Finite Control Volume – Conservation of Energy (continued)

Energy Equation

{ [ u₂ + p₂/ρ + ½ V₂² + gz₂ ]- [ u₁ + p₁/ρ + ½ V₁² + gz₁ ] }dm/dt =

dQ/dt _{net in} + dW/dt_{shaft net in}

Assumptions:

• Steady flow
• Uniform flow
• Incompressible
• One stream entering and one stream exiting

For a pump the net work in is positive.

For a turbine the net work in is negative.

If there is no change in the internal energy, u, then

{ [ p₂/ρ + ½ V₂² + gz₂ ] - [ p₁/ρ + ½ V₁² + gz₁ ] }dm/dt = dQ/dt _{net in} + dW/dt_{shaft net}

Note: Each term is in energy per unit time. i.e. ft lb/sec or Nm/sec

[ p₂/ρ + ½ V₂² + gz₂ ] - [ p₁/ρ + ½ V₁² + gz₁ ] = [dQ/dt _{net in} + dW/dt_{shaft net in}] /dm/dt

Note: Each term is in energy per unit mass. i.e. ft lb/slug or Nm / kg

Click here for examples.

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