Question

A penstock is 3000 meters long. Pressure wave travels in it with a velocity of 1500 m/s. if the turbine gates are closed uniformly and completely in a period of 4.5 seconds, then it is called:

1. rapid closure
2. slow closure
3. sudden closure
4. uniform closure
5.

Answer 1

Correct Answer - Option 2 : slow closure

Concept:

Critical Time of closure is given by:

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

Where 2L/C = Time taken by pressure wave to travel from the valve to the tank and from tank to valve.

L = Length of pipe, C = Velocity of pressure wave

(i) The valve closure is gradual if, \({t_c} > \frac{{2L}}{C}\)

(ii) The valve closure is sudden if, \({t_c} < \frac{{2L}}{C}\)

Calculation:

Given,

L = 3000 m, C = 1500 m/s, t_c = 4.5 second

Critical time of closure, \({t_c} = \frac{{2L}}{C}\)

⇒ \({t_c} = \frac{{2 \ \times\ 3000}}{{1500}} = 4\sec \)

∵ t_c (4.5 sec) > 4 sec, So it is the condition of gradual closure (slow closure).