# SFEE Applications

Steady Flow Energy Equation

\( \dot{Q} - \dot{W} = \Delta H + \Delta KE + \Delta PE \)

## Turbines and Compressors

Where, a turbine has a positive \( \dot{W} \), and a compressor has a negative \( \dot{W} \).

Since fluid usually passes through both systems rapidly and there is not enough time for significant heat exchange, \( \dot{Q} \approx 0 \).

Change in kinetic and potential energy is also *usually* negligible. \( \Delta KE \approx \Delta PE \approx 0 \)

The SFEE simplifies to

\( - \dot{W} = \Delta H ( + \Delta KE ) \)

Where \( \Delta H \) can be calculated by either specific enthalpy or by its definition.

\( \Delta H = \dot{m} (h_2 - h_1) = \dot{m} C_p \Delta T \)

\( \Delta KE \), taking into account the conventional units,

\( \Delta KE = \frac{\dot{m}}{2000} (C_2 ^2 - C_1 ^2) \)

Therefore, the steady flow energy equation with isentropic assumptions in turbines and compressors with possible negligence of change in kinetic energy:

\( \dot{W} = -m (h_2 - h_1) + \frac{\dot{m}}{2000} (C_2 ^2 - C_1 ^2) \)

or

\( \dot{W} = - \dot{m} C_p \Delta T + \frac{\dot{m}}{2000} (C_2 ^2 - C_1 ^2) \)

## Mixing Processes and Heat Exchangers

Mixing chambers assumed to be well insulated, \( \dot{Q} \approx 0 \).

No work is done on the control volume, \( \dot{W} \approx 0 \).

Negligible change in kinetic and potential energies, \( \Delta KE \approx \Delta PE \approx 0 \).

SFEE simplifies to

\( \Delta H = 0 \)

\( \Sigma \dot{m}_{out} h_{out} = \Sigma \dot{m}_{in} h_{in} \)

Where \( \Delta h = C_p \Delta T \)