) kr2 (Dg P)/é kr2 (DgP)/2 , a u = (DgP)2 <-3.05 + 5.0 1n (¥£%E3) >> (15) In the turbulent zone, 30v (DgP) -£g (D — ) > t > 0 kr — — 1 ’2 u = (DgP)% (5.5 + 2.5 1n (119%312>> (16) And using equations (1A), (15) and (16) in equation (6) the general expression for the Critical Distance is: o 1 _ 2 _O % x6 = I (DgP)2(5.5+2.5 1n<(D kr t$(DOP) )dt _%(D__;9_\i_l/) kr (DgP)2 . _i_(D_ 30V ‘ kr2 {DEF/2) L _ 2 2 + (DgP)2(—3.05+5.0 ln((D kr t3(DgP) )dt J k:2(D (Dg P)% —l§ (D - 5V kr (Dg?)1 + 953 (D - kr2t)dt (17) _D_ 2 27 From the above expressions for X, it can be seen that they all take the form: x = ‘7 (18) Therefore, from given initial conditions it ought to be possible to predict values of the critical distance X for given particle diameters using the appropriate form for f(y). Initial Considerations Before the experiment was begun, a preliminary study was carried out to determine the range of slopes fre— quently found on a natural watershed. Open ground was chosen and obvious rills and gullies were avoided. The maximum slopes were measured in every case, since this would be the path taken by flowing water. The distances measured in each case were of the order of 10 cm. and the slopes were determined using a piece of apparatus consist- ing of a level and a 60 cm.straight—edge fastened together in parallel and used in conjunction with a hand held vertical scale. The level was held horizontal with one end of the straight-edge touching the soil surface. The distance between the straight—edge and the soil surface was measured at various points with the vertical scale. The horizontal and vertical distances were recorded in 28 each case and the lepes were calculated. This process was carried out at two separate sites, which are described below. Approximately 50 slopes were measured on each site. Site 1 This site was situated on the west side of Lansing, Michigan, near the Grand River. It was a development site from which most of the surface vegetation had been removed. Vegetation had begun to return, but a large proportion of the soil surface remained bare. The type of soil was pre- dominantly sand, and measurements were taken on locations such as that shown in Figure 2(a). Stones and gravel can be seen exposed by erosion of the surrounding material. Considerable erosion had taken place on parts of the site due to concentration of surface runoff as can be seen in Figure 2(b). The level shown in the figures is 60 cm. long giving a scale to the figures. Results of the slope analysis are given in Table l° Table 1. Data from Site I Slope (%) No. of Slopes Mean Slope Length (cm.) (:0.5) < 2.50 0 __ 2.50 - 7.A9 9 22.6 7.50 -12.A9 31 20.5 12.50 —l7.A9 7 l7.A >17.50 2 19.7 .113: fi 29 Figure 2. Photographs of Site 1. Above: (a) Area on which measurements were taken. Below: (b) Gully erosion on Site 1. (Scale shown is 60 cm. long.) 30 Site 2 This site was also situated on the west side of Lansing and it had been cleared for development. As can be seen from Figures 3(a) and 3(b), considerable runoff has taken place and gully erosion is beginning. The type of soil is a clay loam subsoil, which has been exposed by scalping the tOpsoil. There was little trace of organic matter in the soil. This was considered to give the worst erosion conditions for this type of soil. Again the level is used for a scale (60 cm.). Exposed stones and gravel can be seen on the surface. When examined, the soil was dry and cracking had occurred. Results of the slope analysis are given in Table 2. Table 2. Data from Site 2. Slope (%) No. of Slopes Mean Slope Length (cm.) ($0.5) < 2.50 11 20.8 2.50 - 7.49 35 15.9 7.50 —l2.A9 2 9.5 >12.50 0 -— TS These two types of soil were considered to give the extremes of the soil composition spectrum. Also, the erosion conditions varied from just beginning on Site 2 to advanced gully formation on Site 1. From the results 31 Figure 3. Photographs of Site 2. Above: Area