Fluids — AP Physics 1 Study Guide

For: AP Physics 1 candidates sitting AP Physics 1.

Covers: Density, pressure (hydrostatic, gauge), buoyancy and Archimedes' principle, fluid flow (continuity equation), Bernoulli's equation — AP Physics 1 Unit 8 (CED 2024-25, where Fluids moved from AP Physics 2).

You should already know: Force diagrams (Unit 2), conservation of energy (Unit 4), pressure as F/A.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Physics 1 style for educational use. They are not reproductions of past College Board papers.

1. Why Fluids Matters (CED 2024-25)

Fluids is new to AP Physics 1 in the 2024-25 redesign — moved from Phys 2 to put all "macroscopic mechanics" in one course. About 10-12% of the new exam covers fluids. Two big concepts: statics (fluids at rest) governed by pressure & buoyancy, and dynamics (fluids flowing) governed by continuity & Bernoulli.

2. Density and pressure

Density: $\rho =m/V$ (kg/m³). Water $\approx 1000$ kg/m³; air $\approx 1.2$ kg/m³ at sea level.

Pressure: $P=F/A$ (N/m² = pascal, Pa). Atmospheric pressure $\approx 101325$ Pa = 1 atm.

Hydrostatic pressure (depth $h$ in a fluid of density $\rho$): $$P=P_0+\rho gh$$

Where $P_0$ is the pressure at the surface (often atmospheric). This is gauge pressure when $P_0$ is excluded; absolute when included.

Pascal's principle: pressure applied to an enclosed fluid transmits undiminished — basis of hydraulic systems. A small force on a small piston produces a large force on a big piston: $F_1/A_1=F_2/A_2$.

3. Buoyancy — Archimedes' principle

A fluid exerts an upward buoyant force on any submerged or floating object equal to the weight of the fluid displaced: $$F_b={\rho }_{\text{fluid}}\cdot V_{\text{displaced}}\cdot g$$

Sinks vs floats: object floats if ${\rho }_{\text{object}}<{\rho }_{\text{fluid}}$, sinks if ${\rho }_{\text{object}}>{\rho }_{\text{fluid}}$, neutral if equal.

For a floating object: $F_b=mg$ — the displaced fluid weight equals the object weight. Submerged volume = $V_{\text{displaced}}$, so the fraction submerged equals ${\rho }_{\text{object}}/{\rho }_{\text{fluid}}$.

4. Continuity equation (mass conservation)

For an incompressible fluid in a closed pipe, mass flow rate is constant: $$A_1{v}_1=A_2{v}_2$$

Where $A$ is cross-sectional area and $v$ is fluid speed. So narrower pipe → faster flow. This is why a garden hose with a thumb pinched over the end shoots water faster.

5. Bernoulli's equation (energy conservation for fluids)

For an incompressible non-viscous fluid in steady flow: $$P_1+\frac{1}{2}\rho v_1^2+\rho g{y}_1=P_2+\frac{1}{2}\rho v_2^2+\rho g{y}_2$$

Three terms: pressure, kinetic energy density, gravitational PE density. Total stays constant along a streamline.

Common applications:

• Faster fluid → lower pressure: airplane wings (faster air on top → lower P → lift), Venturi tubes.
• Torricelli's law: speed of fluid escaping a tank with water height $h$ is $v=\sqrt{2gh}$ (Bernoulli applied between top and exit).

6. Worked Example

A solid cube of side 0.10 m and density 600 kg/m³ floats in water (1000 kg/m³). (a) Calculate the volume submerged. (b) Calculate the buoyant force on the cube. (c) An external force pushes the cube fully under (depth 0.10 m). Calculate the new buoyant force and the magnitude of the external force needed.

Solution.

(a) Cube volume = $(0.10{)}^3=1.0\times 10^{-3}$ m³. Mass = ${\rho }_{\text{cube}}\cdot V=600\cdot 10^{-3}=0.60$ kg. Weight = $mg=5.88$ N. For floating: $F_b=mg=5.88$ N. So $V_{\text{disp}}=F_b/({\rho }_{\text{water}}\cdot g)=5.88/(1000\cdot 9.8)=6.0\times 10^{-4}$ m³.

(b) $F_b=5.88$ N (calculated above).

(c) Fully submerged: $V_{\text{disp}}=V_{\text{cube}}=10^{-3}$ m³. New $F_b=1000\cdot 10^{-3}\cdot 9.8=9.8$ N. Free-body: external (down) + cube weight (down) = buoyant (up). External force = $9.8-5.88=3.92$ N downward.

7. Common Pitfalls

• Forgetting gauge vs absolute pressure: gauge pressure can be negative (vacuum); absolute pressure cannot.
• Bernoulli + viscosity: Bernoulli assumes inviscid flow. Real fluids lose energy to viscous friction; AP Phys 1 ignores this but real-world questions about flowing through long pipes do not.
• Buoyancy and submerged objects: don't confuse the weight of displaced fluid (= buoyant force) with the weight of the object.
• Continuity is not Bernoulli: continuity is mass conservation (no $\rho$ change for incompressible fluids); Bernoulli is energy conservation. Both can apply at once.

8. Practice Questions (CED Style)

1. A 5.0 kg block of unknown density floats with 60% of its volume submerged in water. Determine the block's density.
2. Water flows through a horizontal pipe that narrows from 4.0 cm to 2.0 cm in cross-sectional area. If the speed at the wide end is 3.0 m/s, find the speed and the pressure change at the narrow end ($\rho =1000$ kg/m³).
3. A diver descends to 30 m depth in seawater ($\rho =1025$ kg/m³). Calculate the gauge pressure at this depth and explain why the diver's lungs would be crushed if they did not breathe pressurised air.

9. Quick Reference Cheatsheet

• $\rho =m/V$. $P=F/A$ (Pa).
• Hydrostatic: $P=P_0+\rho gh$.
• Pascal: $F_1/A_1=F_2/A_2$.
• Archimedes: $F_b={\rho }_{\text{fluid}}\cdot V_{\text{disp}}\cdot g$.
• Float fraction = ${\rho }_{\text{obj}}/{\rho }_{\text{fluid}}$.
• Continuity: $A_1{v}_1=A_2{v}_2$.
• Bernoulli: $P+\frac{1}{2}\rho v^2+\rho gy=$ const.
• Faster fluid → lower pressure (for horizontal flow).

10. What's Next

Fluids ties together everything from Newton's Laws (Unit 2) and energy conservation (Unit 4). It pairs naturally with Oscillations (Unit 6 / 7) when looking at waves in fluids, and with Thermodynamics (AP Phys 2) for fluid behaviour at varying temperatures. Use Ollie to step through any combined free-body + buoyancy problem or to verify the algebra of a Bernoulli question.