Show that the power produced by a wind turbine is proportional to the cube of the wind velocity and to the square of the blade span diameter.

A power plant operates in an idealized Rankine cycle, using water as the working fluid (Figure 3). The steam at the exit of the boiler has a pressure of 6 MPa and temperature of 600 °C (point 1). The water at the exit of the condenser has a pressure of 15 kPa (point 3). The condenser employs a nearby river as the cooling source, which can be regarded to have a constant temperature of 25 °C. The mass flow rate of the steam is 80 kg/s. The hot reservoir has a temperature of 1400 K. Regard water as an incompressible liquid. During pumping, the density of water remains unchanged as Point 3 in Figure 3. Qin Boiler i wwwwww Pump Turbine Wp 3 Figure 3 W₁ Cooling water Condenser

A four-stroke turbocharged V-16 diesel engine built by a car manufacturer company to power fast trains produces mechanical 3500 hp (2.609 MW) at 1200 rev/min. Determine the amount of work produced in kJ (a) per cylinder per mechanical cycle and (b) per cylinder per thermodynamic cycle.