When water falls from a height of 80 m at the rate of 20‌kg‌s−1 to operate a turbine the losses due to frictional force are 20% of input energy. How much power is generated by the turbine?
To determine the power generated by the turbine, we need to consider the input energy, losses due to friction, and the rate at which water falls. The potential energy of the falling water can be calculated using the formula: P.E=mgh where: m is the mass of the water per second (20‌kg‌s−1) g is the acceleration due to gravity (9.8ms−2) h is the height from which the water falls (80m) Substituting the values, the potential energy per second is: ‌P.E=20‌kg‌s−1×9.8ms−2×80m ‌P.E=15680J∕s This is the input energy per second, which is also the power input. However, because 20% of the input energy is lost due to frictional forces, only 80% of the input energy is effectively used by the turbine. Therefore, the power generated by the turbine P is:
‌P=15680×0.80 ‌P=12544W ‌P=12.544‌kW Thus, the power generated by the turbine is approximately: Option A: 12.8 kW.