Page 128 - ebook fluid mechanics_finalize

FLUID MECHANICS

Example 5.4

Water from a large reservoir is discharged to atmosphere through a 100 mm diameter

pipe 450 m long. The entry from the reservoir to the pipe is sharp and the outlet is 12 m

below the surface level in the reservoir. Taking f = 0.01 in the Darcy formula, calculate the
discharge (refer to Figure 5.6).

Solution to Example 5.4

Apply Bernoulli’s theorem to A and B, assuming velocity at A is zero and that pA = pB =

atmospheric pressure

Total energy at A = Total energy at B + loss at entry + frictional loss

v 2 1 v 2 4 fL v 2
H = + +
2 g 2 2 g d 2 g

Putting H = 12 m, f = 0.01, L = 450 m, d = 100 mm = 0.1 m

v2  1 4 fL 
H =  +1 + 
2 g  2 d 

.
0
v 2  4  01  450  v 2
12 =  5.1 +  181= 5 . = v 1= . 14 m s /
2g  1 . 0  2 g

 d 2  ( ) 1.0 2
Discharge, Q = v = ( 14.1 ) = . 8 96 10 − 3 m 3 s /
4 4

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