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.

References

  1. Momentum The Navier-Stokes Equations