What is the 100 mm diameter taken to be in the solution?

The diameter of each jet at the nozzle outlet

How is 2.59 treated to get the number of jets?

Rounded up to the next whole number, 3

2072 Kartik · 4 marks

Number of jets of Pelton wheel (300 m, 1.5 m³/s)

Short answer

Jet velocity is 73.65 m/s and each 100 mm jet carries 0.5785 m3/s; 1.5 m3/s divided by this gives 2.59, so use 3 jets.

Water is being supplied to a Pelton wheel under a head of 300 m through 100 mm diameter pipes. If the quantity of water supplied to the wheel is 1.50 m³/s, find the number of jets in the wheel. Assume coefficient of velocity is 0.96.

Interpretation

The 100 mm diameter is taken as the diameter of each jet (nozzle outlet). Head $H = 300$ m, $C_v = 0.96$ , total $Q = 1.5\ \text{m}^3/\text{s}$ .

Velocity of jet

V_1 = C_v\sqrt{2gH} = 0.96\sqrt{2 \times 9.81 \times 300} = 73.65\ \text{m/s}

Discharge through one jet

q = \frac{\pi}{4}d^2V_1 = \frac{\pi}{4}(0.1)^2 \times 73.65 = 0.5785\ \text{m}^3/\text{s}

Number of jets

n = \frac{Q}{q} = \frac{1.5}{0.5785} = 2.59 \approx 3

Answer: 3 jets (the next whole number above 2.59).

✓ Answer checked by Claude Opus 5.5 (high effort)

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Number of jets of Pelton wheel (300 m, 1.5 m³/s)

Interpretation

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Discharge through one jet

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