Other Forms of Bernoulli’s Equation


The various forms of Bernoulli’s equation can be used to determine the pressure distribution in a wide number of industrial systems.  Although Bernoulli’s equation was derived for incompressible fluids, it can also be applied to low speed flows involving gasses since density changes in this flow regime are generally small.

By my own work (Own work) [GFDL, CC-BY-SA-3.0 or CC-BY-SA-2.5-2.0-1.0], via Wikimedia Commons

Bernoulli’s equation can be written in several different forms. Each form can facilitate the solution of a particular type of problem. The units of each term in Bernoulli’s equation must be the same since all terms add together. Depending on the mathematical manipulations performed on the equation it can have units of pressure, distance, or velocity squared.

When evaluated at two points, 1 and 2, on a streamline, Bernoulli’s equation can be written as

Note the units for each term in Bernoulli’s equation written in this form are those for velocity squared.  Another common form for Bernoulli’s equation is obtained by dividing both sides by g.  This operation yields the equation

The units for each term in this form of the Bernoulli’s equation are distance (ft or m).   The terms in this form of the equation are part of the “pressure head” or just “head” for the system.  In terms of the specific weight, ϒ, of the fluid, this equation can written as

Bernoulli’s equation can also be written in terms of pressure by multiplying the first equation by the density

All of these forms are encountered in the technical literature.  The specific form to use depends on the type of problem being solved.


Learning Objectives:

Learn the various forms that are commonly encountered when working with Bernoulli’s equation.