A 0.5 m diameter concrete pipe (5.0 cm wall thickness with rigid pipe walls) car

Question

A 0.5 m diameter concrete pipe (5.0 cm wall thickness with rigid pipe walls) carries water 600 m before discharging it into another reservoir. The surface elevation of the downstream resevoir is 55 m lower than the supply reservoir. A gate valve just upstream of the lower reservoir controls the flow rate. If the valve is closed in 0.65 seconds, what is the maximum water hammer pressure?

The book gives the equation P=CV, where is the density of water, C is the speed of at which the wave propagates upstream (is also represented by "a" in other textbooks), and V is the original speed of the wave.

How do I find V in this equation, or is this even the equation I should be using? Thanks

Explanation / Answer

the equation you used (P = CV) is correct

But C = (E/water) and

(1/E)=(1/Ewater)+(1/w*Econcrete)

where

Ewater = 2.2*109 Pa,

w = thickness of pipe = 0.05

Econcrete = 30*109 Pa

So E = 1273885350

And hence C = (1273885350 / 1000) = 1128.665

from given data, V2 = 2gh = 2*9.8*55 = 32.88 and V1 = 0

So V = V2 -V1 = 32.83

P = CV = 1000 * 1128.665 * 32.83 = 37.054 MPa

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