Question

A 60 m diameter rotor experiences an undisturbed wind speed of 10 m/s. If it is operating at maximum cp, calculate: maximum possible thrust on the rotor maximum power developed by the rotor torque developed at maximum power. Take air density as 1.165 kg/m2

Answer 1

Answer:

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Answer 2

Given : Diameter D = 60m

          :Wind speed $V_{air}$ =  10 m/s.

         :Air density $\rho$ =  1.165 kg/m2

         :$C_{pmax}$ = $\frac{16}{27}$

To calculate : Maximum possible thrust $T_{max}$ on the rotor

$T_{max}$ = 0.5$\rho A_{D}V_{air} ^{2}$

$T_{max}$ = 0.5x 1.165 x $\frac{\pi}{4}$ $60^{2}$ x $10^{2}$

$T_{max}$ = 164.69 kN

To calculate: Maximum power developed by the rotor

Maximum power $P_{max}$ = $C_{pmax}0.5\rho A_{D}V_{air} ^{3}$

$P_{max}$ = $\frac{16}{27}$ x 0.5x 1.165 x $\frac{\pi}{4}$$60^{2}$ x  $10^{3}$

$P_{max}$ = 975.98  kW

To calculate: torque developed at maximum power.

$P_{max} = T \ohm$Ω

$\lambda$ = Ω$\frac{R}{V}$

  = Ω $\frac{30}{10}$

Ω = $\frac{2}{9}$

$P_{max} = T \ohm$Ω

975.98 = T $\frac{2}{9}$

T = 4391.91 kNm

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