Water flows 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.
To calculate the rate at which mechanical energy is transferred to the turbine blades, we need to calculate the power transfer.
First, we need to find the potential energy of the water as it falls vertically. The potential energy can be calculated using:
Potential Energy = mass * gravity * height
Where:
mass = 660 kg/s (rate of water flow)
gravity = 9.8 m/s² (acceleration due to gravity)
height = 86 m
Potential Energy = 660 kg/s * 9.8 m/s² * 86 m
Next, we need to find the power transfer rate by calculating the change in potential energy per unit time:
Power Transfer Rate = Potential Energy / Efficiency
Efficiency = 53% = 53/100 = 0.53
Power Transfer Rate = (660 kg/s * 9.8 m/s² * 86 m) / 0.53
Now we can calculate the power transfer rate to the turbine blades.