(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.
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