AP exam review verified for 2027

AP Physics 1 Unit 8 Review: Fluids

Q: What topics are covered in AP Physics 1 Unit 8?

AP Physics 1 Unit 8 covers four topics: **8.1 Internal Structure and Density**, **8.2 Pressure**, **8.3 Fluids and Newton's Laws**, and **8.4 Fluids and Conservation Laws**. Together they build a complete picture of how ideal fluids behave, from why objects sink or float to how energy and momentum are conserved in moving fluids. See everything for this unit at /ap-physics-1-revised/unit-8 .

Q: How much of the AP Physics 1 exam is Unit 8?

Unit 8 makes up 10-15% of the AP Physics 1 exam, making it one of the more significant units to know well. It covers fluids topics including density, pressure, buoyancy, and conservation laws applied to fluid systems. That weight means you can expect several multiple-choice questions and a possible FRQ drawing from this material.

Q: What's on the AP Physics 1 Unit 8 progress check (MCQ and FRQ)?

The AP Physics 1 Unit 8 progress check includes both MCQ and FRQ parts drawn from all four unit topics: Internal Structure and Density, Pressure, Fluids and Newton's Laws, and Fluids and Conservation Laws. MCQ questions typically test conceptual understanding of density and pressure relationships, while the FRQ section asks you to apply Newton's laws and conservation principles to fluid scenarios. For matched practice questions, head to /ap-physics-1-revised/unit-8 .

Q: How do I practice AP Physics 1 Unit 8 FRQs?

The best way to practice AP Physics 1 Unit 8 FRQs is to focus on the two topics that generate the most free-response material: **8.3 Fluids and Newton's Laws** and **8.4 Fluids and Conservation Laws**. FRQs in this unit often ask you to set up force diagrams for submerged objects, justify buoyancy using pressure differences, or apply continuity and energy conservation to fluid flow. Practice by writing out full justifications, not just equations, since College Board awards points for reasoning. Find Unit 8 FRQ practice at /ap-physics-1-revised/unit-8 .

Q: Where can I find AP Physics 1 Unit 8 practice questions?

You can find AP Physics 1 Unit 8 multiple-choice and free-response practice questions at /ap-physics-1-revised/unit-8 . That page pulls together MCQ sets and practice test questions covering all four topics: density, pressure, fluids and Newton's laws, and fluids and conservation laws. Working through timed MCQ sets is especially useful since 10-15% of the real exam comes from this unit.

Q: How should I study AP Physics 1 Unit 8?

Start with **8.1 Internal Structure and Density** to lock in the relationship between mass, volume, and density before moving on. From there, build up through pressure (8.2), then connect fluids to Newton's laws (8.3) by drawing force diagrams for objects in fluids. Finish with conservation laws (8.4), where continuity and Bernoulli-style reasoning show up. A few concrete steps that help: - Sketch pressure diagrams for every scenario, not just equations. - Practice explaining buoyancy in words, since FRQs reward written justification. - Do at least one timed MCQ set per topic to catch gaps before the exam. All unit resources are at /ap-physics-1-revised/unit-8 .

Review AP Physics 1 Unit 8 to build fluency with pressure, buoyancy, and fluid flow using density, Newton's laws, and conservation principles. This unit carries 10-15% of the exam and connects directly to force and energy reasoning from earlier units.

Use the topic guides, practice questions, and FRQ practice available for this unit to work through every major concept before exam day.

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AP exam review verified for 2027

What is AP Physics 1 unit 8?

Unit 8 applies the force and energy tools from Units 2 and 3 to substances that have no fixed shape. Fluids include both liquids and gases, and the unit treats them as ideal: incompressible and without viscosity. That simplification makes the math tractable and the physics clean.

Unit 8 is about how fluids exert pressure, how that pressure creates buoyant forces on submerged objects, and how conservation of mass and energy constrain fluid flow through pipes and openings.

Density and pressure are the entry points

Everything in this unit starts with rho = m/V and P = F_perp/A. Density tells you how much mass is packed into a volume; pressure tells you how much perpendicular force acts per unit area. Both quantities feed directly into buoyancy and flow calculations.

Buoyancy comes from pressure differences

The upward buoyant force on any submerged object equals the weight of the fluid it displaces: Fb = rho*V*g. Whether an object floats or sinks depends on whether its weight exceeds, equals, or falls below that buoyant force, which is a direct application of Newton's second law.

Flow obeys conservation laws

For an ideal fluid in a pipe, mass conservation gives A1v1 = A2v2: a narrower pipe means faster flow. Energy conservation gives Bernoulli's equation, which links pressure, height, and speed at any two points along a streamline. Torricelli's theorem is a special case derived from Bernoulli.

Fluids unify force and energy reasoning

Unit 8 is not a standalone topic. Pressure is a force-per-area argument. Buoyancy is Newton's second law applied to an object in a fluid. The continuity equation is conservation of mass. Bernoulli's equation is conservation of mechanical energy. Every major idea in the unit is a restatement of something you already know, applied to substances without a fixed shape.

AP Physics 1 unit 8 topics

8.1

Internal Structure and Density

Defines fluids as substances with no fixed shape and introduces density (rho = m/V) as the key characterizing property. Covers the distinction between solids, liquids, and gases based on intermolecular interactions, and defines an ideal fluid as incompressible and inviscid.

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8.2

Pressure

Defines pressure as P = F_perp/A (a scalar) and develops the depth-pressure relationship P = P0 + rho*g*h. Distinguishes absolute pressure from gauge pressure and explains why pressure in an incompressible fluid depends on depth, not container shape.

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8.3

Fluids and Newton's Laws

Applies Newton's laws to fluid particles and to objects submerged in fluids. Derives the buoyant force Fb = rho*V*g from pressure differences and states Archimedes' principle. Uses free-body diagrams to determine whether objects float, sink, or remain in equilibrium.

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8.4

Fluids and Conservation Laws

Applies conservation of mass to get the continuity equation A1v1 = A2v2 and conservation of mechanical energy to get Bernoulli's equation. Derives Torricelli's theorem as a special case. Explains the inverse relationship between fluid speed and pressure in a horizontal pipe.

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practice snapshot

Hardest AP Physics 1 unit 8 topics

This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.

62%average MCQ accuracy

Across 5.4k multiple-choice practice attempts for this unit.

5.4kMCQ attempts

Practice activity included in this snapshot.

38%average FRQ score

Across 16 scored free-response attempts for this unit.

Hardest topics in unit 8

MCQ miss rate

8.4

Fluids and Conservation Laws

Review Fluids and Conservation Laws with attention to how the concept appears in AP-style source and evidence questions.

40%1,640 tries

8.2

Pressure

Review Pressure with attention to how the concept appears in AP-style source and evidence questions.

34%1,321 tries

Unit 8 review notes

8.1

Properties of Fluids and Density

A fluid is any substance with no fixed shape, so both liquids and gases qualify. The distinction between solids, liquids, and gases comes from the strength of intermolecular interactions and molecular spacing. An ideal fluid is incompressible (constant density regardless of pressure) and has no viscosity. Density is the foundational quantity for the rest of the unit.

