Correct Answer - Option 2 : 15 N/cm
2
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:
\(p=\frac{\rho VL}{t'}\)
\(p=\frac{1000\times 1.5\times 2500}{25}=15\times10^4\;N/m^2=15\;N/cm^2\)