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Steady Flow Processes

In this notes sheet:

  1. Modelling steady flow through a control volume

  2. The Steady Flow Energy Equation (SFEE)

  3. Applications of the SFEE

  4. Mass & volume flow rates

  5. The Rankine Cycle

The basic form of the first law, ΔQ – ΔW = ΔE, only applies to closed systems - no mass can transfer across the system boundary, only energy in the form of heat and work.


In reality, perfectly closed systems are quite rare (take a turbine, for example: air flows in as well as heat, shaft work and hot air flow out), and as such a different model is required:

The energy transfers across the control volume surface are:

  • Shaft work

  • Heat transfer

  • Energy in the working fluid (kinetic, potential, and internal energies)

To simplify the process, we only look at the energy inputs and outputs: what goes on inside the control volume is irrelevant.

We call where the working fluid enters and exits ports.

  • The control volume above has two ports: one inflow and one outflow port.



The Steady Flow Energy Equation (SFEE)

In order to solve problems involving steady flow through a control volume, we use the Steady Flow Energy Equation (SFEE) instead of the simple first law equation:

In a less mathematically intimidating form:

  • Left hand side: rate of energy transfer – rate of shaft work

  • Right hand side: sum of output mass energy flow rates – sum of input mass energy flow rates

Note: The dot above the letters means it is a rate of change with respect to time: