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THE FACTOR LOSSES —

IN THE PIPING SYSTEM OF
THE MICHIGAN AGRICULTURAL COLLEGE HYDRAULIC LABORATORY.

The Thesis Submitted To The Faculty
of
MICHIGAN AGRICULTURAL COLLEGE

by

MO
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PM Coy
M.V.Hunter and V.M. Nagler
x

Candidates for the degree of
BACHELOR OF SCIENCE
June 1922.
JHES!S ;

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POR EWOR  D

The purpose of thia thesis is to determine by a
series of experiments the factor losses for various
commercial fittings which are installed in the piping
syatem of the Michigan Agricultural College Hydraulic

Laboratory.

101°747
INTRODUCTION.

The Michigan Agricultural College Hydraulic Laboratory
is located in the east end of the basement of the engineer=-
ing building. The laboratory itself was built in 1916, but
the commercial fittings were not installed wmtil the summer
of 1921. The Civil Engineering Class of 1922 was the firat
to perform any experiments in the laboratory. Before the
fittings were installed the apparatus waa very limited, only
a few nozzles, short tubes, and the weir in the steam
laboratory being available.

The souree of supply of the water which is used in the
laboratory comes from wella which are located on the college
grounds back of the Forestry Building. From the wells the
water is pumped to the water tower which ia located just
east of the Power Plant. From the water tower, by means of
a system of pipes and valves the water is run into a tank
located in the top of the Engineering Building. From there
it is drawn directly through the piping System on which we
performed our experimenta. <After running through the piping
system it ia discharged into a pit in the floor of the
laboratory which empties directly into the sewer.

The water waa run through the pipea for several hours
before any good results were obtained. This was due to a

collection of rust and various bacterial collections in the

pipes.
For references on the subject of hydraulics the follow-
ing texts were used:
Hydraulics-----------= Hughes and Stafford
Hydraulics ee--------- Russell
Kings Hydraulic Handbook
Merrimams Hydraulics
Hydraulics ---------- Church
Waterworks Handbook--Flinn
Engineering News Record

Wegman's Conveyance and Distribution

We wish to thank Mr. Ren Saxton and H. L. Publow for
the personal assistance which they rendered us while

working on this thesis.
   
  

Pressure Tana.

 

Weighing Tank and

Scales =|

 

 
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OUTLINE

Determination of the Weight of Water.

Calibration of the Weir.

Calibration of the Venturi Meter.

Calibration of the Pitometer.

Coefficient of Friction in the Two-Inch Pipe.

Coefficient or Friction in the Three-Inch Pipe.

Losses on Abrupt Expansion.

¥ " Contraction.

in Two-Inch Valves (Straight and Angle Globe
Valves & Gate Valvea)

in Flanges.
in Unions.
in Straight and Angle Tees.
in Elbows.

Curves and theoretical valves on each of the Losses and
Calibrations.
GAUGES

This discussion of gauges is made that the reader may
know in detail the kinds of gauges used. The two principal
kinds of gauges used were the Differential Gauge and the
Hook Gauge.

The Differential Gauge was used to measure losses over
fittings. The gauge itself consisted of a glass U-tube with
@ valve on each end so that it could be closed ‘hue shutting
off the pressure. The two legs of the U were half filled
with Mercury (Hg) or Carbon Tetrachloride (CCl), and the
other half with water. The ends of the U were each connected
to the pipe, one on each side of the fitting over which the
loss of head was desired. If the loss of head was great

enough, Mercury was used, otherwise Carbon Tetrachloride.

|

Differential U Gauge.

 
        
The water in the U was under a different intensity of
pressure in each leg, which gave the difference in elevation.
If the liquids are quiet, the equation of equilibrium, using
heads to represent pregsures, may be written as follows:

s(4.+ h.+d)= s(+h)+5'd

S$ = the specific gravity of the lighter liquid.

S's the specific gravity of the heavier liquid.
Then tH t = d (S=8).
Y here is the weight of a unit column of the lighter liquid.
fherefore to change feet of Mercury or Carbon Tetrachloride
to feet of water the following formula is used.

d= d' (s* = s) in which s is the specific gravity of
water, and 3° the specific gravity of the heavier liquid,
a* the difference in levels of the liquid in the tube, and
a the equivalent difference in feet of water. For Mercury
the conversion is d = 12.594". For Carbon Tetrachloride the
conversion is a= 0.584da'. It is easily seen from these
conversion factors that Carbon Tetrachloride shows a much
greater difference in elevation than Mercury under the same
he ade

fhe scale graduated in feet and decimals of feet. was
between the two legs on the mounting of the U-tube. The sero
of the scale was in the middle. The readings above and below
the sero mark were taken, added together and their sum
divided by two.

The gauge which was used to calibrate the Pitometer was

somewhat different from the one described above. The shape
of this gauge somewhat resembled an inverted U. A valve was
in the end of each leg of the U to shut off the water. At
the upper part of the gauge between the two legs of the U
another valve was attached. An air pressure pump was attach-
ed at this valve and air pumped into the U until the water
was forced about one-half way down the gauge. Since there
was an equal intensity of pressure of air in each leg, the
difference in levels of the two water columns would give the
true difference in head in feet of water. The scale was
placed between the two legs of the U and graduated in feet
and decimals of feet. The zero of the scale was at the
bottom. The level of the water in each leg of the tube was
read and the difference taken as the difference in head in

feet of water.

Diverted Differential U Gauge
used in Calibrating Pitometer.

 

A Hook Gauge was used to measure the difference in
levela of water in the weir. The Hook Gauge is a graduated
gliding scale with a sharp hook on the lower end fitted with
a vernier, and attached vertically to a frame. The hook was
placed in a still box outside of the weir. MThe purpose of
the still box was to keep the water quiet while the readings
were being taken. The still box was comnected to the bottom
of the weir by means of a tube, so that the water in the
still box was exactly the same elevation as the water in the
weir due to the fact that water everywhere seeks its ow
level.

With this preliminary discussion of the gauges used, it
is seen that any time a particular kind of gauge is referred
to, the reader has only to refer to this discussion to

understand the principle on which it works.

Hook Gauge.

