Question

2 (b) A blade of a wind turbine can be considered as a thin rod, of mass m, length a and cross- sectional area A. (i) Show that the moment of inertia of the blade about an axis passing through its centre of mass and perpendicular to its length is 1 = izma? [8] (ii) By applying the parallel axis theorem or otherwise, deduce the moment of inertia of the blade about an axis passing through one end of the rod and perpendicular to its length. 141 (iii) A cylindrical volume of air passes through the area swept out by the turbine's blades each second. The air has density p and velocity vi before it reaches the turbine, and velocity Ve after it has passed the turbine. Determine the change in kinetic energy of the air as it passes the turbine. 151 (iv) Determine an expression for the power generated by the turbine, assuming that no energy is lost in conversion. (v) Calculate the power generated by the turbine if a is 100 m, pis 1.2 kg m, viis 10 m/s and vf is 0 m/s. (vi) Could this be power be achieved in reality? Explain your answer,

Answer 1

dm 1 dmade moment of inertia of am total m. I I dI = dm. antall - = lai doar x - -a/2) all سااعه -all a = { 2 - (-2)] = [2 as a Io from - Ip - Tot m car Parallel exis theorem on mat Jo - 103 M ACE = I m cury = I evcrri) (Vanah) P=0.018 - Led (0) - - & exa3v = -x 112 xâx (10033x 10² (P= 1.8840109 t Not really aschied