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Rewrite (2.16) as
where
and
. Thus,

(2.19) 
When the vorticity
the flow is
called irrotational. If, in addition, the flow is steady,
(2.19) reduces to
or, on integrating,

(2.20) 
This is called Bernoulli's equation. It says that the total
energy (pressure plus gravitational plus kinetic energy) is constant.
The implication is that the pressure falls where the fluid flows
faster and visaversa. For example, if neglect gravity, ,
then for the air flow over an aeroplane wing we find that, as shown
in Figure
2.6,
Figure 2.6:
Airflow over an aeroplane wing. Flow is faster of the upper
surface of the wing and so the pressure is lower there.

the air travels further over the top
surface than the lower surface. Hence, it must travels faster over the
top surface. From Bernoulli's equation (2.20) we see that if the velocity is
higher then the pressure must be lower. With a lower pressure on the
upper surface and a higher pressure on the lower surface, there is a
vertical pressure force that generates the lift.
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Prof. Alan Hood
20001106