Project ForgeA 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).
Explanation
Overall head balance: H = (losses) + (runner work head) + (exit KE head). 200 = (5+10+2) + Hr + 3.5²/(2×9.8) ⟹ Hr = 200−17−0.625 = 182.375 m. ηh = Hr/H = 182.375/200 ≈ 91.19%.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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