How can you determine the mass flow rate

[darkmagic]

Homework Statement

How can you determine the mass flow rate, given that net power output is 100 MW, of the cooling water if it enters the condenser at 20 C and leaves at 35 C.

Homework Equations

The Attempt at a Solution

I thought that mass flow rate is the same all through out. I have the power and the net work but the required is mass flow rate at those given temperature.

The question is from the rankine cycle.

 

[darkmagic]

How can the problem be solved, the mass flow rate of the cooling water at the condenser?

 

[Marcheline]

You have the power lost at 100MW.

The heat lost is absorbed by the water, making it's temperature rise from 20 C to 35 C.

$$\dot{Q}$$ = $$\dot{m}$$$$C_{p}$$$$\left(T - Ti)$$

That's the mass flow-rate you require to achieve the required heat loss.

 

[darkmagic]

Q is the Q out at the condenser and the cp is the specific heat at constant pressure of water?

 

[Marcheline]

$$\dot{Q}$$ in this case is the flowrate of heat, which is measured in Watts.

$$C_{p}$$ is the specific heat of water flowing through a control volume, which in this case is your condensor. Evaluate the specific heat at the mean temperature $$T_{m}$$, which is simply the average between the outlet and inlet temperatures.

 

[darkmagic]

how can i know cp and Q dot?

 

[Marcheline]

$$C_{p}$$ can be found from generic steam tables that list the properties of substances at different temperatures.

$$\dot{Q}$$ is already given to you.

 

[darkmagic]

so Q dot is the 100MW. In what part of the steam table can I find the cp values?

 

[darkmagic]

Here is an example problem:

net power output is 45MW
Turbine inlet pressure and temperature are 7MPa and 500C
Condenser pressure of 10kPa
Cooling water rate of 2000kg/s

Find:

thermal efficiency of the cycle
mass flow rate of steam
temperature rise of cooling water

I got the thermal efficiency, which is 38.9% and
mass flow rate of 35.998 kg/s

I do not know the temperature rise.
What should I do?
I do not know where the cp can be found at the steam table.

Additional question:

What can be mean by this?

The heat transfer to the steam in the boiler occurs at the rate of 400000 kW.
Does this mean that the power input in the boiler is 400000 kW? or
This mean that the net power is 400000 kW?

 

[darkmagic]

what do i do next?

 

[darkmagic]

Please someone answer me

 

[darkmagic]

how can this be done?