 

 
UNIT WEIGHT OF WATER

The weight of water per ou. ft. is ordinarily taken as
62.5#, but in this thesis work in order to get accurate
reaults, it was thought best to accurately determine the unit
weight of water. This was done by means of the Westfall
Balance. The Weatfall Balance consists of a balance arm with
a weight on one end and a counterpoise on the other suspended
in water, the arm itself being supported in the middle on a
knife edge. In finding the unit weight of water, water was
allowed to run out of the faucet until it was of about the
same temperature as the water in the laboratory. Then water
was drawn from the faucet and put in the glass until the
weight was entirely submerged. Weights were then put on the
balance arm until it balanced. The specific gravity of water

was then determined by adding the weights.

 

 

 

 

I f Westfal/ Balance.

 

 

 

 

 

 
The specific gravity of the water was found to be
larger than one because of the impurities in it. Also we
found that the specific gravity increased as the temperature
decreased. &fter determining the specific gravity of the
water, the unit weight of it was easily found. (See sample
of Computation.) We found that the average unit weight of
water to be 62.6415 at 14 degrees Centigrade.

Results:
frial Spe Gr. femp.e Unit wt. of Water
1 1.001 20.7 62.578 #
2 1.0015 16.0 62.6103#
3 1.002 14.2 62.6415¥
4 1.002 14.2 62.6415#
5 1.002 14.0 62.6415#

Sample of Computation:
1 ou. ft. = 28,320 cu. om.

1.001 is the weight in grams of one cu. om. of water
at 20.7 degrees Centigrade.

Then 1.001 x 28, 320 = 28,348.32 gms. the weight of one
cu. ft. of water.

One pound avoirdupois = 453 gms.

28,348.32 divided by 453 = 62.5784 the weight of a cu.
ft. of water.

Conclusion:
The value of 62.65 was used as the unit weight of water

in the experiments in this thesis.
WEIR

A description of the weir will first be given.

The weir was set in one end of a tank of which the
approximate dimensions were 20" x 44" x 44". Water flowed
into the tank from a two inch pipe at the upper end. The
amount of flow was regulated by a valve set in the incoming
pipe, only very low heads being used. The weir itself was
of the rectangular type made of sharp edged thin metal. The
length of crest was 5 and 15/16 inches.

In the work of calibrating the weir, water waa first
allowed to run freely through the weir for some time in order
to get the water to a constant temperature, and also to get
rid of any sediment which might have collected in the tank.
Then the water in the tank was allowed to become quiet. The
Hook Gauge was then set at zero. (See discussion of gauges
and the picture of the Hook Gauge.) Water was then turned
into the tank and allowed to run freely a few minutes in
order to obtain a uniform flow, after which we began to take
readingse

fhe readings consisted in measuring the difference in
levels of the water in the tank by means of the Hook Gauge
and measuring the actual quantity flowing through the weir
in a certain time by weighing it on the scales and changing
to equivalent cu. ft. per sec. About thirty readings were
taken, the head varying from 0.047° to 0.248',
In obtaining the theoretical quantity the weir formula
q = oLH* was used. For example: Time = 180 sec., Weight of
water = 892.5#, Hook Gauge reading = 0.125".

Actual quantity = 892.5 = 0.0729 cu. ft. per sec.
Theoretical quantity = LH or 0.496! x 0.0442 = 0.0219 where
0.495 is the length of the crest in feet and 0.0442 is H
raised to the 3/2 power. The weir ooefficient "c" = actual
quantity / theoretical quantity.

In this example "o" = 0.0729/0.0219 = 3.329.

Velocity of approach was neglected in all our computa-
tions. We followed this procedure in all of our readings.

Our results were very consistent. We took the average
of thirty readings and found the mean value to be 8.494. All
of the values of the coefficient were close to this value
except under very low heads when the highest value of "c"
obtained was 4.52. ‘The actual quantity was plotted against
the difference in head for each of the thirty readings. A
smooth curve was drawn through these points. The greatest
variation of head from the curve was .001 feet which would
seem to indicate that our resulta were quite acourate. The
relation of quantity to head was found to be a constant
for heads over 0.15".

The result that we obtained in our calibration was
higher than Francis obtained in his experiments. His value
of "co" was 3.33. However, Francis used heads which varied
from 0.5' to over 2", while our greatest head was about 0.3".

Taking into account the consistency of our results and
the fact that Francis obtained a value of "co" but slightly
higher than ours by using higher heads, we wish to recommend
the weir coefficient "c" for the weir in the Michigan
Agricultural College Hydraulic Laboratory to be 3,494.

End View of the Weir.

 
ty
B

WDAIHOMH ANH

Lbs.of
Water

892.5
60325
1128.2
1126.5
1430.7
904.5
546.0
1136.3
1166.2
1081.0
668.5
671.7
898.5
893.0
978.2
1009.0
1316.5
988.2
1312.5
1419.0
935.6
918.0
931.0
930.2
791.5
585.0
1167.0
257.6

Actual
Quant.

0.0729
0.0803

0.1500

0.1498
0.1521
0.0803
0.0726
0.207

0.207

0.0719
0.1186
0.1191
0.1196

0.1190

0.1736
0.1790
0.1750
0.1755
0.1749
0.2524
0.2488
0.2445
0.1654
0.1652
0.1053
0.0518
0.2071
0.0228

CALIBRATION OF WEIR

H

0.125
0.128
0.198
0.199
0.1985
0.125
0.116
0.249
0.249
0.1145
0.166
0.167
0.169
0.166
0.219
0.224
0.221
0.2205
0.2215
0.284
0.2835
0.2800
0.213
0.211.
0.154

0.0985

0.248
0.047

)Hooks
) Gauge

q

0.0442
0.0458
0.0881
0.0888
0.0881
0.0442
0.0395
0.1243
0.1243
0.0387
0.0676
0.0682
0.0695
0.0676
0.1025
0.1060

0.1039

0.1035
0.1043
0.1514
0.1510
021482
0.0983
0.0969
0.0604
0.0309
0.1235
0.0102

Av. Value of C @ 3.494

Theor.
Quant e

0.0219
0.0227
0.0436
0.0440
0.0436
0.0218
0.0196
0.0616
0.0616
0.0192
0.0335
0.0340
0.0344
0.0334
0.0507
0.0525
0.0514
0.0513
0.0517
0.1750
0.0748
0.0735
0.0487
0.0480
0.0299
0.0153
0.0613

5.490
3.685
Se 700
3.560
3.560
3.745
5-540
3.508
5.475
3.561
35.425
3-410
5.406
5.420
5.581
5.568
3-526
5.526
5.595
5-440
3-522
3.585
5.580

0.00505 4.520

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CALIBRATION OF THE VENTURI METER.

