Pelton wheel 70 kW: flow rate and diameter

Data

$P = 70$ kW (shaft), $H = 100$ m, $N = 400$ rpm, $\eta_o = 0.85$, speed ratio $\phi = u/V_1 = 0.46$, penstock 200 mm.

(i) Volumetric flow rate

$$Q = \frac{P}{\eta_o \gamma H} = \frac{70}{0.85 \times 9.81 \times 100} = 0.0839\ \text{m}^3/\text{s}$$

($= 83.9$ litres per second; velocity in the 200 mm penstock $= 2.67$ m/s.)

(ii) Wheel diameter

Jet velocity (taking $C_v \approx 1$, as no nozzle coefficient is given): $V_1 = \sqrt{2gH} = \sqrt{2 \times 9.81 \times 100} = 44.29$ m/s.

Bucket speed $u = 0.46 \times 44.29 = 20.37$ m/s.

$$D = \frac{60u}{\pi N} = \frac{60 \times 20.37}{\pi \times 400} = 0.972\ \text{m}$$

(If $C_v = 0.98$ were used, $V_1 = 43.40$ m/s, $u = 19.97$ m/s and $D = 0.953$ m.)

Answer: $Q = 0.0839$ m³/s; wheel diameter $\approx 0.97$ m.