Shear flow themselves. In a shearing flow, adjacent layers of fluid move parallel to each other with different speeds. Viscous fluids resist this shearing motion. For a Newtonian fluid, the stress exerted by the fluid in resistance to the shear is proportional to the strain rate or shear rate. A simple example of a shear flow is Couette flow, in which a fluid is trapped between two large parallel plates, and one plate is moved with some relative velocity to the other. Here, the strain rate is simply the relative velocity divided by the distance between the plates. Shear flows in fluids
Incompressible flow to ensure incompressible "flow". When we speak of the partial derivative of the density with respect to time, we refer to this rate of change within a control volume of "fixed position". By letting the partial time derivative of the density be non-zero, we are not restricting ourselves to incompressible "fluids", because the density can change as observed from a fixed position as fluid flows through the control volume. This approach maintains generality, and not requiring that the partial time derivative of the density vanish illustrates that compressible fluids can still undergo incompressible flow. What interests us is the change