GATE 2018 ME (ME2) – Question 55
A one-fifth-scale Francis turbine model is tested at head 2 m, volume flow 1 m³/s and 450 rpm. Take water density 10³ kg/m³ and g = 10 m/s². Assume no losses in model or prototype. Find the power (MW) of the full-size turbine at head 30 m, to two decimal places.
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Correct answer: 28.85 to 29.25
Explanation
Geometrically similar turbines obey $Q\propto D^2\sqrt H$. Diameter ratio is 5 and head ratio is 15. Therefore $Q_p=1(5^2)\sqrt{15}=96.8246$ m³/s. Ideal power is $\rho gQ_pH_p=1000(10)(96.8246)(30)=$ **29.05 MW**.