Bernoulli

Definition

Bernoulli's Equation describes the relationship between pressure, velocity, and elevation in a moving fluid. It is derived from the principle of conservation of energy for flowing fluids.

5 Must Know Facts For Your Next Test

1. Bernoulli's Equation can be written as $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$, where $P$ is pressure, $\rho$ is fluid density, $v$ is velocity, and $h$ is height.
2. The equation assumes incompressible flow with no friction losses.
3. It explains why an increase in a fluid’s speed results in a decrease in pressure or potential energy within the fluid.
4. Bernoulli's principle can be used to explain various phenomena such as airplane wing lift and the Venturi effect.
5. The equation applies along a streamline; different streamlines can have different constant values.

Review Questions

• What are the main assumptions made when applying Bernoulli’s Equation?
• How does Bernoulli’s Equation explain the functioning of an airplane wing?
• Can Bernoulli’s Equation be applied to compressible fluids? Why or why not?

Related terms

Continuity Equation: A principle stating that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a pipe to another.

Venturi Effect: A phenomenon where fluid speed increases while its pressure decreases when passing through a constricted section of pipe.

Dynamic Pressure: \(\frac{1}{2}\rho v^2\), representing the kinetic energy per unit volume of a fluid particle.