Since we are now concentrating on steady flows, 
. Taking the dot product of 
with Eq. (2.22), and
remembering that 
, we have
If we now consider displacements 
along a streamline, since is tangent to the streamline Eq. (2.23) becomes
or,
This is the famous Bernoulli's equation
for steady flow in a nonviscous fluid. If, in addition, the fluid is
irrotational so that 
, then we have a stronger form of
Bernoulli's equation:
We've derived Bernoulli's equation in a somewhat mathematical fashion, but
keep in mind that it is simply a statement of conservation of energy in the
fluid. The term 
is the kinetic energy density of the
fluid, and the pressure p can be thought of as a type of potential energy
(per unit volume).
