Fluid Mechanics

Fluid mechanics is the study of fluids (liquids and gases) at rest (fluid statics) and in motion (fluid dynamics). The behavior of fluids is governed by fundamental principles including pressure, Pascal's principle, Archimedes' principle, and Bernoulli's equation. Unlike solids, fluids cannot sustain shear stress at rest — they flow and deform continuously. This flowing behavior, combined with the concept of pressure acting equally in all directions, gives rise to a rich set of phenomena from hydraulic lifts to airplane flight.

Fluid statics deals with fluids in equilibrium. Pressure in a static fluid increases linearly with depth (P = P_0 + rho*g*h), Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid, and Archimedes' principle states that the buoyant force on a submerged or partially submerged object equals the weight of the displaced fluid. These principles explain why ships float, how hydraulic brakes multiply force, and why atmospheric pressure decreases with altitude.

Fluid dynamics describes fluids in motion using the continuity equation (conservation of mass: A1*v1 = A2*v2 for incompressible flow) and Bernoulli's equation (conservation of energy: P + (1/2)*rho*v^2 + rho*g*h = constant along a streamline). Bernoulli's equation reveals the counterintuitive relationship between fluid speed and pressure: where fluid flows faster, pressure is lower. This principle explains the lift on airplane wings, the curve of a spinning baseball, and the operation of a Venturi meter. AP Physics 1 and 2 require students to reason qualitatively and quantitatively about pressure, buoyancy, flow rate, and the speed-pressure relationship.

Practice a little. See where you stand.