Power And Efficiency

Step 1: Understand the power-momentum relationship.
The power

P

produced by the turbine is related to the rate of change of momentum tangential to the rotor. The formula for power in terms of momentum is:

P%20%3D%20%5Cfrac%7Bd(mv)%7D%7Bdt%7D%20%5Ctimes%20v

Where: -

P%20%3D%2050%20%5C%2C%20%5Ctext%7BkW%7D%20%3D%2050%20%5Ctimes%2010%5E3%20%5C%2C%20%5Ctext%7BW%7D

(Power), -

v%20%3D%20400%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

(blade mean speed), -

%5Cfrac%7Bd(mv)%7D%7Bdt%7D

is the rate of change of momentum. Step 2: Calculate the rate of change of momentum.
Rearranging the equation:

%5Cfrac%7Bd(mv)%7D%7Bdt%7D%20%3D%20%5Cfrac%7BP%7D%7Bv%7D%20%3D%20%5Cfrac%7B50%20%5Ctimes%2010%5E3%7D%7B400%7D%20%3D%20125%20%5C%2C%20%5Ctext%7BN%7D

So, the rate of change of momentum tangential to the rotor is 125 N. Final Answer:

%5Cboxed%7B125%20%5C%2C%20%5Ctext%7BN%7D%7D

Chapter Questions
1 MCQs