Question

Thermodynamics.

2. A circular windmill with a 7-m diameter rotor is used to pull the air from a narrow channel to a wider channel, slowing the air. The wind enters the narrow channel at 8 m/s on a day with atmospheric pressure is 100 kPa and the air temperature is 20°C. If the wind speed downstream of the rotor is measured at 6.5 m/s, determine the diameter of the wider channel and the power produced by the windmill. Due to the low speeds at which the air is traveling, you can assume that the air is incompressible and that both the narrow and wide channel are open to the atmosphere. Flow channel

Show all the steps, calculations and thought process.

Answer 1

Calculate density of air from ideal gas equation RT 100 kPa (0.287 kJ/kgK)×(20+273) K = 1.189 kg/m3 Calculate the mass flow rate of air. kg π = 1.189 m, x 4(7 m)2 x(8 m/s) 366.06 kg/s

From the energy equation, the power required is due to kinetic energy. Therefore, v2-v2 ( ) 82 -6.52 366.06 3980.9025 W W 3.98 kW Calculate the diameter of wind channel from conservation ofmass relation. maiAV 366.06 kg/s -1.189 (d) x(6.5 m/s) d, - 7.766 m m 4