Designing of a steam power plant

[wantedstudent]

Homework Statement

electric power = one million kW
working fluid = steam
maximum steam temperature = 550°C
river mean speed = 10m/min
river,8m deep,60 meter wide

Homework Equations

It is proposed to build a one million kW electric power plant with steam as the working fluid. The condensers are to be cooled with river water (see figure below). The maximum steam temperature will be 550°C. As an engineering consultant, you are to convince the authorities that the discharge to the river will not be harmful to the environment.

The Attempt at a Solution

this question may have several answer

 

[rock.freak667]

Well what is the range of temperatures can the heated water enter the river again at? (35C? Also what the exit condition of the steam turbine? Vacuum/Back pressure? If so you will need that pressure condition.

 

[rude man]

Initial assumptions:
1. Carnot efficiency
2. River entering temperature T_in

Then:
1st equation: 1st law expressed in time-derivative form
2nd equation: 2nd law expressed in time-derivative form
Third equation: temperature buildup of river water as function of dm/dt, c and dQ₂/dt where dQ₂/dt is rate of expelled heat into river, dm/dt = rate of water mass flow, c = water specific heat, J/C-kg.

So: 3 knowns: dW/dt = 1 MW, T₁ = 550C, T_in
3 unknowns: dQ₁/dt, dQ₂/dt, ΔT
where dQ₁/dt = heat rate into system and ΔT = T_out - T_in = temperature rise of river water.

Assume T₂, the effective lower temperature in the Carnot cycle, is halfway between T_in and T_out, i.e. T₂ = (T_in + T_out)/2.

Finally, you must do some research to find what the typical steam-generated electric plant mechanical efficiency is beyond the Carnot efficiency.

 

[wantedstudent]

the the range of temperatures is 6c that is between 32-38c
thanks guys...i will try to finish it up.

 

[DeeNos]

. One possible solution would be to design the steam power plant with a closed-loop cooling system, using a cooling tower instead of directly discharging water into the river. This would ensure that the river is not affected by the temperature of the discharged water. Additionally, implementing measures such as proper filtration and treatment of the cooling water can further minimize any potential harm to the environment. It is also important to consider the location of the power plant and its proximity to other water sources, to ensure that the river is not the sole source of cooling water. Overall, careful design and management of the power plant can ensure that the discharge to the river is not harmful to the environment.