Flow Work In Thermodynamics

The flow work, significant only in a flow process or an open system, represents the energy transferred across the system boundary as a result of the energy imparted to the fluid by a pump, blower and a compressor to make the fluid flow across the control volume. Flow work is analogous to displacement work. Let p be the fluid pressure in the plane of the imaginary piston, which acts in a direction normal to it. The work done on this imaginary piston by the external pressure as the piston moves forward is given by

dW (flow) = pdV,

where dV is the volume of fluid element about to enter the system.

dW(flow) = pv dm,

where dV = v dm,

Therefore, flow work at inlet

dW (flow in) = p1 v1 dm1.

If the normal pressure p1 is exerted against the area A1, giving a total force (p1 A1) against the piston, in time dt, this force moves a distance V1dt, where V1 is the velocity of flow (piston). The work in the time dt is p1 A1 V1 dt, or the work per unit time is p1 A1 V1. Since the flow rate

w1 = A1V1 / v1 = dm1 / dt

the work done in time dt becomes

dW(flow in) = p1v1 dm1

Similarly, flow work of the fluid element leaving the system is ,

dW( flow out) = p2 v2 dm2

The work flow per unit mass is thus,

dW(flow) = pv

It is the displacement work done at the moving system boundary.

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