Density formula: rho = m/V, measured in kg/m^3. Density is an intensive property: it does not change with the amount of substance.
Ideal fluid: Incompressible (volume and density stay constant under pressure) and inviscid (no internal friction). AP Physics 1 treats all fluids as ideal.
Solids vs. liquids vs. gases: Solids have strong intermolecular forces and fixed shape; liquids have moderate forces and fixed volume but no fixed shape; gases have weak forces, no fixed shape, and no fixed volume.

If a 0.5 kg object has a volume of 0.0002 m^3, what is its density? (Answer: 2500 kg/m^3.) Would it float or sink in water (rho_water = 1000 kg/m^3)?

Property	Solid	Liquid	Gas
Fixed shape	Yes	No	No
Fixed volume	Yes	Yes	No
Intermolecular forces	Strong	Moderate	Weak
Counts as a fluid	No	Yes	Yes

8.2

Pressure at a Surface and Pressure with Depth

Pressure is the perpendicular force per unit area on a surface: P = F_perp/A. It is a scalar, so it has no direction. In a fluid, pressure increases with depth because the weight of the fluid above adds to the reference pressure. Absolute pressure at depth h is P = P0 + rho*g*h, where P0 is the surface (reference) pressure. Gauge pressure is the amount above P0, equal to rho*g*h.

P = F_perp/A: Pressure equals the perpendicular force component divided by the area over which it acts. Units are Pascals (Pa = N/m^2).
Absolute pressure: P = P0 + rho*g*h. Total pressure at depth h, including the reference pressure P0 at the surface.
Gauge pressure: P_gauge = rho*g*h. The pressure above the reference pressure; what a pressure gauge reads.
Scalar nature of pressure: Pressure has no direction. A fluid exerts pressure equally in all directions at a given depth.
Incompressible fluid and pressure: For an ideal fluid, density stays constant regardless of pressure, so rho*g*h applies uniformly at a given depth.

A diver is 10 m below the surface of water (rho = 1000 kg/m^3, P0 = 101,000 Pa, g = 10 m/s^2). What is the absolute pressure at that depth? What is the gauge pressure?

Quantity	Formula	What it measures
Absolute pressure	P = P0 + rhogh	Total pressure including surface reference
Gauge pressure	P_gauge = rhogh	Pressure above the reference level
Surface pressure	P0 (e.g., P_atm)	Reference pressure at the fluid surface

8.3

Buoyancy and Newton's Laws in Fluids

Newton's laws apply to fluid particles just as they do to solid objects. The macroscopic behavior of a fluid results from the combined internal particle interactions and external forces such as gravity. The buoyant force is the net upward force a fluid exerts on a submerged object, arising from the pressure difference between the bottom and top of the object. Archimedes' principle states that this force equals the weight of the displaced fluid.

Buoyant force formula: Fb = rho_fluid * V_displaced * g. The fluid's density and the volume of fluid displaced determine the upward force, not the object's own density.
Archimedes' principle: The buoyant force on any object equals the weight of the fluid it displaces. This follows from the pressure difference between the bottom and top surfaces of the object.
Floating condition: An object floats when Fb = weight of the object, meaning rho_object = rho_fluid for full submersion, or the object displaces only enough fluid to match its weight when partially submerged.
Sinking condition: An object sinks when its weight exceeds the maximum buoyant force (full submersion), which occurs when rho_object > rho_fluid.
Free-body diagram in a fluid: Draw weight (mg downward) and buoyant force (Fb upward). Apply Newton's second law: net force = ma. For equilibrium, Fb = mg.

A wooden block (mass 2 kg, volume 0.004 m^3) is fully submerged in water (rho = 1000 kg/m^3, g = 10 m/s^2). What is the buoyant force? What is the net force on the block, and in which direction will it accelerate?

Scenario	Condition	Net force direction
Object floats	rho_object < rho_fluid (partial submersion)	Zero (equilibrium)
Object is neutrally buoyant	rho_object = rho_fluid	Zero (equilibrium)
Object sinks	rho_object > rho_fluid	Downward

8.4

Continuity Equation and Bernoulli's Equation

Two conservation laws govern ideal fluid flow. Conservation of mass gives the continuity equation: A1v1 = A2v2. Where a pipe narrows, the fluid speeds up to keep the flow rate constant. Conservation of mechanical energy gives Bernoulli's equation, which relates pressure, gravitational potential energy per unit volume, and kinetic energy per unit volume at any two points along a streamline. Torricelli's theorem is a direct application of Bernoulli to a fluid exiting an opening.

Continuity equation: A1v1 = A2v2. The volume flow rate Q = Av is constant for an incompressible fluid. A smaller cross-section means a higher speed.
Volume flow rate: Q = Av, in m^3/s. It equals the volume of fluid passing a cross-section per unit time.
Bernoulli's equation: P1 + rho*g*y1 + (1/2)*rho*v1^2 = P2 + rho*g*y2 + (1/2)*rho*v2^2. Expresses conservation of mechanical energy per unit volume along a streamline.
Bernoulli's principle (qualitative): Where fluid speed increases, pressure decreases, and vice versa. This follows directly from Bernoulli's equation when height is constant.
Torricelli's theorem: v = sqrt(2*g*delta_y). The speed of fluid exiting an opening at the base of a tank equals the speed a free-falling object would reach after falling the same height delta_y. Derived from Bernoulli's equation.

Water flows through a pipe that narrows from area 0.02 m^2 to 0.005 m^2. If the speed in the wide section is 1 m/s, what is the speed in the narrow section? If the pressure in the wide section is 200,000 Pa and both sections are at the same height, what is the pressure in the narrow section? (rho = 1000 kg/m^3)

Law	Equation	What is conserved
Continuity equation	A1v1 = A2v2	Mass flow rate (volume flow rate for incompressible fluids)
Bernoulli's equation	P + rhogy + (1/2)rhov^2 = constant	Mechanical energy per unit volume
Torricelli's theorem	v = sqrt(2gdelta_y)	Mechanical energy (special case of Bernoulli)

Practice AP Physics 1 unit 8 questions

Try stimulus-based AP practice questions and written prompts after you review the notes.

Example stimulus-based MCQs

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graph

Stimulus-based practice question

A graph shows the mass $m$ as a function of volume $V$ for two different fluids, Fluid 1 and Fluid 2, at a constant temperature. A claim is made that Fluid 1 has a greater density than Fluid 2.

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Question

Which of the following best justifies this claim using the provided graph?

The slope of the line for Fluid 1 is greater, and the slope represents the ratio $m/V$ , which is the density of the fluid.

The area under the line for Fluid 1 is greater, and the area represents the product of mass and volume, which is the density of the fluid.

The line for Fluid 1 reaches a higher maximum mass, indicating that Fluid 1 contains more particles per unit volume.

The slope of the line for Fluid 1 is greater, and the slope represents the ratio $V/m$ , which means the fluid is more compressible.

visual_answers

Stimulus-based practice question

Three solid objects A, B, and C have identical volumes but different masses, such that $m_A < m_B < m_C$ . All three objects are held completely submerged in a tank of water. The bar chart shows the mass of each object.

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Question

Which of the following bar charts could represent the magnitude of the buoyant force $F_b$ exerted on each object while fully submerged?

