# Flow Work

## flow_work.jpg

The pressure acting on the differential area moves through an incremental distance as it exists or enters a control volume.  The flow work rate or power is equal the integral of the pressure times normal velocity component over the surface area.

Flow work is similar to the work done by a force moving through a distance. In the case at hand, pressure times velocity is integrated over a surface to give the rate at which work is done, or, power.

There are two ways that work can be done on or by the control volume.  The first of these is shaft work, in which a shaft enters or exits the control volume. The power or rate at which shaft work can be performed is given by the equation

where T is the torque transmitted through the shaft and  is the angular velocity of the shaft.

The second way that work can be done on or by the control volume is through flow work, which is the work done by the fluid pressure as the fluid exists or enters the control volume.  Flow work is given by the equation

Multiplying and dividing the integral term by the density, allows the flow work to be written as

In the above equation, ν is the specific mass and is equal to one over the density.  The reason for writing flow work in this form is so that it will easily combine with other terms in the Conservation of Energy equation.

## Learning Objectives:

Define flow work, define power, differentiate between flow work and shaft work.