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Flashcards · AP® Physics 1: Algebra-Based · Unit 8

Unit 8: Fluids flashcards

26 cards on topics 8.1 to 8.4. Pick a topic or study the whole unit.

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8.1 Internal Structure and Density

What is density?
ρ = m / V, in kg/m³. It describes a material, not a sample: cutting a uniform object does not change its density.
How do you convert g/cm³ to kg/m³?
1 g/cm³ = 1000 kg/m³. Remember 1 cm³ = 10⁻⁶ m³ (cube the length conversion), 1 mL = 1 cm³ and 1 L = 10⁻³ m³.
How do you find the density of an object made of several parts?
Average density = total mass ÷ total volume. Add masses and volumes separately; never add densities.
What is an ideal fluid?
One that is incompressible (constant density) and has no viscosity (no internal friction). Liquids and gases are both fluids; gases are not incompressible.
How do you find density from several samples of one material?
Plot mass against volume and take the slope of the best-fit line, rather than using one data point.
How do solids, liquids and gases differ?
Solid: fixed shape and volume. Liquid: fixed volume, no fixed shape. Gas: neither, and easy to compress. The differences come from particle spacing and interaction strength.

8.2 Pressure

What is pressure?
P = F⊥ / A, the perpendicular force per unit area, in pascals (1 Pa = 1 N/m²). It is a scalar; a force along the surface adds nothing.
How does pressure vary with depth in a fluid at rest?
P = P₀ + ρgh, where h is vertical depth. Each layer supports the weight of the fluid above. Container width or shape does not matter.
What is the difference between absolute and gauge pressure?
Absolute pressure is the total. Gauge pressure is the amount above a reference, usually atmospheric pressure (1.0 × 10⁵ Pa): P = P_atm + P_gauge.
What is the gauge pressure 2.0 m below the surface of fresh water?
ρgh = 1000 × 9.8 × 2.0 ≈ 2.0 × 10⁴ Pa. The absolute pressure is about 1.2 × 10⁵ Pa.
The depth in a liquid doubles. Does the pressure double?
Only the gauge pressure doubles. Absolute pressure also includes the atmospheric pressure, so it rises by less.
What does the slope of a pressure–depth graph give?
ρg, in Pa/m, so density = slope / g.

8.3 Fluids and Newton’s Laws

What causes the buoyant force?
Fluid pressure is greater on an object's bottom than its top, so the pressure forces add to a net upward force: F_b = (P_bottom − P_top)A.
What is Archimedes' principle?
The buoyant force equals the weight of the displaced fluid: F_b = ρ_fluid V_disp g. Use the fluid's density and the submerged volume.
What fraction of a floating object is under the surface?
V_sub / V = ρ_object / ρ_fluid. A block of density 920 kg/m³ in water is 92% under, 8% above.
A block reads 12.0 N on a scale in air and 9.0 N fully under water. What are the buoyant force and its volume?
F_b = 12.0 − 9.0 = 3.0 N. V = F_b / (ρg) = 3.0 / (1000 × 9.8) ≈ 3.1 × 10⁻⁴ m³.
Does the buoyant force increase with depth?
Not for a fully submerged object in an ideal (incompressible) fluid: the pressure difference between top and bottom is the same at any depth.
Does an object weigh less in water?
No. Its weight mg is unchanged; the scale reading is less because the buoyant force also supports it: T = mg − F_b.
What makes fluid in a level pipe accelerate?
A pressure difference: the fluid accelerates from high to low pressure. No pressure difference is needed for constant velocity in an ideal fluid.

8.4 Fluids and Conservation Laws

What is the continuity equation?
A₁v₁ = A₂v₂ for an incompressible fluid in a full pipe. It comes from conservation of mass: volume flow rate V/t = Av is the same at every section.
Water flows into a section whose diameter is three times larger. How does its speed change?
Area ∝ d², so the area is 9 times larger and the speed becomes 1/9. Square the diameter ratio.
What is Bernoulli's equation?
P₁ + ρgy₁ + ½ρv₁² = P₂ + ρgy₂ + ½ρv₂². It is energy conservation per unit volume for an ideal fluid in steady flow; each term is in Pa = J/m³.
In a level pipe, is pressure higher where the fluid moves faster?
No, lower. With y₁ = y₂, Bernoulli gives P + ½ρv² constant. Water speeding up from 2.0 to 4.0 m/s drops ½ × 1000 × (16 − 4) = 6000 Pa.
What is Torricelli's result?
Fluid leaves an opening at depth h below the open surface of a wide tank at v = √(2gh), like free fall through h. Density cancels.
What assumptions are behind Bernoulli's equation?
Ideal fluid (incompressible, no viscosity), full pipes and steady flow. For Torricelli, a tank much wider than the hole and both surface and jet at atmospheric pressure.
What is the mass flow rate in a pipe?
ρAv, in kg/s. The volume flow rate is Av, in m³/s.

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