Example FRQs

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FRQ

Fluid pressure in narrowing horizontal pipe system

2. Water flows steadily through a horizontal pipe that narrows and then discharges into a vertical transparent cylinder that contains a floating piston, as shown in Figure 1.

Figure 1. Steady flow of water through a horizontal pipe with a constriction, discharging into a vertical cylinder that lifts a frictionless piston.

Single clean line diagram (no perspective) showing a left-to-right horizontal pipe that narrows and then connects to a vertical transparent cylinder.

Overall layout (page-relative placement):
- The horizontal pipe occupies the lower half of the figure and spans from the left margin to slightly past the center of the figure.
- The constriction is centered horizontally: the narrowest cross section (cross section 2) is located at the horizontal midpoint of the figure.
- A vertical cylinder is attached immediately to the right of cross section 2 and rises into the upper half of the figure.

Horizontal pipe geometry and labels:
- The pipe is drawn as two parallel horizontal lines (top and bottom wall) with a constant large diameter on the left, then a smooth symmetric taper to a smaller constant diameter at the constriction.
- Cross section 1 is drawn as a vertical dashed line cutting the large-radius region in the left third of the figure; label directly below it: "1".
- Cross section 2 is drawn as a vertical dashed line at the narrowest point (the throat) at the center of the figure; label directly below it: "2".
- The taper begins exactly halfway between cross section 1 and cross section 2 and ends exactly at cross section 2; the taper is symmetric top-to-bottom.
- Large radius at cross section 1 is shown with a double-headed vertical dimension arrow from the centerline to the inner wall, labeled: "r₁ = 2.0 cm".
- Small radius at cross section 2 is shown with a double-headed vertical dimension arrow from the centerline to the inner wall, labeled: "r₂ = 1.0 cm".
- A single thick arrow inside the pipe indicates flow direction to the right; the arrow is centered vertically within the pipe and spans from just right of cross section 1 to just left of cross section 2.
- Near cross section 1, place the text label next to the flow arrow: "v₁ = 1.5 m/s".
- Include an explicit text note between the two cross sections, aligned with their centers: "same height" (or "z₁ = z₂") to indicate the centers of cross sections 1 and 2 are at the same vertical level.

Vertical cylinder and piston:
- Immediately to the right of cross section 2, the pipe opens into a vertical transparent cylinder drawn as two parallel vertical lines. The cylinder’s inner diameter is drawn larger than the throat diameter so the piston can be visually wider than the narrow pipe; the cylinder inner diameter is drawn as exactly twice the throat inner diameter (visual ratio 2:1).
- The cylinder bottom connection is drawn flush with the pipe at cross section 2 so that the centerline of the pipe aligns with the centerline of the cylinder.
- A circular piston is represented in side view as a thick horizontal rectangle that fits snugly between the cylinder walls with no gap.
- The piston is located in the upper half of the cylinder, leaving visible water below it.
- The underside (bottom face) of the piston is a clearly drawn horizontal line; the top face is a parallel horizontal line, making the piston thickness about one-tenth of the cylinder’s visible height.

Height label h:
- Draw a vertical double-headed dimension arrow inside the cylinder from the level of cross section 2 (use the horizontal level through the center of cross section 2) up to the level of the piston’s bottom face.
- Label this dimension arrow: "h = 0.60 m".

Piston parameters and atmospheric pressure:
- On the piston, include two text labels with leader lines pointing to the piston body: "m_p = 3.0 kg" and "A_p = 2.0×10⁻³ m²".
- Above the piston (in the air region), draw several short downward arrows uniformly spaced and pointing down onto the piston’s top surface; label centered above these arrows: "P_atm = 1.01×10⁵ Pa".

Fluid identification:
- Label the fluid in the pipe/cylinder region as "water" and include the density text near the pipe: "ρ = 1000 kg/m³".

Styling constraints:
- Use black outlines for all walls and piston edges.
- Transparent cylinder is indicated by thin black lines; water region is unshaded (no fill) to avoid implying changing water level.
- All numeric values must appear exactly as written: 2.0 cm, 1.0 cm, 1.5 m/s, 0.60 m, 3.0 kg, 2.0×10⁻³ m², 1.01×10⁵ Pa, 1000 kg/m³.

Figure 2. Pressure bar chart at cross section 1 (students complete bars).

Bar chart template with fully specified axes and categories for pressures at cross section 1.

Axes:
- Vertical axis label: "Pressure (Pa)".
- Vertical axis range: from [value removed — blank template] at the dashed zero line up to 1.40×10⁵ Pa at the top of the axis.
- Vertical tick marks and labels at every 2.0×10⁴ Pa: show visible tick labels "0", "2.0×10⁴", "4.0×10⁴", "6.0×10⁴", "8.0×10⁴", "1.0×10⁵", "1.2×10⁵", "1.4×10⁵".
- A bold dashed horizontal line across the plot at [value removed — blank template] labeled "0" at the y-axis (this dashed line is the required start line for all shaded bars).
- Horizontal axis label centered below categories: "Pressure components".
- Three category tick positions, left-to-right, equally spaced: "P_g", "P_atm", "P_total".
- No arrows on the ends of the axes (template style).
- The origin is shown implicitly at the intersection of the left axis and the dashed 0 line, with the tick label "0".

Bars (template placeholders; unshaded outlines so students can shade):
- Three empty bar rectangles (white fill) with black outlines (1.5 pt stroke), one centered under each category.
- Uniform bar width: each bar occupies exactly one-half of the horizontal spacing between adjacent category centers, leaving equal gaps on both sides.
- Each bar rectangle base sits exactly on the dashed [value removed — blank template] line.
- Each bar rectangle extends upward to the top y-limit (1.40×10⁵ Pa) as an empty container outline to indicate the drawable region.

Distinct zero-pressure marker rule (printed on the figure):
- Under the plot (small text): "If a pressure equals zero, draw a single horizontal line on the [value removed — blank template] dashed line in that column."

Figure 3. Pressure bar chart at cross section 2 (students complete bars).

Bar chart template identical in scale and formatting to Figure 2, for pressures at cross section 2.

Axes:
- Vertical axis label: "Pressure (Pa)".
- Vertical axis range: [value removed — blank template] to 1.40×10⁵ Pa.
- Vertical tick marks and labels at every 2.0×10⁴ Pa: visible tick labels "0", "2.0×10⁴", "4.0×10⁴", "6.0×10⁴", "8.0×10⁴", "1.0×10⁵", "1.2×10⁵", "1.4×10⁵".
- A bold dashed horizontal line across the plot at [value removed — blank template].
- Horizontal axis label: "Pressure components".
- Three equally spaced category labels left-to-right: "P_g", "P_atm", "P_total".
- No arrows on the axes.

Bars (template placeholders; unshaded outlines so students can shade):
- Three empty bar rectangles (white fill) with black outlines (1.5 pt stroke), one per category.
- Uniform bar width: each bar occupies exactly one-half of the spacing between category centers.
- Bar bases lie exactly on the dashed [value removed — blank template] line; bar containers extend upward to the 1.40×10⁵ Pa top limit.

Printed rule under the plot (same as Figure 2):
- "If a pressure equals zero, draw a single horizontal line on the [value removed — blank template] dashed line in that column."

