# Example Problem with Complete Solution

5B-1 : Flow Work in a Steam Pipe 2 pts
Steam enters a system at 200 kPa and 350oC and leaves the system at the same mass flow rate at 180 kPa and 350oC.
Calculate the flow work in kJ/kg for this process assuming the usual sign convention in which work done by the system is considered to be positive.

Read : This problem reinforces the point that it takes energy to push fluid into a system and it takes energy to push a fluid out of a system into the surroundings. This energy is called flow work and it can be very significant.
In this problem, we apply the definition of flow work to evaluate the net amount of flow work in a simple flow system, perhaps a long pipe.
Diagram: Given: P1 200 kPa P2 180 kPa
T1 350 °C T2 350 °C
Find: Wflow ??? kJ/kg
Assumptions: None.
Equations / Data / Solve:
The net amount of PV or flow work in a flow process is the flow work done by the system through exiting streams minus the flow work done on the system through entering streams. Eqn 1
We know the inlet and outlet pressures, so now we need to determine the inlet and outlet specific volumes. We can get this information from the Steam Tables or the NIST Webbook.
V1 1.4330 m3/kg V2 1.5927 m3/kg
Now, we can plug values into Eqn 1 to evaluate the flow work.
Wflow,exit 286.69 kJ/kg
Wflow,inlet 286.59 kJ/kg Wflow,net 0.1006 kJ/kg
100.6 J/kg
Verify: No assumptions.
Answers : Wflow,net 101 J/kg 