May 2022
Tags: CFD 220507 Transport Equation Conservation of Momentum 220507 Navier-Stokes Equations
Momentum Transport equation
The momentum transport equation defines how the momentum is transported across the field. Essentially, it expresses the Newton’s Second Law applied to a fluid.
For a fluid parcel of volume , Newton’s II law can be expressed as follows
The 220430 Material, Substantial or Lagrangian Derivative is used here as the velocity is function of both time and space. When applied to a fluid parcel, the force per unit volume is given by
Simplifying
It can be shown that
The net forces acting on the fluid parcel can be expressed as follows
- The pressure term is -ve as the velocity increases in the direction of decreasing pressure.