Next: Heat Conduction Up: Momentum Conservation Previous: FCV conversion

PDE conversion

(Book: 5.7)

Write out in index notation, using the expression for Fi from the previous section:

Using the divergence theorem:

Conservation form of the momentum equations:
(9)

Alternate form:

Nonconservative Navier-Stokes equations:
(10)

Material fluxion of velocity:
(11)

Hence is the gravity force per unit volume and the gradient of the stress tensor is the net surface force per unit volume.

Exercise:

Find the net force per unit volume for inviscid flow. Explain by a simple example that the pressure does not give you the net force on the fluid.


Next: Heat Conduction Up: Momentum Conservation Previous: FCV conversion
01/26/00 0:27:43
01/28/00 0:24:43
01/31/00 0:00:16
01/31/00 0:01:58