Steady Flow Open Systems

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.

$$ 0 = \Delta H $$