Figure 4. Reference pressure bar chart for water just under the piston (given).

Completed reference bar chart giving the pressure components for the water immediately below the piston, with explicit numeric bar heights and non-zero error bars.

Compute the shown values (must be printed as bar heights):
- P_atm = 1.01×10⁵ Pa.
- Gauge pressure under piston equals piston weight per area: P_g = (m_p g)/A_p = (3.0 kg × 9.8 m/s²) / (2.0×10⁻³ m²) = 1.47×10⁴ Pa (shown as 1.47×10⁴ Pa).
- Total pressure: P_total = P_atm + P_g = 1.16×10⁵ Pa (shown as 1.16×10⁵ Pa).

Axes:
- Vertical axis label: "Pressure (Pa)".
- Vertical axis range: [value removed — blank template] to 1.40×10⁵ Pa.
- Vertical tick marks and labels every 2.0×10⁴ Pa: "0", "2.0×10⁴", "4.0×10⁴", "6.0×10⁴", "8.0×10⁴", "1.0×10⁵", "1.2×10⁵", "1.4×10⁵".
- Dashed horizontal line at [value removed — blank template] across the plot.
- Horizontal axis label: "Pressure components".
- Categories left-to-right: "P_g", "P_atm", "P_total".
- No arrows on axes.

Bars:
- Three solid medium-gray bars with black outlines (1.5 pt stroke), all with identical widths (each bar occupies exactly one-half of the spacing between category centers).
- Bar 1 (category "P_g"): height exactly 1.47×10⁴ Pa.
- Bar 2 (category "P_atm"): height exactly 1.01×10⁵ Pa.
- Bar 3 (category "P_total"): height exactly 1.16×10⁵ Pa.
- All bars start exactly at the dashed [value removed — blank template] line.

Error bars (must be drawn above each bar with caps):
- Use symmetric vertical error bars with black lines and horizontal caps.
- Cap width: one-third of the bar width.
- Bar "P_g": mean 1.47×10⁴ Pa, error bar endpoints at 1.32×10⁴ Pa and 1.62×10⁴ Pa (±1.5×10³ Pa).
- Bar "P_atm": mean 1.01×10⁵ Pa, error bar endpoints at 9.60×10⁴ Pa and 1.06×10⁵ Pa (±5.0×10³ Pa).
- Bar "P_total": mean 1.16×10⁵ Pa, error bar endpoints at 1.10×10⁵ Pa and 1.22×10⁵ Pa (±6.0×10³ Pa).

Title text placed above the plotting area:
- "Water just under piston"

Draw shaded bars that represent $P_{\text{atm}}$ , $P_g$ , and $P_{\text{total}}$ to complete the pressure bar charts in Figure 2 and Figure 3 for cross section 1 and cross section 2, respectively. Figure 4 shows a bar chart that represents the atmospheric pressure $P_{\text{atm}}$ , the gauge pressure $P_g$ , and the total pressure $P_{\text{total}}$ of the water just under the piston. Gauge pressure is defined by $P_g = P_{\text{total}} - P_{\text{atm}}$ . Atmospheric pressure is the same at all locations. The bars in Figure 4 establish the scale for pressure.

• Shaded bars should start at the dashed line that represents zero pressure.
• Represent any pressure that is equal to zero with a distinct line on the zero line.
• The relative heights of each shaded bar should reflect the magnitude of the respective pressure consistent with the scale used in Figure 4.

Figure 5. Force balance on the piston and hydrostatic pressure relation between cross section 2 and the piston.

Two-panel diagram arranged side-by-side with equal panel widths, separated by a thin vertical divider line.

Left panel: Free-body diagram of the piston
- Draw a simplified piston as a horizontal rectangle centered in the left panel.
- Three forces are shown with arrows whose tails start on the piston and whose arrowheads point in the force direction.
- Upward force: a single vertical arrow starting at the center of the piston’s bottom face and pointing straight up. Label next to the arrow: "F_water = P_under A_p".
- Downward weight: a single vertical arrow starting at the piston’s center of mass (center of rectangle) and pointing straight down. Label: "m_p g".
- Downward atmospheric force: a single vertical arrow starting at the center of the piston’s top face and pointing straight down. Label: "P_atm A_p".
- Include piston parameter text near the rectangle: "m_p = 3.0 kg" and "A_p = 2.0×10⁻³ m²".

Right panel: Hydrostatic column relating pressures
- Draw a vertical cylinder segment as two parallel vertical lines.
- At the top of this right panel, draw the piston bottom face as a horizontal line sealing the cylinder; label the region immediately below it: "just under piston".
- At the bottom of this right panel, draw a horizontal reference line representing the level of cross section 2; label it: "cross section 2".
- Draw a vertical double-headed arrow between these two horizontal levels (from cross section 2 level up to the piston bottom face level) labeled exactly: "h = 0.60 m".
- Indicate increasing pressure with depth: draw three short horizontal tick marks on the right cylinder wall, with small inward arrows pointing toward the fluid at progressively lower positions, and a vertical annotation text: "pressure increases with depth".
- Show the hydrostatic relation as printed text within the panel (not as an equation to be solved, just a labeled relation): "P_2 = P_under + ρ g h".
- Include constants printed near the relation: "ρ = 1000 kg/m³" and "g = 9.8 m/s²".

Starting with a fundamental physics principle, derive an equation for the total pressure $P_{2}$ at cross section 2 in terms of $m_p$ , $A_p$ , $h$ , $\rho$ , $g$ , and $P_{\text{atm}}$ . Your derivation must include (1) an equation representing the force balance on the piston and (2) an equation relating the pressure at cross section 2 to the pressure just under the piston. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The piston rises slowly, so the piston is in vertical force equilibrium at all times (see Figure 5). The bottom of the piston is $h = 0.60\ \text{m}$ above cross section 2. The centers of cross sections 1 and 2 are at the same height. The piston has $m_p = 3.0\ \text{kg}$ and $A_p = 2.0× 10^{-3}\ \text{m}^2$ . Use $\rho = 1000\ \text{kg/m}^3$ , $g = 9.8\ \text{m/s}^2$ , and $P_{\text{atm}} = 1.01× 10^5\ \text{Pa}$ .

Figure 6. Energy-per-unit-volume terms along the flow from cross section 1 to cross section 2 to just under the piston.

Single 2D plot with axes and one pre-drawn curve for the dynamic term. Students add two additional labeled curves.

Axes:
- Horizontal axis label: "Location along flow" (no units).
- Horizontal axis range: from 0 to 3.
- Horizontal tick marks and labels at 0, 1, 2, 3.
- The three labeled locations align exactly with tick marks:
- At x-tick 1: label directly below axis: "1" and beneath it (smaller text): "cross section 1".
- At x-tick 2: label: "2" and beneath it: "cross section 2".
- At x-tick 3: label: "3" and beneath it: "just under piston".
- Vertical axis label: "Energy per unit volume (Pa)".
- Vertical axis range: from [value removed — blank template] to 1.40×10⁵ Pa.
- Vertical tick marks and labels every 2.0×10⁴ Pa: "0", "2.0×10⁴", "4.0×10⁴", "6.0×10⁴", "8.0×10⁴", "1.0×10⁵", "1.2×10⁵", "1.4×10⁵".
- The origin is explicitly labeled "0" at the intersection of the axes.
- Arrows on the positive ends of both axes.
- No grid lines.

