Thermodynamics - Calculate power and dimensions of piping

[NathanLeduc1]

Homework Statement

500 kg/hr of steam drives a turbine. The steam enters the turbine at 60 bara and 500C at a linear velocity of 5.0 m/s. After driving a set of turbine wheels to generate shaft power, the steam exhausts from a pipe that is 10 m below the entrance pipe at 35.0 m/s and at 2.5 bara and 225C. The turbine has an exposed area of 20 m^2 with an average temperature (Ts) of 105F while the factory average air temperature is 75F. The average heat transfer coefficient, h, is 2.5Btu/(hr*ft^2*F) and the heat loss form the turbine can be calculated by q = hA(Ts - Tair).
a) How much power (rate of work) is delivered to the turbine's shaft?
b) What is the area of the pipe at the inlet and outlet?

Homework Equations

q=hA(Ts - Tair)
U + (1/2)v^2 + gz = Q - w

The Attempt at a Solution

I've calculated the heat loss from the turbine to be 16150 Btu/hr. However, I have absolutely no idea where to go from here. I would love to provide a more detailed attempt but I am completely at a loss as to how to even begin this problem. Thank you.

 

[KataKoniK]

Hi there,

First of all, great job on calculating the heat loss from the turbine. That's an important step in solving this problem.

To find the power delivered to the turbine's shaft, we can use the energy conservation equation:

U + (1/2)v^2 + gz = Q - w

Where:
U = internal energy of the steam (not relevant in this case)
v = velocity of the steam
g = acceleration due to gravity
z = height difference between inlet and outlet pipes
Q = heat energy added to the steam
w = work done by the steam on the turbine's shaft (what we're trying to find)

Since we know the initial and final velocities of the steam, we can calculate the change in kinetic energy (1/2mv^2) and the change in potential energy (mgz) and plug them into the equation. We also know the heat loss from the turbine (Q), so we can rearrange the equation to solve for w (power delivered to the shaft).

For part b), we can use the ideal gas law to find the volume of the steam at the inlet and outlet, and then use the equation for linear velocity (v = Q/A) to solve for the area.

I hope this helps and gives you a starting point for solving the problem. Let me know if you have any other questions or need further clarification. Good luck!