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).

Wed Sep 10 01:02:02 EDT 1997