Conservation of mass, enthalpy (flow work and internal energy), energy (kinetic and potential).

Flow Work: $$W_f = PV; w_f = Pv$$

## General Steady Flow Energy Equation

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

Where enthalpy, $$H = PV + U$$.
$$KE = \frac{1}{2} m C^2$$
$$PE = mgz$$

For a perfect gas

$$H = m C_p \Delta T$$

## Open System Ideal Gas Law

$$P \dot{V} = \dot{m}RT$$

## Applications

### Nozzles and Diffusers

$$\dot{Q} \approx 0; \dot{W} \approx 0; \Delta PE \approx 0$$

$$0 = \Delta H + \Delta KE$$

$$0 = \dot{m} (h_2 - h_1) + \frac{\dot{m}}{2000} (C_2 ^2 - C_1 ^2)$$

### Turbines and Compressors

Turbines generate work from input fluid, thus is attributed with positive $$W$$. Compressors require work and is attributed with negative $$W$$.

Isentropic assumptions:
$$\dot{Q} \approx 0; \Delta KE \approx \Delta PE \approx 0$$

$$- \dot{W} = \Delta H$$

For a perfect gas:

$$- \dot{W} = \dot{m} C_p \Delta T$$

### Mixing Processes

$$\dot{Q} \approx 0; \dot{W} \approx 0; \Delta KE \approx \Delta PE \approx 0$$

$$0 = \Delta H$$

### Heat Exchangers

$$\dot{Q} \approx 0; \dot{W} \approx 0; \Delta KE \approx \Delta PE \approx 0$$

For entire system as CV:

$$0 = \Delta H$$

For one fluid as CV where heat transfer from the other fluid(s) is a factor:

$$\dot{Q} = \Delta H$$

### Throttling Valves

Causes a significant pressure and temperature drop.

$$0 = \Delta H$$