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Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
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.
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Force per unit area: P = F/A. In a fluid at rest, pressure acts equally in all directions at a given depth. Pressure increases with depth in a fluid: P = P_0 + rho*g*h. SI unit: pascal (Pa) = N/m^2.
Example: A diver at 10 meters depth experiences pressure of 1 atm + (1000 kg/m^3)(9.8 m/s^2)(10 m) = 1 atm + 98,000 Pa, roughly 2 atmospheres total.
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the container. This enables hydraulic force multiplication: F1/A1 = F2/A2.
Example: In a hydraulic car lift, a small force on a small piston creates the same pressure as a large force on a large piston. If the large piston has 100x the area, the force is multiplied by 100.
Any object wholly or partially submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced: F_b = rho_fluid * V_displaced * g.
Example: A block of wood floats because it displaces water equal to its own weight before it is fully submerged. A steel ship floats because its hull displaces a large volume of water weighing more than the ship.
The net upward force exerted by a fluid on an immersed object, caused by the pressure difference between the bottom and top of the object. Equal to the weight of displaced fluid.
Example: A 1 kg block with volume 0.002 m^3 submerged in water experiences a buoyant force of (1000)(0.002)(9.8) = 19.6 N upward.
For an incompressible fluid flowing through a pipe, the product of cross-sectional area and flow velocity is constant: A1*v1 = A2*v2. This is conservation of mass for fluids.
Example: A garden hose with a nozzle: the narrow nozzle (smaller A) forces water to flow faster (larger v), which is why squeezing the hose opening makes water spray farther.
For an ideal, incompressible fluid flowing along a streamline: P + (1/2)*rho*v^2 + rho*g*h = constant. This is conservation of energy per unit volume for fluids. Where speed is high, pressure is low.
Example: Air flows faster over the curved top of an airplane wing than under the flat bottom. By Bernoulli's equation, the faster air has lower pressure, creating net upward lift.
Absolute pressure is the total pressure including atmospheric. Gauge pressure is the pressure above atmospheric: P_gauge = P_absolute - P_atm. Many instruments (tire gauges, blood pressure cuffs) measure gauge pressure.
Example: A tire gauge reading 32 psi means the pressure inside is 32 psi above atmospheric pressure. The absolute pressure is about 32 + 14.7 = 46.7 psi.
A measure of a fluid's internal resistance to flow. High-viscosity fluids (honey, motor oil) flow slowly; low-viscosity fluids (water, air) flow easily. Viscosity causes energy dissipation in real fluid flow.
Example: Honey pours much more slowly than water because its viscosity is about 10,000 times greater. This is why Bernoulli's equation (which assumes no viscosity) is an idealization.
More terms are available in the glossary.
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