The Motion of Fluids

Fluid dynamics is all about how fluids move. This includes the speed, direction, and type of flow (laminar or turbulent). Understanding these concepts helps explain weather patterns, airplane flight, and even how we breathe.

Continuity Equation

The principle of conservation of mass gives us the continuity equation for fluids:

\( A_1 v_1 = A_2 v_2 \)

where \( A \) is the cross-sectional area and \( v \) is the fluid velocity. This means that as a pipe narrows, the fluid speeds up.

Bernoulli’s Principle

Bernoulli’s equation relates pressure and velocity in a moving fluid. It shows that faster-moving fluids exert less pressure—a principle used in airplane wings and carburetors.

Applications

From garden hoses to arterial blood flow, fluid dynamics affects many real-world systems.