What Is Bernoulli's Principle and How Does It Apply to Sport? (HL)

Bernoulli's principle states that an increase in a fluid's velocity is associated with a decrease in its static pressure, provided the fluid follows approximately steady flow. In sport, this pressure difference can generate lift or a sideways force on balls and aerodynamic equipment.

The Mechanism

For steady, incompressible and non-viscous flow along a streamline, Bernoulli's equation is:

$$P+\frac{1}{2}\rho v^2+\rho gh=\text{constant}$$

Here, $P$ is static pressure, $\rho$ is fluid density, $v$ is fluid velocity, $g$ is gravitational acceleration and $h$ is height. The equation represents conservation of mechanical energy per unit volume.

At approximately equal height, faster airflow has greater kinetic energy per unit volume and therefore lower static pressure. If air moves at different speeds on opposite sides of an object, the resulting pressure gradient produces a net force toward the lower-pressure region.

For example, if air speeds on opposite sides of a ball are $20\ \text{m s}^{-1}$ and $25\ \text{m s}^{-1}$, with air density $1.2\ \text{kg m}^{-3}$, the idealized pressure difference is:

$$\Delta P=\frac{1}{2}(1.2)(25^2-20^2)=135\ \text{Pa}$$

A common misconception is that Bernoulli's principle alone completely explains lift. In real sport, viscosity, boundary-layer separation, circulation and Newton's laws also contribute.

Exam Technique

For an IB SEHS B.2.2 explain question, give the causal chain: unequal fluid velocity leads to unequal pressure, producing a net force that changes the object's trajectory. State Bernoulli's assumptions and connect the force to a specific sporting example.