Question

A vertical shaft Francis turbine rotates at 300 rpm. The available head at the inlet to the turbine is 200 m. The tip speed of the rotor is 40 m/s. Water leaves the runner of the turbine without whirl. Velocity at the exit of the draft tube is 3.5 m/s. The head losses in different components of the turbine are :

(i) stator and guide vanes: 5.0 m,

(ii) rotor: 10 m, and

(iii) draft tube: 2 m.

Flow rate through the turbine is 20 m³ /s. Take 𝒈 = 9.8 m/s² . The hydraulic efficiency of the turbine is ______________ % (round off to one decimal place).

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Answer :

Correct answer is : 91.87

Hinlet = 200 m, HL, stator + Guide = 5 m, Hrotor = 10 m, Hdraft tube = 2 m, V3 = 3.5 m/s, g = 9.8 m/s2

From equation (i)

200 = Hturbine + 5 + 10 + 2 +  3.5 2 2 × 9.8

Hturbine = 182.375 m

η H = H t u r b i n e H i n l e t 182.375 200 = 0.9118 = 91.87 %

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