Bernoulli's Equation

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

Bernoulli's Equation is a way of describing the conservation of energy principle in an incompressible fluid.  Bernoulli's Equation relates the pressure (p), with the kinetic energy (½ ρ v2) and the gravitational potential energy (ρ g h).  When the speed decreases in expanded areas and increases in narrowing areas, the pressure of a fluid in a narrowing flow will decrease and the pressure of the fluid will increase as the flow expands.  In a system Bernoulli's equation will have the same constant value at various points.  This makes it very useful for solving for varying pressures in different points. 

The following assumptions must be met for the Bernoulli's equation:

  • The fluid must be incompressible, even though pressure varies, the density must remain constant.
  • The streamline must not enter the boundary layer.  (Bernoulli's equation is not applicable where there are viscous forces, such as in the boundary layer.)


Bernoulli's Equation (Pressure)

\(\large{ static\;pressure + dynamic\;pressure + hydrostatic\;pressure = constant }\)   
\(\large{ p  + \frac {\rho}{2} \; v^2  + \rho \;g \; h = constant }\)  (along a streamline) (Bernoulli's Equation)
\(\large{ p  + \frac {1}{2} \; \rho\; v^2  + \rho \;g \; h = constant }\)  (along a streamline)  
\(\large{ pressure\; energy  + kinetic \;energy + potential\; energy = constant }\)  


Bernoulli's Equation (Energy)

\(\large{ \frac{ p }{ \rho }  + \frac {v^2}{2} + g \; h = constant }\)  (along a streamline)  


Bernoulli's Equation (Head)

\(\large{ \frac{ p }{ \rho\;g }  + \frac { v^2}{2 \;g}  +  h = constant }\)  (along a streamline)  



\(\large{ \rho }\)  (Greek symbol rho) = density of fluid

\(\large{ g }\) = gravitational acceleration

\(\large{ h }\) = height

\(\large{ p }\) = pressure

\(\large{ v }\) = velocity of fluid


Tags: Equations for Pressure Equations for Pipe Sizing Equations for Constant Equations for Fluid