. 
a GENERAL PRINCIPLES OF HYDRAULICS 465 
ul in the hydraulic gradient at the obstruction, due to the loss of head 
used by it. 
407. Chézy’s Formula for Flow in Pipes.—From the equation 
ht oss Ea Be = RN en 
Waf-5 5, of Art, 404, » NE m= 6 /mi, 
where ¢ stands for 29 
This formula, v =¢ ./mi, is generally called the Chézy formula for the 
flow in pipes, 
408. Examples on Flow of Water in Pipes.—-The following ex- 
amples show the application of the formule which have been discussed 
to practical cases. 
(1) A pipe 18 inches in diameter and 6 miles long connects a storage 
_ reservoir A with a service reservoir B. The difference between the levels 
_ in the two reservoirs is 100 feet. It is required to find the rate of dis- 
charge through the pipe and the hydraulic gradient. 
Let v= velocity of water through the pipe in feet per second. 
2 
The loss of head at the entrance to the pipe is 0°45 os (Art. 396). 
~The loss of head due to friction in the pipe is 
-.) a ? _ 445-872. 
12x 1°5 
The head equivalent to is is lost at the outlet into the lower 
_ reservoir. 
Total loss of head = py (0°48 4445-87 +1)= UT 325 
Hotico uur 32 = 100; from which 0= 3°79, 
Discharge in cubic feet per second =7 x 1:52 x 3°79 = 6°697. 
Discharge in gallons per day 
=6°697 x 60 x 60 x 24 x 6°23 = 3,604,808. 
Applying the equation of energy to 1 Ib. of water at the surface of 
the water in A and to the same quantity at a point in the pipe near to 
the entrance, and taking the level of the water in B as the datum level, 
. P y? ABy2 
100=- +—.+0°45—. Hence 100 —- -= ——— = 0°32 foot. 
w 2g 29 g 
The hydraulic gradient may now be drawn as a straight line joining 
a point in the surface of the water in B immediately over the outlet end 
of the pipe, with a point immediately over the inlet end of the pipe and 
0°32 foot below the surface of the water in A. 
It is obvious that in examples of this kind, where the pipe is very 
long, the only important loss of head is that due to friction in the pipe, 
and the other losses may generally be neglected. 
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Pe eS 
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2¢ 
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