The diameter of downstream channel and power produced by the wind mill

Answer to Problem 121RP
The diameter of downstream channel is
The magnitude of power produced by the wind mill is
Explanation of Solution
Write the expression the specific volume of the air.
Here, specific volume of the air is v, gas constant is R, temperature of the air is T, and pressure of the air is P.
Use the continuity equation, equate velocity of air flow at rotor and wind channel downstream.
Here, area of cross section at rotor is
Write the expression for area in terms of diameter in equation (II).
Here, diameter of the rotor is
Write the expression for the mass flow rate of wind mill.
Here, mass flow rate is
Write the expression for the power produced by the wind mill.
Here, power produced by the wind mill is
Conclusion:
Substitute
Thus, specific volume of the air is
Substitute 7m for
Thus, the diameter of downstream channel is
Substitute 7m for
Thus, mass flow rate is
Substitute
Thus, power produced by the wind mill is
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Chapter 2 Solutions
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