The Venturi Meter was invented by Clemens Herschel in
1886-88, and named after an Italian hydraulican Venturi who
discovered ita principle. Two truncated hollow cones are
inserted in a line of pipe having the same internal diameter
as the base of the cone. ‘The tube is built of cast iron with
a bronze lined throat. Preaaure chambers (Piesometer Rings)
surround the up-stream end and throat and pressure lines lead
from there to the manometer. A valve was placed in each pipe
close to the meter tube 80 that if an accident oceured the

water could be shut off,

 

 

 

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Longitudinal Cross Section of a Venturi Meter.

fhe Venturi Meter is a practical application of
Bernoulli's theorem to the measurement of the flow of water
in pipes under pressure. The same quantity of water passes

through both the inlet and the throat, but since the area at
12

the throat is smaller the velocity will be greater than at

the inlet. They have a constant relation for any meter
depending upon the ratio of the two areas and a simultaneous
observation of the pressure heads at the inlet and throat
provides a method of determining the velocity at the throat,
and from the velocity and areas the discharge can be obtained.

This ratio was taken as

Then K =/fR*( ze)

Then Q = CKD‘ Ht

For a value of R equal to 2/1 the value of K was found to be
6.505. As an example of our computation let: Time = 240. sec.,
Lbs. of water = 1050.5#, H in mercury = 0.21'.

Actual quantity = 1050.5 = 0.0698 ou. ft. per sec.

0.21 x 12.59 = 2.645" head in water.

fheoretical quantity = 6.505 x 00694 x 1.625 = 0.0734.

The coefficient "co" equals actual quantity / theoretical quantity
or in this cage equals 0.0698 / 0.0724 = 0.951. This same pro-
cedure was followed in computing all of our readings.

In calibrating the Venturi Meter we first connected the
prassure lines with the manometer. (See the discussion of
gauges.) Then water was allowed to run through the meter and
@ reading was taken of the difference in level of the mercury
in the gauge. The actual quantity flowing was measured by
catching in a tank for a certain length of time and weighing
on the scales. This weight waa then changed to cu. ft. per

gec. About 20 readings were taken in this manner and comput-

ed by the method outlined above.
13

The actual quantity was plotted against the difference
in head in each case and a amooth curve drawn through these
points. The curve showed that the relation between quantity
and head was a constant when the quantity flowing was more
than 0.1 cu. ft. per min. The average value of "co" for
these 20 readings was found to be 0.9558.

The coefficient "c" varies with the velocity at the
throat, the ratio of the diameters at the inlet and outlet,
and the actual dimensions of the meter. As meters are
ordinarily constructed the coefficient varies between 0.97
and 1.0. Probably the reason why we obtained a lower value
was because of the condition of the meter. The meter had
not been used for about tour months and in that time had
probably collected some rust or other growth.

We wish to recommend as a value of the coefficient "oc"

of the Venturi Meter now in the Michigan Agricultural College

Hydraulic Laboratory as 0.9558.
CALIBRATION OF VENTURI LiEYER

Run Time Lbs.of Actual #H H K Db Q C.
Sec. Water Quant, He Water Theor.
1 240 1050.5 -.0698 e2l1 2.645 6.505 .00694 00734 0.9561
2 180 783 00694 eel 2.645 00734 0.947
3 180 1069.3 .0947 e585 4,848 00995 0.953
4 180 1061.7 .0943 e580 4.78 . 00989 0.954
5 180 1184.6 .1051 e485 6.105 e1116 0.943
6° 150 1186.0 .1262 e675 8,50 eil317 0.960
7 120 1160.5 .1547 1.02 10.85 e1487 1.044
8 240 760.5 .0507 ell 1.385 0532 0953
9 180 569.5 .0506 ell 1.385 00532 e952
10 180 293.8 .0261 003 e578 0278 0939
11 180 430.8 .03825 .065 e818 «0408 0937
12 180 1039.0 .0923 0565 4,60 209 70 0952
13 150 992.0 .1057 e465 5.85 e109 e968
14 120 912.2 1.211 063 7.93 elZ272 0953
15 180 1007.0 .0895 054 4.28 009335 0962
16 150 1174.3 .1250 66 8.50 1301 e960
17 150 1255.5 .1336 e777 9.69 e140 0954
18 150 1320.5 .1405 e85 11.70 01554 0905
19 150 1167.0 .1240 #65 8.18 1286 0965
20 150 1156.5 .1230 064 8.05 elL275 0963

Av. Value of (C) = 0.9558
 

 

 

 

 

 

 

 

 

  
 

 

 

 

 

 
 

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CALIBRATION OF THE PITOMETER

The Pitot tube was first used in 1730 by Pitot to
determine the velocity of flow. His apparatus consisted of
a bent cylindrical tube with one leg horizontal and its
orifive opposed to the current and a straight vertical tube
set with ita opening at the same level as the orifice of
the bent tube. h being the difference in level in the two
vertical tubes, Pitot asaumed that V was equal to (2h) *

