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A large hydraulic turbine is to generate 300 kW at 1000 rpm under a head of 40 m for initial testing, a 1:4 scale model of the turbine operates under a head of 10 m. The power generated by the model (in kW) will be
1. 2.34
2. 4.68
3. 9.38
4. 18.75

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Correct Answer - Option 1 : 2.34

Given that, Np = 1000 rpm, Dp/Dm = 4, H= 40 m, Hm = 10 m

As per turbine similarity law,

\(\frac{{{N_m}{D_m}}}{{\sqrt {{H_m}} }} = \frac{{{N_p}{D_p}}}{{\sqrt {{H_p}} }}\)

⇒ Nm = 2000

Specific speed will be same also,

\(\therefore \frac{{{N_m}\sqrt {{P_m}} }}{{H_m^{\frac{5}{4}}}} = \frac{{{N_p}\sqrt {{P_p}} }}{{H_p^{\frac{5}{4}}}}\)

⇒ Pm = 2.34 kW.

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