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Different Forms of The Bernoulli Equation

In a Nutshell: The Bernoulli equation provides a convenient way to relate changes of pressure,

fluid speed, and gravitational attraction for fluid acceleration in a flow field. Understanding the limitations of the Bernoulli equation is key to its correct application. The table below summarizes different forms depending on the key limitations for each form.

Click here for definition of terms: inviscid, steady flow, irrotational

Key Limitations: Inviscid, steady flow along a streamline (compressible or incompressible)

∫ dP / ρ + ½ V² + g z = Constant along streamline

Key Limitations: Inviscid, steady , incompressible flow along a streamline

P / ρ + ½ V² + g z = Constant along streamline

Key Limitations: : Inviscid, steady, irrotational flow (compressible or incompressible)

∫ dP / ρ + ½ V² + g z = Constant throughout flow field (any points in flow field)

Key Limitations: Inviscid, steady, incompressible, irrotational flow

P / ρ + ½ V² + g z = Constant throughout flow field (any points in flow field)

where P = the pressure at the point of the fluid particle along the streamline

ρ = the mass density of the fluid particle

V = the speed of the fluid particle

g = the acceleration of gravity

z = elevation of the fluid particle

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