on which measurements were taken. Below: State of rill erosion on Site 2. (Scale shown is 60 cm. long.) 32 obtained it can be seen that the slopes most frequently occurring are in the range of from 0 - l2.A9 per cent. These results were used as a guideline in designing the experimental setup for this study. The mean length of lepe is given as an indication of the length expected for a particular slope found in natural conditions and was used in the design of the experimental apparatus. It can be seen from the data in Tables 1 and 2 that the steeper the slope, the shorter the mean slope length. It was indicated therefore that a steep slope produces a more unstable condition, i.e., a short uniform slope is due to more rapid erosion. To ensure that the experimental conditions correspond to those found during runoff on a watershed, it was necessary to find an indication of depth of flow of runoff. An impermeable bed was to be used in these experiments to eliminate infiltration effects. However, most researchers give their runoff data as a volume flow rate per unit channel width without indicating values for velocity and depth of flow. The only precise measurements found were those of Osborn (1955), who states: The normal depths attained by sheet flow under normal field conditions are usually very shallow. Measurement of sheet runoff at rates of 1.25 to 3.68 inches per hour on bare plots up to 20% slope and 116.7 feet length showed depths of flow ranging from 0.06 to 0.15 inches (0.15 to 0.38 cm.). 33 Since this was the only information of this nature available, it was used as an experimental guideline. Choice of Eroded Material Ellison (l9A7) considered the detachability and trans- portability of soils. He classified the susceptability of types of soil to detachment and tranSport in order of highest to lowest as given in Table 3. Table 3. Comparison of Detachability and Transportability. Degree Detachability Transportability Highest Fine sand Clay Medium Silt loam Silt loam Lowest Clay Fine sand It can be seen that fine sand is most easily detached and yet least easily transported. The converse is true for clay, while silt loam falls into the middle category in both cases. This indicated that the silt fraction might be the most commonly eroded fraction of the soil medium. Ellison (l9A7) quotes figures from rainfall studies on aggregation breakdown and runoff when shows that in the runoff for a particular series of tests approximately 87 per cent of the soil material in the surface runoff had a diameter of less than 0.105 mm. (that is, 105 microns) while the original material contained only 53.5 per cent with a diameter of 0.105 mm. or less. I 3 4 According to the U. S. Bureau of Soils Systems (Baver, 1956, p. 16) silt particles are those in the range 0.05 to 0.005 mm. in diameter. It was considered that the silt fraction was the most suitable to use in this work since it is the fraction which has both a high detachability and a high trans- portability. The mechanical properties of silt were given by Buckman and Brady (1960) as follows: In contrast with the plate-like clay, silt particles tend to be irregularly fragmental, diverse in shape, and seldom smooth or flat. in fact, they are really micro—sand particles, quartz being the dominant mineral. The silt separate possesses some plasticity, cohesion, and adSorption due to an adhering film of clay, but, of course, to a much lesser degree than the clay separate itself. This similarity of finely crushed sand was further confirmed when the mechanical properties of non-plastic silt was examined and found to conform closely to those of fine to medium sand in properties such as angle of repose and friction angles as given by chgh (1957): Slope at angle Friction angles at 01 repose Ultimate Peak Strength Strength Non—plastic Silt 26° - 30° 26° - 30° 30° — 3u° Uniform fine to medium sand 26° — 30° 26° - 30° 32° - 36° 35 