# SFEE Applications

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

## 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 $$\Delta h = C_p \Delta T$$