(a) Windmills convert kinetic energy of wind into mechanical energy. Using the kinetic energy conversion theory, derive the expression for available total power Protal in a wind stream. [7 marks] (b) The wind stream intended for use by a small propeller type horizontal axis wind turbine (HAWT) has the following wind characteristics: Average speed of wind V, is 3.8 m sec : The turbine design diameter is 2.5 m; The turbine design operating speed N is 36 rev/min at maximum efficiency. Using the wind characteristics and turbine design data given above, calculate the following: (1) Total power Pronal expected to be produced; [3 marks] (ii) The maximum obtainable power density assuming efficiency -39% [3 marks] (iii) The torque T. [7 marks]