Soil containing an appreciable quantity of silt was obtained from a location on the Michigan State University farm. The soil was dried and coarse—sieved to remove organic matter and stones. It was further dried after the large soil aggregates had been broken up manually. The silt and clay fractions were separated by seiving on a mechanical agitator for five minutes. The fraction passing the finest sieve which was a #300 mesh (62.5 micron apertures) was collected. To remove the silt from the clay, the sample was dispersed with 100 ml. of Calgon solution (containing sodium hexametaphosphate) for 15 minutes in a mechanical mixer. The mixture was then diluted to approximately 1000 ml. with distilled water and placed in a constant temperature bath at 27° C for 30 minutes. The mixture was then thoroughly stirred and left to stand for two hours. Most of the liquid was then carefully poured off and the remaining sediment was washed into a dish and evaporated to dryness. This fraction, whose size range was 5 to 50 microns was used in the experiments in the form of a suspension in distilled water. A particle size analysis of the suspension was performed for each run. Design of Equipment The equipment was designed to produce conditions of uniform flow. To achieve uniform flow the water supply from the water—main was led into a reservoir. The water 36 supply was always in excess of the flow rate so that a constant head of water was produced. The water overflowing the reservoir was led to a drain. In this way water—main pressure fluctuation was eliminated. The head difference of water levels was kept constant for all experimental trials. Two siphons having internal diameters of 0.95 cm. and 1.27 cm. were used to supply low and medium flow condi- tions. The low flow siphon produced a mean velocity of 16 cm./sec. and a mean flow depth of 0.11 cm. on a smooth bed at 5% slope. The medium flow siphon produced a mean velocity of 23 cm./sec. and a mean flow depth of 0.1“ cm. under the same conditions. The siphons were 80 cm. long and made of clear plastic so that the presence of air bubbles could be monitored visually. In preliminary testing it was noted that small air bubbles collected over a period of time on the internal walls of the siphons. This caused an unpredictable change in flow rate. To ensure that this did' not occur during testing the flow rate was monitored several times to ensure uniformity and the test completed in about five minutes after the last flow measurement. The siphon was led to the bottom of the stilling section, a box constructed of plywood having internal dimensions 30 x 30 x 30 cm. for a volume of approximately 0.03 cubic meters of water which was sufficient to damp out most of the turbulence. The assumption was shown to be reasonable by considering the relationship between 37 velocity and depth for a smooth bed (see Figure M). The linear relationship indicates smooth laminar flow conditions as predicted by Newton (Streeter, 1958, p. h). The stilling section and the flow bed were made in one piece to eliminate sealing problems between the two. The combination was provided with a tilting device to alter the lepe of the bed. This was achieved by providing a hinge on the lower edge (see Figure 6). The wedge was calibrated using a level on the bed, and so the bed could be set at any desired inclination. The tilting of the stilling section had negligible effect on the volume or on the head difference in water levels between the stilling section and the reservoir. The stilling section was provided with a rapid emptying device, which consisted of an inverted U—shaped siphon having an internal diameter of 3.8 cm. In operation this was filled with water and one end placed below water- level in the stilling section. With the water supply removed the remaining water on the bed drained away. The bed down which the water flowed consisted of a plywood channel 