Bxperiments have proved that in tubes having small
points so Shaped as not to disturb the flow, with openings
of cylindrical or converging or diverging cone form, h very
nearly equals V/2¢; Therefore if h can be measured the
velocity at any point can be obtained. The apparatus that
Pitot used did not give a true measure of the velocity head
because the vertical tube is not a true piezometer and did
not accurately measure the pressure head. Darcy found that
oscillations of the water surface in the tube made an accurate
reading of the velocity head difficult, so he made the orifices
much amaller than the tubes. Also the water in a pipe does
not flow at the same velocity at the center as on the outside,
the velocity at the center being greater so it was necessary
for us to first determine some ratio between the center
velocity and the mean velocity before we could calibrate the

pitometer. This ratio is called the pipe coefficient.
In finding the pipe coefficient we used the same shaped
orifice as shown in the drawing. Water flowed against the
orifice and the upper end of the tube was connected to the
gauge. Another tube was run from the pipe to the gauge so
that the difference in levels in the gauge was the velocity
head. Then water was caused to flow through the pipe at a
constant velocity. Spot readings were taken at pointa in
the pipe 1/8", 3/8", etc. up from the bottom. The velocity
at each of the points was then obtained. The mean velooity
was obtained as the arithmetical mean of the observations
made at the center of rings of equal value, or the mean
velocity of the whole pipe is the total of these ring volumes
divided by the area of the pipe. The mean velocity divided
by the center velocity as read from the curve is the pipe
coefficient. We took five triala in determining the pipe
coefficient and we found the average value of pipe coefficient
to be 0.953. ‘This value was found to be practically a constant
for different velocities. Now with this value of a pipe co-
efficient, by simply taking readings at the center of the pipe
and multiplying by this coefficient the average velocity in
the pipe was obtained. The quantity was then easily obtained
by multiplying by the cross-sectional area of the pipe. We
were then ready to calibrate the pitometer.

It was necessary that we make three calibrations, one with
the impact tube, and two with Pitot tube shaped ag the one shown
in the drawing. One calibration wag made of the Pitot tube when

the impact opening was against the atream and one when it was
with the stream. The first calibration made was of the
impact tube. A series of about 20 readings were taken in
Galibrating the tube under different heads. The opening

was held in the center of the pipe in each case, and a read-
ing taken of the difference in levels in the gauge. (See
discussion of gauges.) The average velocities were plotted
against quantities in each case and a smooth curve drawn
through these points, The curve was practically a straight
line. This shows that the quantity of water discharged
increased as the velocity increased.

The second calibration to be made was of the Pitot tube
with the opening turned against the stream. <About the same
number of readings were taken as in the previous ocslibration,
and the same method of procedure was followed, This method
of measuring the discharge of a stream is not as acourate as
the Venturi meter method but it is useful in finding losses
in pipe systems.

fhe third calibration was made with the opening with
the current. In this case a negative head was developed and
no accurate readings could be obtained. The curve plotted
from our results followed no definite gourse showing that
our results were not accurate. The reason that the attempt
was made to calibrate this pitometer with the opening with
the current was to show the impossibility of its accomplish-
ment. Only about ten readings we're taken, this being deemed
all that was necessary to show how inaccurate our rosults

Were.
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ea a el

 

 
by
B

OOWO HN PON

Time
Sec.

120

120
120

CALIBRATION OF THE PITOT TUBE
Short Nozzle

Lbs.of
Water

823.0
922.0
995.0
1068.0
1121.5
1205.0
869.0
586.5
1083.0
102.9
950.5
898.0
818.0
770.0
731.0
601.0
531.5
464.0
419.0
374.0
$23.0
600.0
234.0
155.0

Quant. v* CCl, vV* H,o
2g

Cu.Ft. &
Sec.
e1096 0.875
1228 095
01925 1.21
01422 1.82
o149E 1.49
e1605 1.75
01542 1.61
1561 1.55
01441 1.43
e1569 1.24
oi1248 1.09
21195 094
«1089 82
«1026 o 76
00973 063
0801 044
0708 eo4
0618 o27
00557 e225
0498 e185
00430 —=—s«wWdL' SG
20399 ell
003115 .10
0206 04

512
«555
«707
0772
e871
1.022
0941
906
e836
o 724
0637
o 549
0479
444
«568
0257
0199
158
e131
108
088
0064
058
0234

Vay

Sec.

5.75
5.98
6.74
7.05
7249
8.12
7.78
7.64
71.54
6.83
6.40
5.95
5. 56
5.35
4.87
4.07

5.19
2.91
2.64
6.39
£035
1.93
1.23

Vo

5.48
5.70
6.42
6.73
7.14
7.75
7.435

7.01
6.52
6.11
5.68

5.11
4.65
5.88
5.42
5214
2.78
2.52
2.28
1.94
1.84
1.175
        

 

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Time

Run sec.

WODWO HP OW eH

120

CALIBRATION OF PITOT TUBE (Long Nozzle)

AGAINST THE DIRECTION OF FLOW

Lbs.of

Water

436
1103
1042

890
791

7104
659
618
573
524
490
460

574
522
285
242

218.5

Quant. H = y¥*
Actual ™ “Sg
Cu. Ft.

Sec.
«0582 e114
01470 096
01385 087
«1300 68
21185 «59
1053 e 50
eL011 045
00937 e 38
20877 e354
0825 050
00763 25
20697 eel
0652 18
00612 el?
0540 e1l3
0497 ell
~0429 08
0379 06
0322 e045
e0291 204

V

3.01
7.88

Ve

2.87
752
7215
6.29
5.86
5.58
5.15
4.72
4.47
4.19
5.85
6.51
525
3.16
2.75
2.54
2.16
1.88
1.63
1.54

Quant e
Theor.

00625
1639
«1560
01370
01277
01172
e112

«1028
00973
0914
©0836
00766
0708
~0688
«0600
©0555
00472
~0409
0355
003357

Qa

Qy

093
90

0947
928
0904
0905
910
«900
0903
0912
e910
0922
«890
90
~895
-908
0927
0907
«870
 

 

 

 

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aves

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oe

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Fra i Vea iexo ty WA Ye |
| |
| |
|
/ |
Run

O Of 2 FE

fime
Sec.

Lbs.of
Water

Quant.
Actual
Cu. Ft.

Sec.

00712
01182
01436
00913
00658
«0360

H = y*

he Se

0.04
28
220
015
eO1
205

Vv

1,61

CALIBRATION OF PITO@ TUBE (Long Nozzle)
WITH THE DIRECTION OF FLOW :

Ve

1.535
4.06
5.44
2.98
2242
1.72

Quant.
Theor.

00334
-0887
075
e065
0528
00375

Q+

£2213
1.335
1.91
1.40
1.25
096
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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LOSSES THROUGH COMMERCIAL ITIILGS.

