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 determine the power output of the turbine.
The power output can be calculated using the formula:
Power = Efficiency * Rate of transfer of mechanical energy
First, we need to calculate the rate of transfer of mechanical energy.
The rate of transfer of mechanical energy is given by:
Rate of transfer of mechanical energy = Mass flow rate * Gravitational potential energy
Here, the mass flow rate is given as 660 kg/s, and the height through which the water falls is 86 m.
The gravitational potential energy is given by:
Gravitational potential energy = Mass * Gravity * Height
where Mass is the mass of the water falling and Gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values, we can calculate the rate of transfer of mechanical energy:
Rate of transfer of mechanical energy = (660 kg/s) * (660 kg/s) * (9.8 m/s^2) * (86 m)
Now, we need to calculate the power output by multiplying the rate of transfer of mechanical energy by the efficiency given (53%) and converting it to watts:
Power = (Rate of transfer of mechanical energy) * Efficiency * 100%
Finally, we divide the power by 1000 to convert it from watts to kilowatts:
Power = (Rate of transfer of mechanical energy) * Efficiency * 100% / 1000
Now, we can plug in the values and calculate the power output of the turbine blades.