30 cm. wide and N cm. deep. The sides of the channel were topped by rails of 1.25 x 1.25 cm. angle section to provide support for the depth measuring device. Fulford (196“, p. 177) gives a review of measuring tech- niques for mean film thickness. The first and most simple method consists of direct determination of the position of 38 / 5‘7. Slope 30 A Q 25 _ Mean Flow Velocity (cm./sec.) 20 - Q / 1°/. Slope E] 15 ._ (3 [J 10 _ C! o / 5 — / a O / l3 0 I I I 0.10 0.20 0.30 Mean Flow Depth (cm.) Figure 4. Graph of velocity of flow against depth of flow for a glass plate. The linear portion of the curve indicates laminar flow . 39 Figure 5. Photographs of experimental stage of study. Above: (a) General View of apparatus used in the study. Below: (b) Removal of sample from bed plate. Note position of squegee and use of wash- bottle. Main water supply 2 Stilling section ‘ / Reservoir /' > ‘\ ’ / Q/ Rapid ‘ \‘ Lemptying '1 I siphon - \. / wed; J To waste Figure 6. Diagram of apparatus used to produce thin film flow. Feed siphon \ 41 the surface by means of a micrometer gauge and pointer. This gives accurate results in the absence of surface waves, which was the case in the study. The depth of the water was found by lowering the pointer to the channel bed until it resisted gentle turn- ing. This ensured that the pointer was on the channel bed in all cases, especially when rough surfaces were used. A reading was then taken. The pointer was raised and lowered again until it Just touched the surface of the water as determined by visual observation and another reading was taken. The flow depth was found by the dif- ference in the two readings.I The process was repeated several times to ensure a uniform film thickness existed in the channel. Preliminary testing showed a uniform flow across the channel and a profile similar to that shown in Figure 7 for all cases tested. Construction of the Bed Plates From preliminary calculations, it was considered that even the finest particles (having a diameter of U.0 microns) should settle out in 11.5 cm (see Appendix B). Preliminary testing indicated that the actual distance of transport was of the order of about 10 cm. A bed length of 60 cm. was chosen to provide a length of s10pe having uniform flow conditions in which experimentation could be performed. The bed plates were made 30 cm. wide to fit the flow channel. U2 .mumHm won mo mwvm wcflpmmfi Eoum .80 OH uawm mo cowuummcH mo :oHuwmoa ouoz.mumaa own CBOp oawwoum Bon Hmowd%u mo camuu .m muswwm A.Eov oumaa won mo ammo wcwpmoa Eoum mocmumfio cm on oq om om 0H _ _ _ _ _ _ o I OH.o Es oooo fits QGOOOGQGOGGOQOOQG Gm Boncmmz O 5 TONS uHHm mo cowupwmcH mo ucflom ”3 To produce the rough surface plate a sheet of 10 gauge steel was cut to size to provide a stiff backing. Strips of abrasive belting were glued to the steel plate using waterproof glue. Care was taken to produce a smooth surface and to ensure that the edges of the strips were firmly attached to prevent the entry of water. The surfaces were pressed together and left to dry for several hours. After drying the surface was checked to ensure smoothness and uniformity. Surfaces with local variations of more than 0.1 cm. were discarded. The center—line of the flow path was marked in pencil and it was divided into 2.5 cm. seg- ments. It was determined during preliminary tests that this division of the deposited traces gave adequate samples for the analysis. After trimming, the surface was coated with six coats of Krylon clear lacquer spray, which provided adequate waterproofing. However, it was found that in order to minimise the effects of the surface tension of water, it was necessary to roughen the surface with fine sand. Water was applied during this process, and the sand was gently rubbed across the lacquered surface by hand. This caused a very slight roughening of the lacquered surface and allowed the water film to spread