13.21: Energy Conservation and Bernoulli's Equation
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is called the potential energy density.
It is important to note that the liquid's density should not change through the flow; that is, it should be incompressible. The flow should also be laminar and not turbulent. Bernoulli's equation is applicable for gases that have negligible compressibility effects. For such gases, the density is assumed to be constant and is treated as an incompressible fluid. Since gases are generally compressible, the equation does not apply to them.
Although a simple restatement of the energy conservation principle with a few critical assumptions, the equation makes it easy to calculate pressure at different points if speeds are known.