key term - Bernoulli’s principle

Definition

Bernoulli’s principle states that in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is constant. This means that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or potential energy.

5 Must Know Facts For Your Next Test

1. Bernoulli’s principle is derived from the conservation of energy for flowing fluids.
2. It explains why airplane wings generate lift; faster airflow over the top surface reduces pressure, creating lift.
3. The principle can be mathematically expressed as $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$ where $P$ is pressure, $\rho$ is density, $v$ is velocity, and $h$ is height.
4. Applications include fluid flow in pipes, blood flow in arteries, and functioning of carburetors.
5. In real-life applications, factors like viscosity and turbulence may cause deviations from ideal Bernoulli behavior.

Review Questions

Related terms

Continuity Equation:

A mathematical statement that describes the transport of some quantity like mass or energy within a fluid.

Viscosity:

A measure of a fluid's resistance to deformation or flow; affects how fluids behave under different conditions.

Streamline:

A line representing the path followed by particles in a fluid flow; tangent to velocity vectors at any point.