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.
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.
The expression for two dimensional velocity field
= = - -----(1)
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.