STEADY FLOW ENERGY EQUATION

First Law for a Control Volume (VW, S & B: Chapter 6) 

1. Frequently (especially for flow processes) it is most useful to express the First Law as a statement about rates of heat and work, for a control volume.



 

1. Conservation of mass (VW, S & B: 6.1)
   








2. Conservation of Energy (First Law) (VW, S & B: 6.2)
   

Recall, dE = dQ-dW
For the control volume,

where
rate of energy transfer to the system as heat
rate of work done by the system


3. For steady-state (VW, S & B: 6.3)
   



so
(units J/s)
or

Neglecting potential and chemical energy (PE and CE)


Where c is the speed of the fluid, and c²/2 is the kinetic energy of the fluid per unit mass relative to some coordinate system.

If we divide through by the mass flow and set the inlet of the control volume as station 1, and the outlet as station 2, then





It is also more convenient to divide the work into two terms: 1) the flow work done by the system which is p₂v₂-p₁v₁, and 2) any additional work which we will term external work or shaft work, w_s. Then we have

or


We will call this the steady flow energy equation.

For an ideal gas dh=c_p dT so






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