Steady Flow Energy Equation

Statement

For an open system (Control Volume) under steady-flow conditions (mass in = mass out, no property changes with time at a fixed point), the conservation of energy is expressed as the Steady-Flow Energy Equation.

Mathematical Form

$\boxed{\dot{Q} - \dot{W} = \dot{m}\left(\Delta h + \frac{\Delta v^2}{2} + g\Delta z\right)}$

where:

• $\dot{Q}, \dot{W}$: Rate of heat and work transfer (kW).
• $h$: Specific Enthalpy ($u + Pv$).
• $\frac{v^2}{2}$: Kinetic energy change.
• $g\Delta z$: Potential energy change.

Applications & Simplifications

• Nozzles/Diffusers: Adiabatic ($\dot{Q}=0$), Passive ($\dot{W}=0$). Trade enthalpy for velocity.
• Turbines: Adiabatic. Produce work from enthalpy drop ($\\dot{W} = \\dot{m}(h_1 - h_2)$).
• Compressors/Pumps: Adiabatic. Consume work to increase enthalpy.
• Throttles: Isenthalpic ($h_1 = h_2$).
• Heat Exchangers: Constant pressure, no work ($\\dot{Q}_{net} = 0$).

Relationships

• Derivation: From First Law of Thermodynamics via Reynolds Transport Theorem.
• Key Property: Enthalpy