Topic: Fluid Mechanics
A Pelton wheel turbine operates under a head of 125 m at a speed of 2000 rpm. To operate very close to the maximum efficiency, the mean diameter of the Pelton wheel is nearly
- A. 24 cm
- B. 48 cm
- C. 12.5 cm
- D. 36 cm
Answer: A. 24 cm
Explanation: Assuming a coefficient of velocity $C_v = 1$, the theoretical jet velocity is $V = \sqrt{2gH} = \sqrt{2 \times 9.81 \times 125} = 49.52 \text{ m/s}$. To achieve maximum efficiency, the blade (bucket) speed $u$ must be approximately half of the jet velocity, thus $u = 49.52 / 2 = 24.76 \text{ m/s}$. Using the formula for tangential velocity, $u = \frac{\pi D N}{60}$, we can write $24.76 = \frac{\pi \times D \times 2000}{60}$. Solving for diameter gives $D \approx 0.2365 \text{ m}$, which translates to 23.65 cm, nearly 24 cm.