Page 190 - Water Engineering Hydraulics, Distribution and Treatment

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EXAMPLE 5.58 PRESSURE INCREASE DUE TO SUDDEN STOP OF FLOW
Determine the expected increase in pressure if the liquid flow is suddenly stopped assuming the following:
1. 12 in. (0.3048 m) rigid pipe.
2. Liquid in pipe is oil with a specific gravity of 0.8.
3. Flow velocity is 4 ft/s (1.22 m/s).
2
2
4. Bulk modulus of oil is 200,000 lb/in. = 200,000 × 144 lb/ft (138.8 × 10 N/m ).
Solution 1 (US Customary System):
0.5
c = (E ∕ )
B
and Chapter 5 Water Hydraulics, Transmission, and Appurtenances 7 2 (5.54)
= ∕g.
0.5
c = (200,000 × 144∕0.8 × 62.4∕32.2) .
c = 4,310 ft∕s.
(ΔP) = c (Δv) (5.53)
( P) = ( ∕g) c (Δv)
= (0.8 × 62.4∕32.2) (4,310)(4 − 0)
= 26,700 lb∕ft 2
2
= 185 lb∕in. .
Solution 2 (SI System):
c = (E ∕ ) 0.5 (5.54)
B
7 0.5
c = [(138.8 × 10 ∕(0.8 × 1,000)] .
= 1,317 m∕s.
(ΔP) = c(Δv) (5.53)
= (0.8 × 1,000) (1,317) (1.22 − 0)
= 1,285,400 N∕m 2
2
= 1,285.4kN∕m .

EXAMPLE 5.59 PIPE TENSILE STRESS DUE TO SUDDEN VALVE CLOSURE
◦
◦
A 48 in. (1,219 mm) steel pipe 3∕8 in. (9.525 mm) thick carries water at 60 F (15.6 C) and a velocity of 6.5 ft/s (1.98 m/s). The pipe is
11,000 ft (3,353 m) long. Assume the steel pipe is elastic and non-rigid and its celerity was determined to be 3,155 ft/s (961.6 m/s).
Determine
1. The time of travel of the pressure wave upstream and back (round-trip).
2. The increase in water pressure within the pipe.
3. The tensile stress in the pipe, if the valve is closed in 2 s.
4. Discuss how the water hammer can be avoided.

Solution 1 (US Customary System):
1. The time of travel of the pressure wave upstream and back (round-trip):
t = 2L∕c (5.52)
t = 2 × 11,000 ft∕(3,155 ft∕s)
t = 7.0s.