Definition:Bernoulli's Equation (Fluid Mechanics)

Definition

Bernoulli's equation is a statement of conservation of energy in the context of fluid mechanics:

$\ds \int \dfrac {\d p} \rho + \dfrac 1 2 v^2 + V = C$

where:

$p$ is the pressure of the fluid

$\rho$ is the density of the fluid

$V$ is the gravitational potential

$C$ is constant for a given stream line.

Bernoulli's Constant

The constant $C$ is known as Bernoulli's constant.

Also see

• Results about Bernoulli's equation in the context of fluid mechanics can be found here.

Source of Name

This entry was named for Daniel Bernoulli.

Historical Note

Bernoulli's equation was first formulated by Daniel Bernoulli in $1738$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Bernoulli's equation: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bernoulli's equation: 2.