The commercial fittings used in the laboratory were
made by the Crane Company. ‘They were all made of cast iron
finished on the inside. Their cross sections were as show
on the page containing the curve. The fittings were in good
condition, water having been run through them for some time
before any readings were taken. Four fittings of each kind
Were placed together in the piping system. In finding the
loss coefficient, one reading was taken over all four
fittings and the result divided by four.

One general method of procedure was followed. The gauge
was firat connected to the fittings in auch a way as to
measure the loss of head. (See discussion of gauges.) Then
about thirty readings were taken of the difference in head
and quantity of water flowing under varying heads. The
quantity was determined in ou. ft. per sec. The method of
determining the quantity was to catch the water in a tank
for a certain length of time and then weigh it. The quantity
equals the weight of water divided by time in seconda times
the unit weight of water. The loss coefficient was found
from the formula E = le where H is the difference in head
in feet of water. <A curve was plotted showing the relation
of quantity to head of water. In each case it was found
that above a certain velocity this relation was a constant.

The resulta obtained for the coefficient were all tabulat-
ed. The logs in head and the loses coefficient varies greatly
with the kind of fitting used. Nearly all the fittings have
coefficients less than one. The part having the greatest
loss coefficient was the angle globe valve. The more the
inside of a fitting obstructs the flow of water the greater
will be the loss coefficient, Friction in a 2* pipe ia
greater than in a 3" pipe. ‘The smaller the diameter of a
pipe, the greater the loss by friction. The reader has only
to read the tabulated value of "c" to make for himaelf a
comparison of the losses for various fittings.

In performing these experiments care was taken to get
as accurate results ag possible, therefore we wish to recom-
mend the results of "co" as tabulated for each fitting, be
accepted as the loas coefficient for that fitting in the

hydraulic laboratorye
TABLE OF AVERAGE VALUES OF COEFFICIENT "Cc"
FOR BACH COMMERCIAL FITTING IN THE LABORATORY.

 

Value of "co"
Commercial Fitting Pour Fittings One Fitting
Straight Globe Valve 2.600 0.650
Angle Tees 3.558 0.8895
Straight Tees 1.5884 0.3471
Couplings 0.4633 0.1158
Flanges 0.7751 0.1938
Elbows 2.625 0.656
Angle Globe Valve 6.761 1.690
Gate Valve 1.1127 0.2781 ©
Unions 0.9511 0.2378
Abrupt Contraction . &.365
 " Expansion 0.5453
Priction in 2" pipe 1.929
1.461

Friction in 3" pipe
g

COEFFICIENT OF FRICTION

ODOWIOMS WH

in a 2" pipe
Time Lbs.of Quant. v* H H C
Sec. Water Cu.Ft. 2g ccl, H 0
Sec.
120 538. 0718 e169 e 51 0292 1.73
693.0 00924 e278 76 0444 1.59
827.0 e110 0392 1.12 655 21.67
874.0 o1165 e442 1.17 684 1.55
955.0 .1274 527 1.42 «830 1.57
857.0 0114 0422 1.13 e660 1.56
777.0  .1036 » 548 096 561 1.61
725.0 00966 0504 84 0491 1.62
641.5 0855 o2a7 067 «450 1.90
554.0 .0738 178 2 54 315 1.77
470.0 00626 01275 «40 0254 1.83
120 395.0 .0525 0990 029 eO17 1.72
150 431.0 00458 0687 0235 e135 1.96
120 3507.5 00409 ~0545 20 e117 215
180 158.0 o0141 00644 03 -018 2.80
120 143.0 0191 e0119 e055 e032 2.69
185.0 .0246 00199 08 2047 2.36
263.0 .0351 0402 =618 088 2.19
296.0 00395 ~0508 0175 e103 2.03
Average Coefficient 1.929
 

 

 

 

 

 

 

 

   
  
  
   

 

 

 

 

 

 

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E

COEPFICIENT OF FRICTION

WODNIOO NW E-

in a 3" pipe
Lbs.of Quant. v* 4 H C
Water Cu.Ft. eg CCl, H,o
Sec.

514.0 00342 00762 .025 e015 1.97
525.0 00466 00141 003 .018 1.28
597.5 0053 0182 0045 e026 1.43
698.5 00619 ~0248 006 0035 1.41
774.5 ©0687 0305 #£#=2.07 e041 1.34
861.5 00764 00377 e085 «050 1.338
611.0 0813 00452 «LO e058 1.29
666.0 0886 e0510 e12 ~070 1.37
872.5 00774 ~0388 e095 0056 1.44
972.0 00738 00353 e085 e050 1.42
514.0 00684 00302 007 0041 1.36
437.5 0581 0218 e055 0052 1.47
460.5 0614 00245 006 e035 1.43
421.5 00561 00204 005 e029 1.42
389.5 e052 ©0176 0045 0026 1.48
568.0 00491 e0156 004 0023 1.47
5353.0 00444 00127 0035 e020 1.57
309.0 00412 ©0110 003 ~018 1.63
243.5 00325 e0069 002 e012 1.75
196.0 00262 000446 .01 e006 1.35

Average Coefficient 1.461
 

 

 

 

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02

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yaya s

p=

pp

a
Time
Run sec.
1 120
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Lbs.of
Water

1442.0
1315.0
1201.0
1117.0
963.0
851.0
768.0
655.5
541.5
448.0
379.0
535.5
649.0
728.0
821.0

LOSSES ON EXPANSION ©

Quant.
Actual
Cu. Ft.

Sec e

1918
©1750
«1598
1485
01282
01132
10235
e0872
©0720
00597
00504
00713
0863
©0970
e1092

yt

2g

1.204
1.002

8354
e721

©5376
e4196
542

02487
«1693
01167
e0830
1662
02438
«5079
053917

H
CCl,

1.10
0.92
0.77
0.67
0.51
0.40
0.335

0.24
0.16

0.105
0.075
0.155
0.235
0.285
0.37

H
H,0

0642
557
045
0592
0298
0254
0193
140
0093
e061
0044
00905
0135
0167
e216

0533
«535
538
e543
554
0557
o 564
562
2 549
0525
« 530
0544
e554
2 542
551
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le a, Pv aae

t

e

va

     

    

     
     

Wa Ua io
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iv

    

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SESS FSS SEC ASS SOG ie ESS BESS NOR.) re SEEDS ERD

 

Quanity

   

Te id lle
ee

   
 
  

(Oia ee)

Actva/

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|
’

   

Reese tari; Cla
Itead -in- feet of |Water |
|

 

/

|

:

a ’
—  SSSSTUSSES COenseates a
by
B

OW IM on > OY

Time
SeCce

120
120
180
180
120
120
180
180
120
120
120
120
120
120
120

Lbs.of
Water

922.0
815.0
872.5

1202.0

648.6
442.5
543.5
281.3
278.0
576.5
435.5
480.0
534.5
705.0
758.5

LOSSES ON CONTRACTION

Quant.
Cu. Ft.
SeG.