Pre-drawn curve (dynamic term):
- A solid black curve labeled "dynamic term (½ρv²)" placed near the curve.
- From location 1 to location 2: the curve is a straight rising line segment (no curvature) showing an increase.
- From location 2 to location 3: the curve is a perfectly horizontal line segment (constant value).
- The dynamic-term curve is drawn so that at location 1 it sits at exactly one-quarter of the full y-range (i.e., at the tick value 3.5×10⁴ Pa), and at locations 2 and 3 it sits at exactly one-half of the full y-range (i.e., at the tick value 7.0×10⁴ Pa). These tick values must be used as the endpoints of the drawn line segments so the increases are numerically locked to the axis.

Student-added curves (blank space reserved):
- Provide no additional curves, but include two empty label callouts (text only, with short leader lines pointing to blank regions): "pressure term P" and "gravitational term ρgh".
- The blank space should clearly allow students to draw:
- A pressure-term curve spanning locations 1→2→3.
- A gravitational-term curve spanning locations 1→2→3.

Styling:
- All axes and ticks in black.
- Dynamic curve in black, medium thickness.
- Labels in plain sans-serif font; use Greek rho "ρ" in "½ρv²" and "ρgh".

Figure 6 is a graph of energy per unit volume along the flow from cross section 1 to cross section 2 and then upward to just under the piston. The curve labeled 'Dynamic term' represents $\tfrac12\rho v^2$ and is already drawn. Assume the speed in the vertical cylinder is equal to the speed at cross section 2. The flow is steady, incompressible, and nonviscous.

Sketch and label a curve on Figure 6 that represents the pressure term $P$ along the flow (from cross section 1 to cross section 2 to just under the piston).

ii.

Sketch and label a curve on Figure 6 that represents the gravitational term $\rho g h$ along the flow (from cross section 1 to cross section 2 to just under the piston).

Indicate whether the speed $v_2$ of the water at cross section 2 is greater than, less than, or equal to the speed $v_1$ at cross section 1. Use $r_1 = 2.0\ \text{cm}$ , $r_2 = 1.0\ \text{cm}$ , and $v_1 = 1.5\ \text{m/s}$ at cross section 1. Water is incompressible.

$v_2 > v_1$
$v_2 < v_1$
$v_2 = v_1$
Justify how your response is consistent with the curves you sketched in Figure 6 in part C.

write this FRQ

FRQ

Fluid pressure and buoyant force in pipe flow

1. A rigid horizontal pipe carries water that flows steadily from left to right, as shown in Figure 1. The pipe narrows from a wide section to a narrow section. At the wide section the pipe has cross-sectional area $A_1$ , and at the narrow section it has cross-sectional area $A_2$ . A pressure gauge measures the fluid pressure at each section. A small spherical object is held fully submerged in the water at the wide section by a light string attached to the bottom of the pipe, as shown in Figure 1.

Figure 1. Horizontal rigid pipe with steady incompressible flow from section 1 (wide, area A1) to section 2 (narrow, area A2). Pressures P1 and P2 are measured at the two sections, and a fully submerged sphere in section 1 is tethered by a light string to the bottom of the pipe.

Single-panel black-and-white physics diagram (no perspective; side view cross-section of the pipe).

Overall layout and orientation:
- Draw a long, straight, perfectly horizontal pipe centered vertically on the page, extending nearly the full width.
- The pipe’s left half is the wide section and the right half is the narrow section, connected by a single smooth converging transition region.
- Define the position axis x along the centerline of the pipe: place a rightward arrow labeled "+x" directly below the pipe, aligned with the pipe, with the arrowhead pointing to the right.

Pipe geometry (explicit spatial relationships):
- Wide section (section 1): occupies the left half of the pipe and has a constant inner height (top and bottom walls parallel).
- Narrow section (section 2): occupies the right half of the pipe and has a constant inner height that is clearly smaller than the wide section (top and bottom walls parallel).
- Transition: between the two constant-area regions, draw a single continuous taper where the top wall slopes downward and the bottom wall slopes upward symmetrically so the centerline stays horizontal.

Section boundaries and labels:
- Mark two vertical dashed reference lines across the pipe interior to indicate the measurement locations:
- The first dashed line is placed in the wide constant-area region, well to the left of the taper, and labeled "1" just above the top wall.
- The second dashed line is placed in the narrow constant-area region, well to the right of the taper, and labeled "2" just above the top wall.
- At section 1 (near the first dashed line), place the text labels "A₁" and "P₁" adjacent to the pipe (A₁ placed near the cross-section label; P₁ placed near the gauge described below).
- At section 2 (near the second dashed line), place the text labels "A₂" and "P₂" similarly.

Flow direction and speed labels:
- Inside the pipe, along the centerline in the wide region, draw a right-pointing arrow labeled "v₁".
- Inside the pipe, along the centerline in the narrow region, draw a right-pointing arrow labeled "v₂".
- Ensure both velocity arrows point exactly to the right (same direction as +x) and are located within their respective constant-area regions (v₁ in the wide region, v₂ in the narrow region).

Pressure gauges (must be explicitly drawn at both sections):
- At section 1: draw a small circular pressure gauge symbol outside the pipe, connected to the pipe by a short thin line (a tap) that meets the pipe wall exactly at the location of the section-1 dashed line. Place the label "P₁" next to this gauge.
- At section 2: draw an identical gauge outside the pipe, connected by an identical tap line meeting the pipe wall exactly at the location of the section-2 dashed line. Place the label "P₂" next to this gauge.
- The two gauges should be drawn at the same vertical height relative to the pipe (for visual symmetry), e.g., both above the pipe or both below the pipe; do not mix.

Sphere and string (fully submerged, tethered to bottom):
- In the wide section (section 1), draw a small sphere inside the water region.
- Place the sphere entirely below the centerline, closer to the bottom wall than the top wall, while leaving a visible gap between the sphere and the bottom wall so it is clearly not resting on the bottom.
- The sphere must be fully submerged: draw it completely inside the pipe interior with water surrounding it on all sides (no part intersecting walls).
- From the sphere’s bottommost point, draw a straight, vertical string segment down to the inner surface of the bottom wall of the pipe.
- The string attaches to the bottom wall at a single point directly below the sphere (no angled string). Indicate the string is light by drawing it as a thin line.

Clean labeling constraints:
- Only the following text appears on the diagram: "A₁", "A₂", "P₁", "P₂", "v₁", "v₂", "1", "2", and "+x".
- No numerical values are shown.
- All lines are solid except the two vertical dashed section markers.

Figure 2. Axes for a student sketch of fluid pressure P versus position x along the pipe from section 1 to section 2.

Single-panel blank graph with grid lines.

