Bernoulli’s equation

Definition

Bernoulli's equation describes the relationship between the pressure, velocity, and elevation in a moving fluid. It is derived from the conservation of energy principle for incompressible, non-viscous fluids.

5 Must Know Facts For Your Next Test

1. Bernoulli's equation is given by $P + \frac{1}{2}\rho v^2 + \rho gh = constant$, where $P$ is the pressure, $\rho$ is the fluid density, $v$ is the fluid velocity, and $h$ is the height above a reference point.
2. The equation assumes that the flow is steady, meaning that variables do not change with time.
3. It also assumes that there are no friction losses in the fluid; hence it applies to ideal fluids.
4. Bernoulli's equation can be used to explain phenomena such as lift in airplane wings and why a shower curtain gets sucked inward when water flows from the showerhead.
5. The term $\frac{1}{2}\rho v^2$ represents the dynamic pressure, $P$ represents static pressure, and $\rho gh$ represents hydrostatic pressure.

Review Questions

• What assumptions must be satisfied for Bernoulli's equation to hold true?
• How does Bernoulli's equation explain the lift force on an airplane wing?
• Write down Bernoulli's equation and identify each term.

Related terms

Continuity Equation:

A principle stating that for any incompressible fluid flowing through a closed system, the mass flow rate must remain constant from one cross-section to another.

Dynamic Pressure:

The kinetic energy per unit volume of a fluid particle. Represented as $\frac{1}{2}\rho v^2$ in Bernoulli's equation.

Static Pressure:

The pressure exerted by a fluid at rest or when there is no motion relative to its surroundings. Represented by $P$ in Bernoulli's equation.