Summarizing Bernoulli’s Equation

Summary

• Bernoulli’s equation states that the sum on each side of the following equation is constant, or the same at any two points in an incompressible frictionless fluid:

  \({P}_{1}+\cfrac{1}{2}{\mathrm{\rho v}}_{1}^{2}+\rho {\mathrm{gh}}_{1}={P}_{2}+\cfrac{1}{2}{\mathrm{\rho v}}_{2}^{2}+\rho {\text{gh}}_{2}.\)

• Bernoulli’s principle is Bernoulli’s equation applied to situations in which depth is constant. The terms involving depth (or height h ) subtract out, yielding

  \({P}_{1}+\cfrac{1}{2}{\mathrm{\rho v}}_{1}^{2}={P}_{2}+\cfrac{1}{2}{\mathrm{\rho v}}_{2}^{2}.\)

• Bernoulli’s principle has many applications, including entrainment, wings and sails, and velocity measurement.

Glossary

Bernoulli’s equation

the equation resulting from applying conservation of energy to an incompressible frictionless fluid: P + 1/2pv² + pgh = constant , through the fluid

Bernoulli’s principle

Bernoulli’s equation applied at constant depth: P₁ + 1/2pv₁² = P₂ + 1/2pv₂²