Axes and scale (all numeric markings must appear):
- Horizontal axis labeled exactly: "x (position along the pipe)" centered below the axis.
- Horizontal axis range: from 0 at the left end to 2 at the right end.
- Horizontal tick marks and labels: ticks at 0, 1, and 2 only, with the numerals "0", "1", and "2" printed below their ticks.
- Vertical axis labeled exactly: "P (fluid pressure)" written along the vertical axis.
- Vertical axis range: from 0 at the bottom to 10 at the top.
- Vertical tick marks and labels: ticks at every 1 unit, labeled with the numerals "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10".
- The origin is explicitly labeled "0" at the intersection of the axes.
- Arrowheads: place an arrowhead on the positive (right) end of the x-axis and an arrowhead on the positive (up) end of the y-axis.

Grid:
- Light, evenly spaced grid lines aligned with every tick mark on both axes (vertical grid lines at x=0, x=1, x=2; horizontal grid lines at each integer P value from 0 to 10).

Section markers on the x-axis:
- The tick labeled "1" corresponds to section 1.
- The tick labeled "2" corresponds to section 2.
- Add small text directly above the x-axis at x=1 reading "section 1" and at x=2 reading "section 2" (these two phrases are the only additional text beyond axis labels and numbers).

Curve requirement (must be blank):
- No pressure curve is drawn anywhere on the axes.
- No points, arrows, or annotations besides the axes, grid, tick labels, and the two section-text markers.

On the axes shown in Figure 2, sketch a graph of the fluid pressure $P$ as a function of position $x$ along the pipe from section 1 to section 2.

ii.

Derive an expression for the speed $v_2$ of the water in the narrow section in terms of $v_1$ , $A_1$ , and $A_2$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

iii.

Derive an expression for the pressure difference $P_1 - P_2$ in terms of $\rho$ , $v_1$ , $A_1$ , and $A_2$ . Assume the water is incompressible, the flow is steady, and the pipe is horizontal. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Indicate whether the magnitude of the tension in the string is greater than, less than, or equal to the magnitude of the buoyant force on the sphere. The spherical object is held fully submerged and at rest relative to the pipe by the string. The water exerts a buoyant force on the sphere. The water also exerts a pressure force on all points of the sphere's surface, but because the sphere is small compared with the pipe diameter at section 1, the pressure in the surrounding water at the sphere's location may be treated as approximately uniform at a given height.

Greater than
Less than
Equal to
Justify your response by applying Newton's second law to the sphere and identifying the vertical forces acting on it.

write this FRQ

FRQ

Fluid pressure changes across varying cross-sectional areas

4. In Scenario 1, water (assumed incompressible) flows steadily through a horizontal pipe segment from left to right, as shown in Figure 1. At location 1 the pipe has cross-sectional area $A_1 = 6.0\times10^{-4}\ \text{m}^2$ , and at location 2 the pipe narrows to cross-sectional area $A_2 = 3.0\times10^{-4}\ \text{m}^2$ . The volumetric flow rate is constant at $Q = 1.2\times10^{-3}\ \text{m}^3/\text{s}$ . The density of water is $\rho = 1000\ \text{kg/m}^3$ . The pressure at location 1 is $P_1 = 2.40\times10^5\ \text{Pa}$ . All viscosity effects are negligible.

In Scenario 2, the same horizontal pipe segment carries the same water with the same constant volumetric flow rate $Q = 1.2\times10^{-3}\ \text{m}^3/\text{s}$ , but the second location has a larger cross-sectional area $A_2' = 9.0\times10^{-4}\ \text{m}^2$ instead of $A_2$ . The cross-sectional area at location 1 remains $A_1 = 6.0\times10^{-4}\ \text{m}^2$ , and the pressure at location 1 remains $P_1 = 2.40\times10^5\ \text{Pa}$ . All viscosity effects are negligible.

Figure 1. Steady incompressible flow through a horizontal pipe: Scenario 1 (constriction to A2) and Scenario 2 (expansion to A2′).

Create a clean, black-and-white physics schematic with TWO clearly separated subpanels side-by-side (left subpanel = Scenario 1, right subpanel = Scenario 2). Use identical styling and the same left-to-right flow direction in both subpanels so the only visual difference is the cross-sectional area at location 2.

GLOBAL LAYOUT (applies to both subpanels):
- Each subpanel contains one straight, perfectly horizontal pipe drawn as a long rectangle (outline only) spanning most of that subpanel’s width.
- The pipe centerline is horizontal; the pipe is not tilted. The left end is open and the right end is open.
- Flow direction is left to right in both subpanels, shown by a large arrow above the pipe pointing directly right.
- Mark two measurement locations with thin vertical dashed lines that cross the pipe from its top boundary to its bottom boundary:
- Location 1 dashed line placed in the left third of the pipe, clearly inside a uniform section (before any diameter change).
- Location 2 dashed line placed in the right third of the pipe, clearly inside a uniform section (after the diameter change has fully completed).
- The pipe changes size only once between location 1 and location 2. The transition region is centered between the two dashed lines:
- The transition is drawn with straight slanted walls (a linear taper) from the first uniform section to the second uniform section.
- No curved walls; no additional bends.
- To emphasize “same height,” draw a faint horizontal reference line behind the pipe (or aligned with the pipe centerline) and label it “same height” centered below the pipe; the pipe sits exactly on this reference line in both subpanels.

TEXT/VARIABLE LABELING (must appear as visible text exactly as written):
- Above each subpanel, centered:
- Left subpanel title: “Scenario 1”
- Right subpanel title: “Scenario 2”
- At location 1 in BOTH subpanels (same labels in same relative positions):
- Place the label “Location 1” just above the location-1 dashed line.
- Place “A₁ = 6.0×10⁻⁴ m²” just below the pipe, directly under the location-1 dashed line.
- Place “P₁ = 2.40×10⁵ Pa” just above the pipe, directly above the location-1 dashed line (but below the flow-direction arrow).
- At location 2 in Scenario 1 (left subpanel):
- Place the label “Location 2” just above the location-2 dashed line.
- Place “A₂ = 3.0×10⁻⁴ m²” just below the pipe, directly under the location-2 dashed line.
- Place “P₂” just above the pipe, directly above the location-2 dashed line.
- At location 2 in Scenario 2 (right subpanel):
- Place the label “Location 2” just above the location-2 dashed line.
- Place “A₂′ = 9.0×10⁻⁴ m²” just below the pipe, directly under the location-2 dashed line.
- Place “P₂′” just above the pipe, directly above the location-2 dashed line.
- Add given fluid information as a small note box (same in both subpanels, positioned in the lower-right corner of each subpanel):
- Line 1: “Q = 1.2×10⁻³ m³/s (constant)”
- Line 2: “ρ = 1000 kg/m³”
- Line 3: “viscosity negligible”

PIPE GEOMETRY REQUIREMENTS (numerically consistent depiction using relative widths):
- The left uniform section (where location 1 is placed) must be the same thickness in both subpanels.
- Scenario 1 (left subpanel):
- The right uniform section (where location 2 is placed) must be exactly HALF the pipe thickness (diameter/height of the rectangular pipe) of the left uniform section, to visually represent A₂ = (1/2)A₁.
- The taper transitions from the larger thickness to the smaller thickness with straight slanted walls.
- Scenario 2 (right subpanel):
- The right uniform section (where location 2 is placed) must be exactly 1.5 TIMES the pipe thickness of the left uniform section, to visually represent A₂′ = (3/2)A₁.
- The taper transitions from the smaller thickness to the larger thickness with straight slanted walls.

