Turbine Efficiency: Calculating Power & Combined Efficiency

[TyErd]

Homework Statement

I have attached the question. I'm not really sure how to do this one

Homework Equations

power = work done/time

The Attempt at a Solution

Is the turbine efficiency simply the power generation (750kW) divided by the mechanical output (800kW) which is so 750/800 x 100 = 93.75% efficiency?

and then there's the combined turbine generator efficiency. How do you do that?

 

[1994Bhaskar]

No it's not what you think.

 

[1994Bhaskar]

You have been given rate of mass flow, height of water(70m). Calculate gravitational energy being converted (mgh).It gives potential energy converted per second.

 

[TyErd]

so i simply do 1500(9.81)(70) = 1030050 J/s ? then what

 

[1994Bhaskar]

Then you know the mechanical power output of turbine.Remember the power from potential energy can only be used by turbine and not by generator.
((800kW)/(1030050))*100
Is efficiency of turbine.

 

[1994Bhaskar]

I think answer's coming out to be 77.66% for turbine efficiency if you do the calculations.

 

[TyErd]

ohh I get it, because j/s is watts - power. okay so then what is the electric power generation and the combined turbine-generator efficiency. is it simply (750000/1030050) x 100?

 

[1994Bhaskar]

No.Just apply unitary method.
800kW of mechanical output gives 750kW of electrical output.
1W of mechanical output gives (750/800)W. ---equation (1)
(kW get cancelled.You can Multiply 1W to both sides)
We know efficiency of turbine as 77.66%.
This means that when 100W of energy is inputted to turbine 77.66W of energy is it's mechanical output.
Now multiply 77.6 to equation (1). answer is on right hand side-((750/800)*77.6).It comes around 72.81%

 

[TyErd]

Ahh okkay thank you i get it now