Fluids — AP Physics 2
1. Core Properties of Fluids ★☆☆☆☆ ⏱ 2 min
Fluids are substances that deform continuously under applied shear stress, including both liquids and gases. Unlike rigid solids, fluids do not retain a fixed shape, so their behavior is described using bulk properties for most AP exam contexts. This topic makes up 10-15% of your total AP Physics 2 exam score, split between fluid statics (fluids at rest) and fluid dynamics (fluids in motion).
2. Density and Hydrostatic Pressure ★★☆☆☆ ⏱ 3 min
\rho = \frac{m}{V}
P = \frac{F}{A}
For static fluids, pressure increases with depth due to the weight of the fluid above a given point. Absolute pressure includes atmospheric pressure at the surface, while gauge pressure is pressure relative to atmospheric pressure.
P = P_0 + \rho g h
3. Pascal's Principle ★★☆☆☆ ⏱ 3 min
Pascal's principle states that a change in pressure applied to an enclosed, incompressible fluid is transmitted undiminished to all portions of the fluid and the walls of its container. This principle is the basis for hydraulic systems, which multiply force using differences in piston area for applications like car lifts.
\frac{F_1}{A_1} = \frac{F_2}{A_2} \implies F_2 = F_1 \times \frac{A_2}{A_1}
A key tradeoff: the smaller piston must move a larger distance to lift the larger piston a small distance, since displaced volume is equal on both sides: $A_1 d_1 = A_2 d_2$.
4. Buoyancy and Archimedes' Principle ★★★☆☆ ⏱ 4 min
F_b = \rho_{fluid} V_{displaced} g
- If $F_b > F_{g, object}$: The object accelerates upward and floats
- If $F_b = F_{g, object}$: The object is neutrally buoyant and remains stationary
- If $F_b < F_{g, object}$: The object accelerates downward and sinks
For floating objects at equilibrium, buoyant force equals the weight of the object, leading to this relationship for the fraction of the object submerged:
\frac{V_{submerged}}{V_{total}} = \frac{\rho_{object}}{\rho_{fluid}}
5. Continuity Equation ★★☆☆☆ ⏱ 3 min
The continuity equation is a statement of conservation of mass for incompressible, laminar (smooth, non-turbulent) fluid flow in a closed system with no leaks. For incompressible fluids, density is constant, so the equation simplifies to conservation of volume flow rate $Q$.
Q = A v = \text{constant} \implies A_1 v_1 = A_2 v_2
This explains why water sprays faster when you pinch the end of a hose: reducing cross-sectional area increases flow speed to keep volume flow rate constant.
6. Bernoulli's Equation ★★★★☆ ⏱ 5 min
Bernoulli's equation is a statement of conservation of energy per unit volume for incompressible, laminar, non-viscous (no friction) fluid flow. Each term represents a form of energy per unit volume: pressure potential energy, kinetic energy, and gravitational potential energy.
P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2
The Venturi effect: for horizontal flow (constant height, $h_1 = h_2$), faster moving fluid has lower pressure. This explains airplane lift, carburetor operation, and the inward pull of shower curtains. A special case for large open tanks is Torricelli's law for exit speed from a hole:
v = \sqrt{2gh}
Common Pitfalls
Why: You mix up the mass of the object and the mass of displaced fluid
Why: You default to adding atmospheric pressure even when the question asks for gauge pressure
Why: You forget the formula's key assumptions
Why: You skip converting diameter to area to save time, and incorrectly scale linearly
Why: You confuse flow speed and volume flow rate