Question

A hydraulic turbine has a discharge of \( 6 \, m^3/s \), when operating under a head of 60 m with a speed of 500 revolutions per minute. If it is to operate under a head of 15 m, for the same discharge, the rotational speed in revolutions per minute will approximately be

• A. 2000
• B. 125
• C. 500
• D. 250

Hint:

For turbines and pumps, speed is proportional to the square root of the head for a constant flow rate.

Answer 1

The Correct Option is D

For turbines, the speed ratio is related to the square root of the head ratio. We can write the relation as: \[ \frac{N_1}{N_2} = \sqrt{\frac{H_1}{H_2}} \] Where \( N_1 \) is the initial speed (500 rpm), \( N_2 \) is the final speed, \( H_1 \) is the initial head (60 m), and \( H_2 \) is the final head (15 m). Solving, we get: \[ N_2 = 500 \times \sqrt{\frac{60}{15}} = 250 \]