# Bernoulli's theorem

From AMS Glossary

## Bernoulli's theorem

As originally formulated, a statement of the conservation of energy (per unit mass) for an inviscid fluid in steady motion.

The specific energy is composed of the kinetic energy (1/2) is valid for steady motion, since the streamline is also the path. If the motion is also irrotational, the same constant holds for the entire fluid. The following special cases are important: 1) as originally formulated for a homogeneous incompressible fluid, and 2) for a perfect gas undergoing adiabatic processes, where

*v*^{2}, where*v*is the speed of the fluid; the potential energy*gz*, where*g*is the acceleration of gravity and*z*the height above an arbitrary reference level; and the work done by the pressure forces ∫ α*dp*, where*p*is the pressure, α the specific volume, and the integration is always with respect to values of*p*and α on the same parcel. Thus, the relationship*c*_{p}is the specific heat at constant pressure and*T*the Kelvin temperature. If there is diabatic heating on the parcel at the rate*dQ*/*dt*per unit mass, thenGill, A. E. 1982. Atmosphere–Ocean Dynamics. Academic Press, . 82–83.