01226

° 1083.

00773
«1066
0863
~0588
00304
00249
0370
~0502
~0599
~0638
0712
00938
- 1009

Average 1.365

y*

"Bg

©4928
- 5840
1959
o3702
2438
eo 1133
00302
e0203
~0448
~0823
«1096
01335
1662
2888
3353

H
ccl,

1.14
0.90
0.47
0.87
0.575
027
07
005
e105
0195
e255
31
0 59
067
- 78

H, 29

«666
« 526
0257
- 508
2536
- 158
-041
e029
~061
-114
e149
181
0228
0592
456

1.352
1.37

1.512
1.372
1.378
1.394
1.358
1.428
1.36

1.385
1.36

1.355
1.572
1.356
1.568
 
g

~~
OVWDAMMEAN HH

ro PE
SOODAMMEMED

Time
SeCe

240
180

180
120
120
180
210
120
120

LOSSES THROUGH STRAIGHT GLOBE VALVES

Lbs.of

Water

476
514.
525
597.5
698.5
774.5
861.5
611.0
666.0
872.5
972.0
514.0
437.5

460.

421.5
389.5
368.0
$3320
509 .0
243.5

Quant.
Cu.Ft.

/ Sec o.

eOSl1
00342
00466
«0530
0619
e0687
00764
008138
0886
00774
00738
00684
00581
00614
0561
e052

00491
00444
00412
00325

y*
2B

00314
0383
00705
00915
L250
01533
e140
e216
e257
e196
e178
e153

elll

0123

e101

0885
~0785
00633
00545
00545

H
He

007
ell
014
o19
o26
edl
2 59
045
o 51
041
2 58

954

022
025
e20
018
e16
0125
e115
007

H
H,0

e882
1.585
1.764
2.39
52275
5.905
4.92
5.67
6.42
5.17
4,79
4.28
2077
5.15
2252
2.27
2.015
1.575
1.45

«882

Average Coefficient 2.605

aN

SSSSreesasesss = &

OND NNNWNHNNNW DD WW
oeoe ete eee e eo © © @© @

te 0
e® ®@
Cn
=3

~ %
eee
O & O1
OwWO WJ

2-56
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Cao

| |

 
g

ODIO MA he OH

Time
Sec.

240
180
180
180
180
180
120
120
180
210
120

LOSSES

Lbs.of
Water

467.0
525.0
597.5
698.5
774.5
861.5
611.0
666.0
872.5
972.0
514.0
437.5
460,5
421.5
3589 5
$68.0
535.0
509 20
243.5
196.0

THROUGH ANGLE GLOBE VALVES

Quant.
Cu.Ft.
/ Sec.

e031

0047

e053

0169
0687
00764
0813
0888
00774
e0739
0684
0583
00614
0561
0052

0491
00444
00412
©0325
e0262

06
0062
005
0042
004
0033
003
002
0012

H,0

252
« 504
«630
e 756

eL1007

1.260
1.588
1.639
1.388
1.260
1.1352
o 756
o 782
063
053
«504
416
0578
e252
e151

Average Coefficient

Fé

8.14
7.15
6.88
6.04
6.53
6.64
6.43
6.38
7.09
7207
7.41
6.81
6.35
6.25
6.06
6.435
6.56
6.93
751
6.78

6.761
a
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es aes a

ona Showing relation Recents
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in Merny aT

{

AGRI Went 27,2 A oY'7-) aa AY 77> A 0) a
| Angle Globe Velves ina

(acc? 7S haf toe tame a aad ee
. .

 

Tad sat ay.
| | Dilference af. Head _ in Feet | of Water. tdeses ees ries

0.6

 

eho)

Le laa 1.6

 
Run

WO 3H om 60

LOSSES THROUGH GATE VALVES

Time Lhsa.of

3aC~6

120

120
150
120

120
150
120

120
90

Water

212.0

-508.5

569.5
638.5
702.0
766.0
794.0

1065.

775.0
740 .0
682.5
625.5
762.0
547.0
471.0
428.0
392.0
367.5
523.0
229 .0

Quant.
Gu.Ft.
[ Sec.

0282
00676
00757
00848
009535
01019
«1056
1133
«1030
0985
20907
e0831
0811
00727
00627
~0569
00521
~0488
00430
00406

Average Coefficient 1.1127

y*
ee

e0260
01494
01872
o2552
2848
e 5390
5642
4205
05478
5176
2690
o 2257
£151

| oe LFB4

01284
©1058
~0888
«0780
~0605
0539

oll

228
0187

070
e064

46

1.115
1.057
1.094
1.119
1.088
1.085
1.077
1.071
1.091
1.121
1.108
1.138
1.060
1.083
1.136
1.105
1.182
1.191
1.158
1.186
 

 

     

 

 

uiie a eee iia ng |
| | | | | | |
| ae ce wa40M 4° PoE aed lad Rake 6
| Seas SERED OE re 02 rae aay
| | |
'
| Cle A Lee eae AT
FA STRL ISS DEOX) ANOF puw sup FAQ soacrad Lote
VATS yA Pee

 

 

 

 

 

REPLY rAd

“woizo/ay)

< =

ie

;

 

 

 

 

VL hh,
“4

Y

 

 

neat ae)

. :
ehh kek Wao ooh? Eee eRe

Va vat TALI)

} | j
a fa EE gn
) )

 

 

 

er 2

;

 

 

 

 

 

 

 

 

 

 

 

 

 
Time

Run sec.

