Bernoulli’s equation

Definition

Bernoulli’s equation describes the conservation of energy in a fluid flow, relating pressure, velocity, and elevation. It is derived from the principle of conservation of mechanical energy.

5 Must Know Facts For Your Next Test

1. Bernoulli’s equation is given by the formula: $$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$$ where $P$ is pressure, $\rho$ is fluid density, $v$ is velocity, and $h$ is height above a reference point.
2. It assumes an incompressible and non-viscous fluid with steady flow.
3. Bernoulli’s principle explains why airplane wings generate lift due to differences in airspeed above and below the wing.
4. The equation can be applied to various biological systems, such as blood flow in arteries.
5. It helps in understanding phenomena like the Venturi effect, where fluid speed increases when passing through a constricted section of pipe.

Review Questions

• What are the three main variables involved in Bernoulli's equation?
• How does Bernoulli's principle explain the lift on an airplane wing?
• Under what assumptions is Bernoulli's equation valid?

Related terms

Continuity Equation: A mathematical statement that describes the conservation of mass in fluid dynamics; it states that the product of cross-sectional area and velocity remains constant along a streamline for an incompressible fluid.

Venturi Effect: The reduction in fluid pressure that results when a fluid flows through a constricted section of pipe.

Hydrostatic Pressure: $P = \rho gh$: The pressure exerted by a static fluid due to its weight at any given point within the fluid.