Vorticity and the equations of motion

The momentum equation is  

(11.9)

The convective term may be written as

[ = 0, by continuity]
Invoking (11.8) into the above one obtains
	(11.10)
The viscous term may be written as
[ = 0, by continuity]
Invoking (11.8) into the above one obtains
	(11.11)

The momentum equation thus reads as

(11.12)

In the above equation and in this section of the text, we shall use p=p/ρ. This equation shows two inferences

• for irrotational flow,

for steady flows

or

= constant (Bernoulli's equation!)

• is analogous to the coriolis force if the coordinate system were rotating with an angular velocity . The vorticity is twice the angular velocity . The vorticity term is also related to lift generated by a vortex line exposed to a velocity . In the equation for , this term is . A graphical interpolation is shown below.

Figure 11.2