Water flows (v approx. 0) over a dam at the rate of 660 kg/s and falls vertically 86 m before striking the turbine blades. Calculate the rate at which mechanical energy is transferred to the turbine blades, assuming 53% efficiency.
mechanical energy available= mass*g*height
mechanical energy rate= mass/time * g* h
turbine energy= .53*600*9.8*86
To calculate the rate at which mechanical energy is transferred to the turbine blades, we need to calculate the power output of the turbine. The rate at which mechanical energy is transferred can be determined using the following formula:
Power output = Efficiency × (Rate of water flow × Gravity × Height)
In this case, the efficiency is given as 53% or 0.53, the rate of water flow is given as 660 kg/s, the acceleration due to gravity is approximately 9.8 m/s², and the height is given as 86 m.
Plug in these values into the equation:
Power output = 0.53 × (660 kg/s × 9.8 m/s² × 86 m)
First, calculate the value inside the parentheses:
Power output = 0.53 × (563088 kg⋅m²/s³)
Next, multiply this value by the efficiency:
Power output = 298023.84 kg⋅m²/s³
Finally, round the value to an appropriate unit. The unit for power is watts (W), so the rate at which mechanical energy is transferred to the turbine blades is approximately 298024 W.