Navier-Stokes. Pressure Force. Each volume element in a fluid is subject to force due to pressure. Assume a rectangular box Pressure force density is the gradient of pressure. d V. d z. d y. p. d x. Equation of Motion. A fluid element may be subject to an external force.
Divide by the density.
Motion in units of force density per unit mass.
The time derivative can be expanded to give a partial differential equation.
Pressure or stress tensor
This is Euler’s equation of motion for a fluid.
There is a general relation between stress and strain
Constants a, b include viscosity
An incompressible fluid has no velocity divergence.