GATE 2021 ME (ME2) – Question 59
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).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 90.74 to 91.66
Explanation
The head converted into runner work is available head minus hydraulic losses and residual discharge kinetic head. Exit kinetic head is $3.5^2/(2\times9.8)=0.625$ m.
Useful head=200−5−10−2−0.625=182.375 m. Thus $\eta_h=182.375/200=\mathbf{91.2\%}$ after rounding. Flow rate cancels in the power ratio.