Question

power generated by a windmill in watts, is proportional with a constant of proportionality of 5) to the density of the area swept out by the windmill rotor blade, and the cube of the velocity of the wind. (a) write the given verbal description as where is the power (W), D is the density of the air (k/m). A is the area swept out by the rotor blade (m2), and is the velocity of the wind (m/s) PED, AV (b) Suppose and A are held constant. Describe the impact on Pif the wind velocity, V. is doubled If the velocity is double the power will be times as much (C) Suppose and we hold constant. Describe the impact on Pif the wind velocity, Vis triple If the velocity is tripled the power will be times as much (d) Suppose and Aareh onant Describe the impact on Pif the wind velocity viscut in half If the velocity is cut in all the power will be times as much

Answer 1

given, Power & Deninity of air (1) Power & Area a swept by blade swept by blade (A) Power & (velocity of wind)? So totally Power (1) = K DAVSI whel ka 2 given (P=%DAVI a) /P(D, A, v) = 1 DAN watts is D&A au constant and velocity is doubled, Po v= 2V to equatim becomes PLD, A, 0) = 1 DA (20² - 8 DAV3 SP(OAV) = 4 DANI so power is. 8 times more whin ves doubled .

c) y velocity is tugled PLO,A,U) = LDA (3 v² = 27 DAV? so power increases 27 times is vis tripled d) If vis halfed Plo, A, 0) – VDA (2) - 4 - so power decreases by 16 halged. times is vis