Question

An impulse turbine produces 50 kW of power when the blade mean speed is 400 m/s. What is the rate of change of momentum tangential to the rotor?

• A. 200 N
• B. 175 N
• C. 150 N
• D. 125 N

Hint:

For impulse turbines, the rate of change of momentum is related to the power and blade speed by \( \frac{P}{v} \).

Answer 1

The Correct Option is A

Step 1: Understand the power-momentum relationship.
The power \( P \) produced by the turbine is related to the rate of change of momentum tangential to the rotor. The formula for power in terms of momentum is: \[ P = \frac{d(mv)}{dt} \times v \] Where: - \( P = 50 \, \text{kW} = 50 \times 10^3 \, \text{W} \) (Power), - \( v = 400 \, \text{m/s} \) (blade mean speed), - \( \frac{d(mv)}{dt} \) is the rate of change of momentum. Step 2: Calculate the rate of change of momentum.
Rearranging the equation: \[ \frac{d(mv)}{dt} = \frac{P}{v} = \frac{50 \times 10^3}{400} = 125 \, \text{N} \] So, the rate of change of momentum tangential to the rotor is 125 N. Final Answer: \[ \boxed{125 \, \text{N}} \]