GATE 2025 AG – Question 57
A horizontal-axis wind turbine has 24 m rotor diameter, wind speed 6 m/s, air density $1.23\,\mathrm{kg/m^3}$,power coefficient .3,transmission efficiency .9 and pump efficiency .6. It pumps water through a total head of 20 m. Use $g=9.81\,\mathrm{m/s^2}$ and water density 1000 kg/m³. Find discharge in L/s, to two decimals.
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Correct answer: 49.00 to 50.00
Explanation
Rotor swept area is $A=\pi24^2/4=452.389$ m². Available wind power is $.5\rho Av^3$; useful hydraulic power is $.5(1.23)(452.389)(6^3)(.3)(.9)(.6)=9735.455$ W. Since $P_h=\rho_wgQH$,discharge is $Q=9735.455/(1000\cdot9.81\cdot20)=.0496201$ m³/s, or **49.62 L/s**.