OO WH OP OD!

120

Los.of

Water

$49 .0
586.5

470.5
512.0
578.5
648.5
673.0
761.0
812.

833.5
943.0
858.0
777.5
720.

698.0
656.0
538.0
466.0
414.0

Quant.
Cu. Ft.
Sec.

0464
00513
«0563
00625
0681
~0768
00863
~0895
«1012
« 1080
1109
01255
e1141
01054
0958
©0929
00873
00715
©0620
«0550

yt
fg

-0705
~0861
01037
«1281
~1518
©1928
«2438
©2618
05547
« 3809
+4028
- 5158
04253
«5508
«2999
2821
02492
01673
01257
-0988

LOSSES THROUGH FLANGES

a:
CCl,

«10
o12
o14
ol’
220
026
eOl
0 34
043
- 46
2 5S
067
255
045
041
057
053
025
oL7
014

e058
e070
e082
099
ell?
0152
e181
198
0251
268
e510
0592
e521
02635
0239
e216
0193
0134
099
e082

Average Coefficient

4&

e823
«813
e791
0772
0772
« 789
o 143
« 756
o 749
e 708
« 770
e 760
« 756
o 749
27197
« 766
775
~801
788
829

07781
 
OO 3K OTH

Time
Run sec,

120

Lbos.of

Water

970.0
909.0
860.5
788.0
653.0
598.0
539 .0
468.0
349.0
195.5
179.5
256 .0
277.5
349.0
386.5
423.0
470.5
512.0
578.5
648.5

LOSSES IN UNIONS

Quant.
Cu. Ft.
Sece

129

©1208
01144
1048
-0869
00796
00717
0623
00464
~0260
00239
00314
~0369
00464
00513
00562
0625
«0680
«0770
0862

Average .9511

y*
Be

e 5449
04772
04285
3597
~ 2470
2071
o1678
el272
0705
0221
0187
0322
0445
0705
0862
ei1031
1276
21513
01937
e 2426

H
cl,

86
077
°69
« 58
041
054
28
21
ell
0035
e025
0045
007
ell
014
017
21
025
032
2 59

H
H.0

503
«450
0402
0509
«240
199
e164
0123
0064

e0Z0 -

e015
0026
e041
e064
e082
2099
0123
2 146
0187
228

4 &

0924
0943
938
0943
0971
0961
0977
0967
~908
0905
~803
«808
0922
908
0951
0959
0965
0964
966
9359
 

a so ——. aa :

Sc aS el aA Ea

:
.

 
J
HOWD IO MR ODE

DO eS ee SY
OCWDUMHNHAD

Time
Run Sec.

120

Lbs.of

Water

673.0
716.0
812.0
943.0
858.0
777.5
720 .0
698.0
538 .0
466.0
$57.0
263.0
212.0
508.5
569.5
638.5
702.0
766.0
794.0

1065.0

LOSSES IN COUPLINGS

Quant.
Cu. Ft.
Sece

~0896
«1013
e LO80
01255
01141
1034
09 58
00929
00715
©0620
00474
00349
e0282
00677
00757
0848
00933
«1019
« 1056
01134

yt
eg

2626

53562
«5809
- 5158
©4253
«3508
02999
£821
ol67Z
«2156
00735
00398
0260
01495
01872
22552
«2848
05397
5642
«4220

H

CCl,

020
026
029
041
054
228
0Z5
022
014
010
06
003
002

H

H 20

0117
0152
169
«240
e199
0164
0146
e128
e082
058
e035
©0175
0117
«070
087
elll
0134
158
e172
0193

Average Coefficient

4&

0445
0452
0444
0465
468
468
2 486
0454
489
0462
0476
2 440
451
468
464
0478
465
0473
452

4633
eaeuert

Pe LOne

 
Run gec.

bal Bd fad ad fad fal Bad ft fd ed
Sob Eane ew OCesonannl

120

LOSSES THROUGH STRAIGHT TEES

Lbds.of
Water

323.0
362.0
593.0
419.6
450 .0
479.0
618.0
604.0
729.0
970.0
909.0
860.5
788.0
653.0
698.0
639.0
468.0
403-6

$49 .0
195.5

Quant.

Cu. Ft.

00431
20482
0524
20858
«0600
00639
20692
00806
20973
en291
eifZlil
o1148
21040
20870
20799
e1718
e0624
00539
00466
0261

y*
Eg

206095
007593
208998
210189
eil 7 58
ol S547
015623
e21210
od092L7
o 5449

04789

—@4002

055375
o24752
e208 26
016828
o22717
009485
e0 7120
eO2259

601,

0145
e185
0205
£45
0875
031
036
049
e 70
1.24
1.09
097
083
9 59
° $1

H
Ho

e085
2108
«20
0145
e161
e181
e210
e286
41

e725
e688
e 566
e485
0545
e289
e240

0181

0134
0105
0035

Average Coefficient 1.2884

4 E,

1-595
1.42

1.5355
1.405
1.569
1.355
1.345
1.348
1.327
1.381
1.353
1.315
1.372
1.595
1.452
1.425
1.423
1.412
1.474
1.56
7
 
g

OO 32 Om O19

Time
Sec.

240
180
180
180
180
180

180
210

120

LOSSES THROUGH ANGLE TEES

Lbs.of

Water

476

597.5
698.5
774.5
861.5
611.0
872.5
972.0
437.5
538.0
693.0
827.0
874.0

857.0 |

777.0
725.0
641.5
554.0
470.0

Quant. v* H
Cu.Ft. be CCl,
/ Sec.

0311 00314 019
0466 00706 041
0529 0915 « 55
20619 e 1250 e 76
20687 1533 290
0765 «190 1.15
20813 e216 1.30
00775 e196 1.15
00739 oL78 1.10
e0583 eitll e711
«0720 e169 1.08
00924 e278 1.73
21105 0413 2.58
e1165 2442 2.81
012141 e426 2.75
21035 e550 2.16
0966 504 1.83
08 56 e239 1.40
007389 eiL79 1.075
e0627 e128 e753

Average Ceefficient 3.558

H,0

elll
2840
e521
0444
526
0672
e760
0672
~643
0415
063
1.01
1.51
1.64
1.61
1.26
1.07
e818
©5629
0440

46

5-53
3.41
5.51
3.56
5.45
3.53
5.52
3243
5.61
5.74
5.73
3.64
3.65
5-72
35.78
3.60
3.52
5.43
3.515
5.41
 

a eens

a es
by
E

OM 1M Om GIO

Time
Sec.