uniformly. It was found that bed plates produced in this way performed satisfactorily and could withstand periods of immersion in water of up to 30 minutes without apparent 4H signs of deterioration. These surfaces also allowed easy removal of deposited silt after drying. Two rough sur- faces were made as indicated and used in the investigation. The abrasive belting used was a product of Minnesota Mining and Manufacturing Company. To produce a medium sand sur— face an 80—grade belting was used. For a very coarse sand surface a UO—grade belt was found satisfactory. Instrumentation The depth measuring device consisted of a micrometer gauge and a pointer, as described earlier. The micrometer gauge has an accuracy of :0.0025 cm. The flow velocity was measured by placing a 1000 m1. measuring cylinder under the drain outlet of the bed section. The time for 1000 ml. was measured with a hand-held stopwatch, with an accuracy of i0.l sec. The flow velocity was measured at least four times to ensure uniformity, and the results averaged. To analyse the sediment samples a Coulter Counter Industrial Model B was used. The Coulter Counter determines the number and size of particles suspended in an electrically conductive liquid. This is done by forcing the suspension to flow through a small aperture having an immersed elec- trode on either side. As a particle passes through the aperture, it changes the resistance between the electrodes. This produces a short duration voltage pulse having a magnitude proportional to the particle volume. During “5 analysis of a sample the series of pulses is electronically scaled and counted. The pulse height and instrument response are essentially proportional to the particle volume, and to fluid resistivity for particles up to 30 to no per cent of the aperture diameter. The particle resistivity has negligible effect. The principal does not permit signifi- cant discernment of particle shape, and results are expressed in equivalent spherical diameters. This proves acceptable as sufficiently high numbers of particles traversing the aperture. The theory of operation of the Coulter Counter is simple and side effects are negligible. The instrument is simple to calibrate. Calibration and sample analysis procedures are given in Appendix A. Figure 8. The Coulter Counter Industrial Model B. Above: (a) General View of Coulter Counter. Below: (b) Close-up of aperture tube stand. TEST PROCEDURES low Test Procedures Tests were conducted in a research laboratory with a mean temperature of approximately 20°C. Attempts were made to protect the bed surface from foreign matter at all times. This was to protect the Coulter Counter aperture from blockage. All tests were conducted in the following manner: 1. The water was turned on and run for approxi- mately 15 minutes to ensure a constant water temperature. The mean water temperature during testing was about 13°C. {\J . The reservoir and stilling section were thoroughly cleaned to remove material that might cause blockage of the Coulter Counter aperture. 3. The rapid—emptying device was also cleaned and one end blocked with a rubber plu . It was 014 filled with water and placed in the stilling section. U. The bed plate was thoroughly cleaned, dried and put in place. The edges were sealed with a plastic sealing tape to prevent seepage round the plate, which would introduce an error into the flow rate and the measured flow depth. '47 10. U8 The bed was checked for alignment and the value of the bed slope was set. The reservoir and stilling section were filled with water. The siphon was chosen, cleaned, filled and put in place. The bed slope was adjusted for uniform slope. A 10 cm. long level was used to detect local variations. The water was allowed to run, and the temperature was taken periodically until a constant water temperature was reached. The temperature was noted. The flow rate was obtained by measuring the time taken to fill a 1000 ml. measuring cylinder. The measurement was repeated four times, and the values noted. 