Converging duct flow is modeled by the steady, two- dimensional velocity field of Prob. 4‒17. Use the equation for volumetric strain rate to verify that this flow field is incompressible.

Step 1:

The given converging duct flow is steady and two dimensional velocity field. We need to show that flow field is incompressible and express the equation for volumetric strain rate.

Step 2:

The expression for two dimensional velocity field

= = - -----(1)

= --------(2)

= --------(3)

Step 3:

Volumetric strain rate is the rate of increase in volume of a fluid element per unit volume. The expression for volumetric strain given by the cartesian coordinate system is

= = ++ ------(4)

Where ,and are the linear strain rates in the cartesian coordinates.

=

=

=