A horizontal axis drag type wind mill with square blades and a horizontal axis lift type wind mill with airfoil section blades having same rotor size are installed at a height of 10 m above the ground. The average wind speed is 25 km h−1. The maximum power coefficient for drag type and lift type wind mills is 0.148 and 0.593, respectively. If the maximum power extracted by drag type wind mill is 5 kW, the corresponding power extracted by lift type wind mill, in kW is
GATE AG - 2012,
Answer: D
The lift type wind mill extracts about 20.03 kW.
Power extracted is \(P = C_{p} \cdot \tfrac{1}{2}\rho A V^{3}\). Both machines have the same rotor size, height and wind, so the available wind power \(\tfrac{1}{2}\rho A V^{3}\) is the same and the extracted power scales with the power coefficient alone:
\[ \begin{aligned} P_{lift} &= P_{drag} \frac{C_{p,lift}}{C_{p,drag}} \\ &= 5 \times \frac{0.593}{0.148} \\ &= 20.03\ \text{kW} \end{aligned} \]
The wind speed and height are not needed. 0.593 is the Betz limit, the theoretical maximum, which is why the airfoil (lift) machine can extract about four times what the drag machine can. The smaller options do not follow from the ratio.
Please log in or register to report this question.