Page 200 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch05_154-193.qxd 8/2/10 9:44 PM Page 162

162 Chapter 5 Water Hydraulics, Transmission, and Appurtenances

Solution 2 (SI System):
Velocity, v Q>A
3
2
(0.0445 m /s)>[(0.300 m) 0.785]
0.62 m/s
Reynolds number, R vd >
3
2
(0.62 m/s)(0.300 m)(0.851 1,000 kg/m )>(0.1 N-s/m )
1,580 2,000, which indicates a laminar flow
Friction factor, f 64>R
64>1,580
0.041
2
Head loss, h f f(L>d) (v >2g)
2
2
(0.041)(3,048 m/0.300 m)(0.62 m/s) >(2 9.81 m/s )
8.2 m

EXAMPLE 5.3 RATIO OF HEAD LOSS IN A PIPE TO THAT IN A PERFORATED PIPE
Show that the head loss h f in a pipe is equal to three times the head loss h f in a perforated pipe,
having the same length, diameter, and friction factor.
Take the flow in the unperforated pipe as Q 0 ; assume a straight-line variation of the flow Q
with distance in the perforated pipe, with Q Q 0 at the inlet of the pipe and Q 0 at the end of
the line. Consider only losses to pipe friction, and assume no variation in the value of f with a
changing Q.

Solution:
2
h f f(L>d)(v >2g) (5.10a)
Since v Q>A (5.4)
2
2
Then h f f (L>D) (Q >2gA ) (5.16)
2
2
h f ( f>D)(1>2gA )Q L (5.17)
2
h f KQ L
2
Where K ( f>D)(1>2gA )
dx

Q 0
Q x

X
I