• id: JME-09-N07
• title: Bernoulli's Theorem
• tags: bernoulli, energy-conservation, pressure

Bernoulli's equation: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$ along a streamline. Each term represents energy per unit volume: $P$ (pressure energy = work done by pressure forces), $\frac{1}{2}\rho v^2$ (kinetic energy density), $\rho gh$ (potential energy density). This is the work-energy theorem for fluid flow. Assumptions: (1) ideal fluid (zero viscosity, incompressible), (2) steady flow, (3) along a streamline, (4) irrotational flow. For real fluids, energy losses due to viscosity must be added.