0 cm. U.) The depth of flow was measured at a point from the upper edge of the bed plate, and in the line of flow to be used in the test. One location was chosen to take the flow depth measurement since this reduced the time taken for the experi- mental run. It was considered necessary to avoid a change in the flow rate due to the collection of air bubbles in the siphon, and also to avoid possible deterioration of the rough surfaces during prolonged immersion in water. From l2. 13. 14. 16. 49 Figure 7 it can be seen that this gives a measure of the flow depth over the area used in the experiment, with a maximum error of :0.005 cm. This measurement was repeated twice and the results averaged. The flow rate was measured two more times. The temperature was checked to ensure no varia- tion was occurring. The silt suspension was thoroughly agitated to ensure complete suspension. An eye dropper was quickly filled with the suspension. The first drop was released into a beaker con— taining 125 ml. of 2 per cent potassium chloride solution. It was quickly covered with transparent plastic to exclude impurities. The suspension thus prepared was used as a standard in the analysis of each run. The eye dropper was held at the 10 cm. mark, about 0.5 cm. above the water surface and 10 drops of the suspension were rapidly released. An average time for this to take place was 6 seconds. A delay of 5 seconds was allowed before the rapid-emptying siphon plug was removed. The water level in the stilling section dropped below the bed level almost immediately. 170 18. 19. 50 The siphons were removed and the water supply turned off. The excess water was allowed to drain from the plate for a few minutes and the sealing strips around the bed plate were removed. The bed plate was quickly removed and dried so that the deposited material could be removed for analysis. Sample Analysis The bed plate was placed in a room with a minimum draft and dust environment, and was allowed to dry for about two hours. After this time the plate was set up at a slight angle (approximately 10°) in two direc- tions at right angles. Using the squegee as shown in Figure 5, the sample was washed into a clean dry dust-free beaker with 2% potassium chloride solution. The squegee was positioned and pressure applied so that only the deposited material was washed away and collected. The sample area from which the sediment was being removed was lightly agitated with a small short- haired brush. The brush was washed and put aside and the sample area rewashed with potassium chloride solution. 51 The volume of potassium chloride solution was made up to a total volume of 125 m1. and the beaker quickly covered with a transparent plastic sheet to prevent the entry of impurities into the sample. The process was repeated for 2.5 cm. strips of the silt trace down the bed trace until the trace became indistinct. The samples were then analyzed with the Coulter Counter as given in Appendix A. 52 Table 4. Sample Of Coulter Counter Data Run No. 14 Slope 3% Surface: 80 - Grade Distance Down Slope: 7.62 cm VVSLIhrthEIA EQUIVALENT MEAN L_ L SPHERICAL RAW (CUBIC DIAMETER TL I A RAW COUNTS COUNT MI CRONS) dL (MICRONS) (A) (B) (c) x1 X2 X3 X4 X1 (D) (E) (F) (G) (H) (I) (J) 20 4 64 26 23 17 18 21.0 30617.6 38.215 20 2 64 194 166 167 199 181.5 15308.8 31.064 20 1 64 629 591 657 615 623.0 7654.4 24.660 20 1 32 1396 1322 1261 1326 1326.25 3827.2 19.577 20 1 16 2178 2131 2157 2088 2138.5 1913.6 15.532 20 1 8 2911 2971 2864 2870 2904.0 956.8 12.372 20 1 4 3390 3422 3341 3432 3396.25 478.4 9.788 20 1 2 3771 3916 3827 3766 3820.0 239.2 7.764 20 l 1 4222 4334 4140 4227 4230-75 119.6 6.166 20 l 5 5262 5464 5265 5398 5347-25 59.8 4.755 53 Table 5. Analysis of Data From Table 4 EQUIVALENT MEAN EQUIVALENT SPHERICAL MEAN SPHERICAL DIAMETER