VELOCITY ARROWS (must encode the correct relative speeds for constant Q):
- At location 1 in BOTH subpanels, draw an internal arrow centered vertically within the pipe, starting slightly left of the location-1 dashed line and pointing right across it. Label it “v₁” above the arrow.
- At location 2 in BOTH subpanels, draw an internal arrow centered vertically within the pipe, starting slightly left of the location-2 dashed line and pointing right across it. Label it “v₂” (Scenario 1) and “v₂′” (Scenario 2) above the respective arrows.
- Arrow length comparison must be unambiguous and consistent with continuity (v = Q/A):
- Scenario 1: the “v₂” arrow must be exactly 2 times the length of the “v₁” arrow (since A₂ is half of A₁).
- Scenario 2: the “v₂′” arrow must be exactly (2/3) the length of the “v₁” arrow (since A₂′ is 1.5 times A₁).
- Keep arrow thickness the same; only change arrow length to represent speed differences.

CONSISTENCY/CLARITY DETAILS:
- Ensure the location dashed lines are placed in fully uniform sections (not in the taper).
- Ensure no extra numerical values are shown other than those specified.
- Keep the two subpanels aligned vertically so the pipes are at the same vertical level, reinforcing “horizontal” and “same height.”

Refer to Figure 1. Indicate whether the pressure at location 2 in Scenario 1, $P_2$ , is greater than, less than, or equal to the pressure at location 2 in Scenario 2, $P_2'$ , by writing one of the following in your answer booklet.

• $P_2 > P_2'$
• $P_2 < P_2'$
• $P_2 = P_2'$

Justify your answer in terms of how the fluid speed and the energy of the fluid-Earth system change between locations 1 and 2 in each scenario. Use qualitative reasoning beyond referencing equations.

Starting with a fundamental physics principle for fluids and the mass conservation relationship, derive an expression for the pressure difference $P_1 - P_2$ . Express your answer in terms of $\rho$ , $Q$ , $A_1$ , and $A_2$ only. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Consider the general case of steady, incompressible, nonviscous flow through a horizontal pipe from location 1 (area $A_1$ , pressure $P_1$ ) to location 2 (area $A_2$ , pressure $P_2$ ) with constant volumetric flow rate $Q$ and fluid density $\rho$ .

Indicate whether the expression for $P_1 - P_2$ you derived in part B is or is not consistent with the claim made in part A. Briefly justify your answer by referencing your derivation in part B and how changing the area at location 2 affects the pressure at location 2.

write this FRQ

Key terms

Term	Definition
Archimedes' principle	The buoyant force on an object equals the weight of the fluid it displaces. Mathematically, Fb = rho_fluid * V_displaced * g.
Bernoulli's equation	P + rhogy + (1/2)rhov^2 = constant along a streamline. Expresses conservation of mechanical energy per unit volume in an ideal fluid.
buoyant force	The net upward force a fluid exerts on a submerged object, resulting from the pressure difference between the bottom and top of the object.
continuity equation	A1v1 = A2v2. For an incompressible fluid, the product of cross-sectional area and flow speed is constant, expressing conservation of mass flow rate.
volume flow rate	Q = Av, in m^3/s. The volume of fluid passing through a cross-section per unit time. Constant throughout a pipe for an incompressible fluid.
scalar	A quantity with magnitude only and no direction. Pressure is a scalar; the force that pressure exerts on a surface is a vector.
macroscopic behavior	The large-scale, observable behavior of a fluid as a whole, arising from the combined internal particle interactions and external forces such as gravity.

Common unit 8 mistakes

Using the object's density instead of the fluid's density in Fb = rhoVg

The buoyant force depends on the density of the fluid, not the object. The V in the formula is the volume of fluid displaced, which equals the submerged volume of the object, not necessarily its total volume.

Confusing absolute pressure and gauge pressure

Gauge pressure is rho*g*h alone. Absolute pressure adds the reference pressure P0 (often atmospheric). When a problem asks for total or absolute pressure, include P0. When it asks for gauge pressure, use only rho*g*h.

Forgetting that pressure is a scalar

Pressure has no direction. Do not assign a vector direction to pressure itself. The force that pressure exerts on a surface does have a direction (perpendicular to the surface), but pressure is magnitude only.

Applying the continuity equation to compressible fluids or open systems

A1v1 = A2v2 holds only for incompressible fluids in a closed pipe. It does not apply to gases that can compress or to situations where fluid enters or exits the system at multiple points.

Misidentifying which terms cancel in Bernoulli's equation

Before solving, check whether the two points are at the same height (y1 = y2 cancels the rho*g*y terms) or whether one surface is large enough that its speed is approximately zero (v1 = 0 simplifies the kinetic energy term). Skipping this step leads to algebra errors.

How this unit shows up on the AP exam

Quantitative free-response problems combining multiple fluid concepts

AP Physics 1 free-response questions on fluids often require students to apply two or more concepts in sequence: for example, using density to find whether an object floats, then calculating the buoyant force and applying Newton's second law to find acceleration. Setting up a correct free-body diagram and labeling all forces with correct formulas is essential for earning full credit.

Qualitative and proportional reasoning about pressure and flow

Multiple-choice and free-response items frequently ask students to predict what happens to pressure, speed, or buoyant force when one variable changes, such as when a pipe narrows or an object is pushed deeper. Bernoulli's equation and the continuity equation are the tools for these proportional reasoning tasks. Explaining the physical reasoning behind a prediction, not just stating the answer, is a common scoring requirement.

Derivation and justification tasks using conservation laws

The exam may ask students to derive Torricelli's theorem from Bernoulli's equation or to justify why the continuity equation follows from conservation of mass. These tasks require students to start from a general principle, state assumptions (ideal fluid, incompressible, steady flow), and show algebraic steps. Citing the correct conservation law by name and connecting it to the equation is part of the expected response.

Final unit 8 review checklist

Final Unit 8 review checklistUse this list to confirm you can handle every major skill in the fluids unit before the exam.
Calculate density and identify fluid typeUse rho = m/V to find density in kg/m^3. Identify whether a substance is a solid, liquid, or gas based on intermolecular forces, and confirm whether it qualifies as an ideal fluid.
Apply the pressure equationsCalculate pressure using P = F_perp/A. Find absolute pressure at depth h using P = P0 + rho*g*h and gauge pressure using P_gauge = rho*g*h. Recognize that pressure is a scalar.
Analyze buoyancy with free-body diagramsDraw weight and buoyant force on a submerged or floating object. Apply Fb = rho_fluid*V_displaced*g and Newton's second law to determine whether the object floats, sinks, or is in equilibrium.
Use the continuity equationApply A1v1 = A2v2 to find the speed of an incompressible fluid in a pipe of changing cross-section. Calculate volume flow rate Q = Av and confirm it is constant throughout the pipe.
Apply Bernoulli's equation and Torricelli's theoremSet up P1 + rho*g*y1 + (1/2)*rho*v1^2 = P2 + rho*g*y2 + (1/2)*rho*v2^2 between two points on a streamline. Apply Torricelli's theorem v = sqrt(2*g*delta_y) for fluid exiting an opening in a tank.
Connect fluids to earlier unitsRecognize that buoyancy is a Newton's second law problem, that Bernoulli's equation is an energy conservation statement, and that the continuity equation is mass conservation. Draw on Units 2 and 3 reasoning throughout.

