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Bernoulli's equation

Since we are now concentrating on steady flows, tex2html_wrap_inline1167 . Taking the dot product of tex2html_wrap_inline1019 with Eq. (2.22), and remembering that tex2html_wrap_inline1184 , we have


If we now consider displacements tex2html_wrap_inline1186 along a streamline, since tex2html_wrap_inline1019 is tangent to the streamline Eq. (2.23) becomes




This is the famous Bernoulli's equation  for steady flow in a nonviscous fluid. If, in addition, the fluid is irrotational so that tex2html_wrap_inline1190 , 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 tex2html_wrap_inline1192 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).

Vittorio Celli
Wed Sep 10 01:02:02 EDT 1997