RAW COUNT DIAMETER E (MICRONs) COUNT DIFFERENCE (MICRONS) dL x1 x2 - x1 38.215 21.0 160.5 34.64 31.064 181.5 441.5 27.49 24.660 623.0 703.25 21.83 19.577 1326.25 812.25 17.32 15.532 2138.5 765.5 13.74 12.327 2904.0 492.25 10.91 9.788 3396.25 423.75 8.66 7.764 3820.0 410.75 6.87 6.166 4230.75 1116.5 5.46 4.755 5347.25 DATA ANALYSIS Most of the measurements taken to establish experimental conditions were repeated several times and averaged as indicated in the test procedures. The principal data reduction was concerned with the results from the Coulter Counter. The calculation of the calibration constant is given in Appendix A. The value used in this study was h = 5.89 and was found to vary only slightly during the series of experiments giving a variation in mean particle diameter values of :1 micron. A sample of the data obtained from the Coulter Counter is given in Table 4. The significance of each column is given by reference to the identifying letter. (A) The threshold setting tL (B) The aperture current setting I (C) The amplification setting A (D), (E), (F), (G) The four counts obtained at the above settings (x1, x2, x3, x“) (H) The mean count x = «(x1 + x2 + x + X4) 3 (I) The volume of the smallest particle registering on the counter at the settings given vL = htL IA 54 55 (J) The equivalent spherical diameter of the particle whose volume is given in condition (I) dL = 1.241 ivL The sample of data analysis given in Table 5 is con- tinued from Table 4. To find the number of particles in the sample in a given size range, the difference between two adjacent values of the mean count E was determined for example, from Table 5: x - x2 = f = the number of particles in the size range d2 — d1 = d microns. The operation of averaging the limits of the particle size implied that there were i particles of dize d in the sample. To find the particle size distribution, the values of i were divided by the total number of particles in the sample. A percentage size distribution for each sample was obtained. However, it is necessary to relate all the samples. This was achieved by comparing all the samples of the run to the master silt analysis, which was obtained rom the analysis of the sample of suspended material taken before each run. The master silt sample was analyzed in the manner given in Appendix A and the results processed as given above. The number of particles in each size range of the master silt sample was multiplied by 10 since 10 drops of suspended material were used in each test. The A"... .- .. .— 56 .11... result gave the total number of particles present initially in the test. By dividing the particles of a particular size in a given sample by the total number of particles of that size, a percentage of the total particles deposited at a location was obtained. In this manner the deposition curves for particles of given size can be obtained for each run, which is given in numerical form in Appendix C, and an example of which is given graphically in Figure 9. The distance from the point of insertion of the suspended material to its point of maximum deposition is called the Critical Distance X. Its value can be extracted from the data and is given in each case in Appendix C. The values obtained for the Critical Distance X are compared against the theoretical models described earlier. 57 A.zo~u aswvoa suds macaw NM um oumflm can moosw co mofioquuoo couofia m.uH mo acauwuomoav .ooamumwn Hmowuwuu mm cu popuommu ma swam oauauumm ocu Ham coHuHmomop EBwamE mo ucaom Ou cowumofiHmnm wo uaaoa scum ouamumaa .oNHm ofiuwuumm amasowuumm o Ham m>uso cofluwmomop Hmoamma .a muswflm A.Eov :ofiuummaw we ucfiom Eoum oucmumwo mu om ma OH m b _ _ h a //// ANS mucoumwn nu co>wo um nouwmoaon nu oufim co>Hu mo moH0fiuumm mo owmucoouom o.