Mass flow rate of cooling water in condenser needed

[staceybiomed]

Homework Statement

Adiabatic Steam turbine produces 4000 kW
Steam is fed at 21 bar/475 deg C
Exhaust is saturated steam (P=0.1bar)
Exhaust is fed into condenser where it is cooled to 30 deg C

Problem asks for flow rate of cooling water supplied to condensener if water enters at 15 deg C and is heated to 25 deg C

Homework Equations

Turbine:
Assume Q = 0
H2 - H1 = -W
m dot steam * (H2 - H1) = - Power (or W dot)
Condenser:
Power (in) = Power(out)
m dot steam in (H steam in) + m dot water in (H water in) = m dot steam out (H steam out) + m dot water out (H water out)
m2U2 - m1U1 - H'(m2 - m1) = 0

The Attempt at a Solution

i fond the mass flow rate of steam going into turbine using m dot * delta H = -Power
- 4000 kW (1 kJ/s / 1 kW) = m dot steam (2584.8 kj/kg - 3411.3 kJ/kg)
mass flow of steam = 4.84 kg/s

then when i try to use the last equation in the above section I get stuck because I can't
figure out U2 or the outlet states. H' = 2779.7 kj/kg, U1 = 2438.0 kJ/kg, m1 = 25000 kg, m2 =?

please help!

 

[Topher925]

Problem asks for flow rate of cooling water supplied to condensener if water enters at 15 deg C and is heated to 25 deg C

In order to solve this problem you have to assume a pressure for the cooling water in the condenser. I recommend 1 atm.

I don't really understand where you are having a problem. You found the states of the steam entering the condenser and you know the states of the cooling water coming in and out of the condenser. It is a simple energy balance;

dQ_steam/dt = dQ_water/dt

dm_s/dt * (hi - ho)_s = dm_w/dt * (ho - hi)_w

 

[piercas]

To calculate the mass flow rate of cooling water needed in the condenser, you can use the energy balance equation for the condenser:

Power (in) = Power(out)

In this case, the power in is the power produced by the turbine (4000 kW). The power out is the power carried by the steam at the outlet of the condenser. We can assume that the steam is saturated at the outlet, so we can use the steam tables to find the specific enthalpy (H) and specific internal energy (U) at the outlet temperature of 30 deg C (H = 251.86 kJ/kg and U = 251.86 kJ/kg).

We also know the inlet temperature and outlet temperature of the cooling water (15 deg C and 25 deg C, respectively). We can use the specific heat capacity of water (4.18 kJ/kgK) to calculate the specific enthalpy of the cooling water at these temperatures (H = 62.7 kJ/kg and H = 104.3 kJ/kg).

Now, we can plug these values into the energy balance equation and solve for the mass flow rate of cooling water (m dot water):

4000 kW = 4.84 kg/s * (251.86 kJ/kg + 251.86 kJ/kg) + m dot water * (104.3 kJ/kg - 62.7 kJ/kg)

m dot water = 14.63 kg/s

Therefore, the mass flow rate of cooling water needed in the condenser is 14.63 kg/s.