120
120

Lbs.of

Water

395.0
431.0
307.5
147.5
143.0
185.0
22540
240.0
263.0
296.20
525.0
562.0
593.0
419.5
450.0
479.0
518.0
556.0
604.0
729 0

Quant.
CuFt.
SeCe

e0526
«0459
00408
~0196
©0190
00246
00296
00519
©0350
00394
20430
~0468
e0522
e0558
20598
o0637
e0689
00739
e0803
09 70

y?
eg

00903
~0986
00544
e0125
-0118
-0198
0287
00332
~0400

* 20508

-0604
00715
-0888
«1019
01167
«1526
e 1552
01787
02112
«5079

Average Coefficient |

LOSSES THROUGH ELBOWS

H
CCl,

0.40

NN
c™

TC) OO) OO 10 WD gO 3 3
SAMACHAR AOHHOREOHODRAS

NOHNHNNNYNNHMWONNHNNHNHWNWWD WW

2.625
 

 

 

 

 

     
       
  

 

 

uaa a2 ; a eek La)
. eh en Elbow

a ee io ss

 

 

D a ; aesscats fi ie it fy . | Lah rts oH) ving FeVation ~~ | ae

pe aire geet acti er el ig

BeeeeceepreseTs tara Bee 907 1214 1a a Ee ae ae

abi Saaae RAEN ies aetet Laos Reed teet dese ste OREN REE 080177, AA Ad

Se eee ee
Distas Setagetsel f . itt Mista te Et i a ci k-inth Fipe. :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

eae bien sscibreaa
aye easihgy | -juee erage fbb et? < ee: eas) |
aT eesitetn §
ence fee ot Water. ob oReaebe Beeibbedts HS Sean e302

 

 

 

 

 

 

 

 

 

 

 
 
ROCIA USE ONLY.

 
 

 
Run sec.

OP bal al ad ad al ed Bk fed ed
SoG Ea aan Owawomaunl

120

LOSSES THROUGH STRAIGHT TEES

Lbs.of
Water

523.0
362.0
593.0
419.5
450 .0
479.0
518.0
604.0
729 .0
970.0
909.0
860.5
788.0
653.0
598.0
539.0
468.0
4036

$49.0
195.5

Quant.

Cu. Ft.

/ Sec.

00431
e0482
0524
e05858
20600
20639
20692
00806
209 73
es291
eiZil
01148
«1040
20870
20799
e1718
e0624
00539
00466
0261

y*
"eB

006095
007593
208998
210189
v11758
oL S547
015623
e21210
ed09L7
05449

04789

4502

055575
024762
e208 26
016828
obfLT17
009485
007120
eO22S9

0145
0185
e205
0245
0875
051
036
049
e 70
1.24
1.09
097
083
9 59
eS1
041]
ed1
o£5
018
206

H.o

085
e108
e120
0143
o161
e161
e210
e286
041

e725
638
o 566
0485
0545
2289
2240

0181

0154
0105
0035

Average Coefficient 1.8884

4

1.595
1.42

1.535
1.405
1.569
1.355
1.345
1.348
1.527
1.331
1.553
1.2515
LeS72
1.393
1.4352
1.425
1.423
1.412
1.474
1.56
 
é

OO 3M OP OVD

Time
Sec.

240
180
180
180
180
180
120
180
210

120

LOSSES THROUGH ANGLE TEES

Lbs.of
Water

476

597.5
698.5
774.5
861.5
611.0
872.5
972.0
437.5
538.0
693.0
827.0
874.0
857.0
777.0
725.0
641.5
554.0
470.0

Quant.
Cu.Ft.

/ 3ec.

0311
00466
e0529
00619
20687
~0765
00813
00775
00739
0583
e0720
00924
e1105
©1165
©1141
21035
0966
0856
00739
0627

y*
£8

o0314
00705
0915
«1250
«1533
«190
216
e196
0178
elll
169
0278
0413
0442
426
«550
504
e259
0179
0128

H

CCl.

19

041

2 55
o 76
90
1.15
1.30
1.15
1.10
071
1.08
1.73
2.58
2-81
2-75
2.16
1.83
1.40
1.075
e 753

Average Ceefficient 3.558

elll
e840
e521
0444
« 526
0672
e 760
0672
»643
0415
063
1.01
1.51
1.64
1.61
1.26
1.07
e818
«629
2440

46

5-53
3.41
5.51
5.56
5.45
3.53
3.52
5243
3.61
3-74
5.73
3.64
3.65
5072
5.78
3.60
3.52
5243
3.515
5.41
 

 
 

by
B

OOWM Oh OIE

fime
Sec.

120
120

Lbs.of

Water

595.0
431.0
307.5
147.5
143.0
185.0
225.20
240.0
263.0
296.20
525.0
562.0
593.0
419.5
450.0
479.0
518.0
556.0
604.0
729 .0

 

LOSSES THROUGH ELBOWS

Quant. v* H
Cu.Ft. bg CCl,
Sece

0526 00903 0.40
0459 0986 32
20408 0544 021
0196 eO125 206
20190 0118 055
0246 0198 209
0296 0287 0125
00319 0332 0155
0350 0400 0185
00394 ° .0508 023
0430 0604 228
0468 0715 035
0522 0888 » 39
00558 1019 041
20598 01167 053
00637 01326 259
0689 01552 70
00739 01787 80
0803 2112 095
20970 » 3079 240

H

H,0

o£54
0187
0125
e055
0032
053
0073
e091
2108
0134
0164
e205
228
240
e510
0345
408
0467
555
-818

Average Coefficient

2
c™

oes @ 0 0@8 6@ 8 ®@

NWHNHWDWHNIDN DW WW W019 TW HS 9 1H WD DD TH ~H
e.h|6©8

ADDON AD vw on cw OV aj ~J or ~~ gl

SAM RAOGROONMGARoOHORAS

2.625
ee