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Water is flowing with a velocity of 1.5 m/s in a pipe of length 2500 m and of diameter 500 mm. At the end of the pipe, a valve is provided. What is the rise in pressure if the valve is closed in 25 seconds? (Take the value of C as 1460 m/s)
1. 12 N/cm2
2. 15 N/cm2
3. 16 N/cm2
4. 18 N/cm2
5.

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Correct Answer - Option 2 : 15 N/cm2

Concept:

Reference time:

\(T=\frac{2L}{C}\)

where C is the sonic velocity in the pipe.

When t' > T it corresponds to the gradual closure of the valve, where t' is time of closure fo valve.

For gradual closure:

\(p=\frac{\rho VL}{t'}\)

Calculation:

Given:

V = 1.5 m/s, L = 2000 m, D = 500 mm = 0.5 m,

C = 1460 m/s and t' = 25 sec

Reference time:

\(T=\frac{2L}{C}\)

\(T=\frac{2\times 2500}{1460}=3.425\;sec\)

t' = 25 sec

 t' > T it corresponds to the gradual closure of the valve.

For gradual closure:

\(p=\frac{\rho VL}{t'}\)

\(p=\frac{1000\times 1.5\times 2500}{25}=15\times10^4\;N/m^2=15\;N/cm^2\)

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