© U x oocmumfia Hmoouauo 58 10 _ X4 5 _ X5 Critical Distance (logarithmic scale) X3 (cm.) X 2 4 6 x1 X2 1.0 ._ 0.5 _ 0.2 -— 0.1 I I l I T T l I 5.46 6.87 8.66 10.9 13.7 17.3 21.8 27.5 Particle Size (logarithmic scale) (microns) Figure 10. Graphs of theoretical models having the general form: X=.K.. krl 59 ////// iii? 27%; (13.44) ' 7//// (24.47) 21.8 (9.17) ///// 92-59 (6.63) 17.3 ///// (6.28) 13.7 (4.64) ///// (4.11) (3.29) ////4 8°66 (1.68) 7///// (3.40) (4.38) ///// 5-46 (6.26) ////6 (6.55) ol 9} 4' 6! g 10, 1:; Critical Distance (cm.) Figure 11. Comparision of two tests on 40-grade using 1% slope. Mean flow velocity Mean flow depth Water temperature (ungfigdgd) (sfigged? 8.7 8.5 (cm./sec.) .27 .28 (cm.) 11.1 11.4 (°C) (Numbers in parentheses give the percentage deposited at Critical Distance.) 60 Particle ETTgrons) (11.80) 3“ /////////fl (.2...) (7.87) 27.5 ////////////////A ‘9' 7” (5.21) 21.8 ////Z (6.85) (3.69) 17.3 ///// /////////// ““8” (2.57) h 13.7 f////////////// “75> (2.47) 10.9 ////////////// 1/ ”'58) 8.66 (1'94) ///////////////. <2- 34> (3.22) 6.87 7 ” ///////////// “"0“” (3.02) 5.46 r //fl///////////J 9'19 I I I I I l I 0 2 4 6 8 10 12 Critical distance (cm.) Figure 12. Comparision of two tests on 80~grade bed surface using 3% slope. (unsfigged? (shgdgdg4 Mean flow velocity 16.2 14.6 (cm./sec.) Mean flow depth .20 .19 (cm.) Water temperature 11.7 11.1 (°C) (Numbers in parentheses give the percentage deposited at Critical Distance) (Numbers in parentheses give the 61 percentage deposited at 7//////////////////////// 3:33: (mm ///////////////////////// :56?” ” '3 V//////////////////////// 333:: > /////////////////////// 33 :33 ////////////////////// // 8' 66 /////i//////[///////////M/j . /////////////////////2 i: Q I / /////////////////////}1}>/3 Siiiggia. ClmptthtI:‘:H::“d> g£:;:§::;3s:f..: 1.1:. . 62 ‘(35.15) 34-6 \\C\§)\C\C‘ (43.85) Particle $23 (48 29) Size (microns) I (27.34) 27.5 W (29.95) (33.72) (21.17) . ‘\Q\{\t\\. . 21 8 Eéj (19.8) (18 53) I (14.89) (14.17) 17'3 (13.83) I (10.94) 13.7 ‘\Q\C\\ (10.77) (10.83) I I (9.44) 10.9 W (7.98) 7 (8.17) I I (6.83) (4 ) .32 8.66 (4.83 l (11.07) 6.87 ‘\T\C\.\\54 (10.70) (10.91) I (12.50) , (11.80) I r I I I l 0 2 4 6 8 10 Critical Distance (cm.) Figure 14. Comparison of runs (1% bed slope and low flow) Top to bottom: Run 8 — Glass,RJn l2 - 80-grade, Run 22 - 40- grade.See reduced data. (Numbers in parentheses give the percentage deposited at Critical Distance) 63 I (25.48) 34.6 3) (21.76) Particle , (18.29) Size (microns) (19.h3) .7..- \\X\ 7...... (13.44) + I (13.95) 21,8 \\;\f\Q\C\C\Q\\\\§\>\5§5\\\§\>\>\3\:\] (6-29) (3.35) 10 . 9 \\ \\\\\\\\\\\\\\\\\\\\\ W (1.66) .66 (\\\\\ \\K\\\\\\\1 (11.57) (2.51) (3.87 \\\\\\\ \\\\X\\N (4.79) (5.33) 3 . \\\\\\ \\\\\I <4 . 90) 323 (6.51) (23.06) (22.1 ) (15.1“) I (11.92) I (9.19) 4:" 0\ CD C\ U) C "1‘ v v AA I (4.58) I (11.96) I IT 4‘1 I I I 0 2 4 6 8 10 Critical Distance (cm.) Figure 18. Comparison of runs (5% slope and low flow) TOp to bottom: Run 4 - Glass, Run 11 - 80-grade, Run 18 - 40— grade. See reduced data. (Numbers in parentheses give the percentage deposited at Critical Distance.) 67 (18.14) Particléh.o (15 21) (microns) I(2l.80) 27. 5 \\\\\\\\\\\:\\\\\\I (9 .87) (7.48) I (15.04) 21 . 8 \\(>\\)\\\\\\\\\\\\\\I (9. 54) .70 I(9.50) 1743 E25ri>f\535\§\§<§C\C\§\§{§C\§\§§5§fl (8.96) 3.96 J(7.60) 13 .7 §X1\\\\\\\\\\\\\\\\\\I (8 55) (l 22) I (4.63) 10.9 ‘\€\§§5C\C\C\C\§\§§;5Q\C\C\C\§ \\\\\\§\\\\\\\ (4.57) 8.66 \\\\\\\\\\\\\\ (3.23) (\\\\\\\\\j (4.32) \\\\\\ \\\\ \\\I (4. 79) 6.87 \\;\\5\(\\_ (3.95) \\5\\5\\\\j\ (10.70) \\\\\ \\\I (4.90) 5.46 \\§\:\\ (5.63) \\\ (13.48) b 3’ ‘1 6' 8' 16 flz Critical Distance (cm.) Figure 21. Comparison of slopes (SO-grade bed and low flow) Top to bottom: Run 11 - 5%, Run 14 - 3%, Run 12 - 1%. See reduced data. (Numbers in parentheses give the percentage deposited at Critical Distance.) 70 (22.81) 34.6 E§§2§32§32§3 (15'35) Particle (48-29) Size (microns) (18.13) 27.5 ‘ (11.96) Egg (33.72) . 7.42 21.8 W (5.37) (19.80) (6.01) 17.3 , (2.69) , (13.83) (3.35) 13.7 PSer§%(>