How to study unit 8

Start with density and ideal fluid properties (8.1)Read the 8.1 topic guide and practice calculating density using rho = m/V. Make sure you can distinguish solids, liquids, and gases by intermolecular forces and explain what makes a fluid ideal. This foundation is required for every other topic in the unit.

Work through pressure at a surface and with depth (8.2)Practice applying P = F_perp/A and P = P0 + rho*g*h to numerical problems. Drill the difference between absolute and gauge pressure. Use the 8.2 topic guide and attempt several practice questions that vary depth and reference pressure.

Build buoyancy skills with free-body diagrams (8.3)For every buoyancy problem, draw the free-body diagram first: weight down, buoyant force up. Apply Fb = rho_fluid*V_displaced*g and Newton's second law. Practice floating, sinking, and equilibrium scenarios using the 8.3 topic guide and available FRQ practice.

Practice continuity and Bernoulli problems (8.4)Work through pipe-flow problems using A1v1 = A2v2 before adding Bernoulli's equation. Then practice full Bernoulli setups that combine pressure, height, and speed changes. Finish with Torricelli's theorem problems. The 8.4 topic guide and FRQ practice are available for this topic.

Do a full unit review and use the score calculatorAfter covering all four topics, attempt mixed fluids problems that combine density, pressure, buoyancy, and flow in a single scenario. Use the AP score calculator to estimate where your performance puts you on the exam scale and identify which topics need more attention.

More ways to review

Topic study guides

Open the individual guides for Unit 8 when you want a closer review of one topic.

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Practice questions

Use AP-style practice after you review the notes so you can check what you understand.

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FRQ practice

Practice free-response reasoning and compare your answer with scoring guidance.

practice FRQs

Cheatsheets

Use unit cheatsheets for a quick visual review after you work through the notes.

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Score calculator

Estimate your broader AP score goal after you review the course and exam format.

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Frequently Asked Questions

What topics are covered in AP Physics 1 Unit 8?

AP Physics 1 Unit 8 covers four topics: **8.1 Internal Structure and Density**, **8.2 Pressure**, **8.3 Fluids and Newton's Laws**, and **8.4 Fluids and Conservation Laws**. Together they build a complete picture of how ideal fluids behave, from why objects sink or float to how energy and momentum are conserved in moving fluids. See everything for this unit at /ap-physics-1-revised/unit-8.

How much of the AP Physics 1 exam is Unit 8?

Unit 8 makes up 10-15% of the AP Physics 1 exam, making it one of the more significant units to know well. It covers fluids topics including density, pressure, buoyancy, and conservation laws applied to fluid systems. That weight means you can expect several multiple-choice questions and a possible FRQ drawing from this material.

What's on the AP Physics 1 Unit 8 progress check (MCQ and FRQ)?

The AP Physics 1 Unit 8 progress check includes both MCQ and FRQ parts drawn from all four unit topics: Internal Structure and Density, Pressure, Fluids and Newton's Laws, and Fluids and Conservation Laws. MCQ questions typically test conceptual understanding of density and pressure relationships, while the FRQ section asks you to apply Newton's laws and conservation principles to fluid scenarios. For matched practice questions, head to /ap-physics-1-revised/unit-8.

How do I practice AP Physics 1 Unit 8 FRQs?

The best way to practice AP Physics 1 Unit 8 FRQs is to focus on the two topics that generate the most free-response material: **8.3 Fluids and Newton's Laws** and **8.4 Fluids and Conservation Laws**. FRQs in this unit often ask you to set up force diagrams for submerged objects, justify buoyancy using pressure differences, or apply continuity and energy conservation to fluid flow. Practice by writing out full justifications, not just equations, since College Board awards points for reasoning. Find Unit 8 FRQ practice at /ap-physics-1-revised/unit-8.

Where can I find AP Physics 1 Unit 8 practice questions?

You can find AP Physics 1 Unit 8 multiple-choice and free-response practice questions at /ap-physics-1-revised/unit-8. That page pulls together MCQ sets and practice test questions covering all four topics: density, pressure, fluids and Newton's laws, and fluids and conservation laws. Working through timed MCQ sets is especially useful since 10-15% of the real exam comes from this unit.

How should I study AP Physics 1 Unit 8?

Start with **8.1 Internal Structure and Density** to lock in the relationship between mass, volume, and density before moving on. From there, build up through pressure (8.2), then connect fluids to Newton's laws (8.3) by drawing force diagrams for objects in fluids. Finish with conservation laws (8.4), where continuity and Bernoulli-style reasoning show up. A few concrete steps that help: - Sketch pressure diagrams for every scenario, not just equations. - Practice explaining buoyancy in words, since FRQs reward written justification. - Do at least one timed MCQ set per topic to catch gaps before the exam. All unit resources are at /ap-physics-1-revised/unit-8.

Ready to review Unit 8?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

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AP Physics 1 Unit 8 Review: Fluids

What is AP Physics 1 unit 8?

Density and pressure are the entry points

Buoyancy comes from pressure differences

Flow obeys conservation laws

AP Physics 1 unit 8 topics

Internal Structure and Density

Pressure

Fluids and Newton's Laws

Fluids and Conservation Laws

Hardest AP Physics 1 unit 8 topics

Hardest topics in unit 8

Unit 8 review notes

Properties of Fluids and Density

Pressure at a Surface and Pressure with Depth

Buoyancy and Newton's Laws in Fluids

Continuity Equation and Bernoulli's Equation

Practice AP Physics 1 unit 8 questions

Example stimulus-based MCQs

Stimulus-based practice question

Stimulus-based practice question

Example FRQs

Fluid pressure in narrowing horizontal pipe system

Fluid pressure and buoyant force in pipe flow

Fluid pressure changes across varying cross-sectional areas

Key terms

Common unit 8 mistakes

Using the object's density instead of the fluid's density in Fb = rho*V*g

Confusing absolute pressure and gauge pressure

Forgetting that pressure is a scalar

Applying the continuity equation to compressible fluids or open systems

Misidentifying which terms cancel in Bernoulli's equation

How this unit shows up on the AP exam

Quantitative free-response problems combining multiple fluid concepts

Qualitative and proportional reasoning about pressure and flow

Derivation and justification tasks using conservation laws

Final unit 8 review checklist

How to study unit 8

More ways to review

Topic study guides

Practice questions

FRQ practice

Cheatsheets

Score calculator

Frequently Asked Questions

What topics are covered in AP Physics 1 Unit 8?

How much of the AP Physics 1 exam is Unit 8?

What's on the AP Physics 1 Unit 8 progress check (MCQ and FRQ)?

How do I practice AP Physics 1 Unit 8 FRQs?

Where can I find AP Physics 1 Unit 8 practice questions?

How should I study AP Physics 1 Unit 8?

Using the object's density instead of the fluid's density in Fb = rhoVg