Question

A Pelton wheel develops 5520 kW under a head of 225 m at an overall efficiency of 80% when revolving at a speed of 300 rpm. Then the unit speed is

• A. \( 10 \)
• B. \( 15 \)
• C. \( 20 \)
• D. \( 25 \)

Hint:

Unit quantities (unit speed, unit discharge, unit power) are important concepts in hydraulic turbines as they allow for the comparison of performance of different turbines or the same turbine under varying conditions by normalizing their performance to a unit head. These parameters are constant for a given turbine under different heads and speeds.

Answer 1

The Correct Option is C

Step 1: Identify the given data.
Power developed, \( P = 5520 \, \text{kW} \)
Head, \( H = 225 \, \text{m} \)
Overall efficiency, \( \eta_o = 80% = 0.80 \)
Speed, \( N = 300 \, \text{rpm} \)
We need to find the unit speed, \( N_u \).
Step 2: Recall the formula for unit speed.
The unit speed (\( N_u \)) of a turbine is the speed at which a geometrically similar turbine would run under a unit head (1 meter). It is given by the formula:
$$N_u = \frac{N}{\sqrt{H}}$$
Where:
\( N \) = Actual speed in rpm
\( H \) = Actual head in meters
Step 3: Substitute the given values into the formula and calculate \( N_u \).
$$N_u = \frac{300 \, \text{rpm}}{\sqrt{225 \, \text{m}}}$$
First, calculate the square root of the head:
$$\sqrt{225} = 15$$
Now, substitute this value back into the unit speed formula:
$$N_u = \frac{300}{15}$$
$$N_u = 20$$
Step 4: Select the correct option.
Based on the calculation, the unit speed is \( 20 \).
$$\boxed{20}$$