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Fluids

8. Fluids — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 7 parts Lesson 1 of 14 2 quizzes

📚 AP PHYSICS 1 Hub / Topical Revision
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Lesson summary

8. Fluids — AP PHYSICS 1 notes: Calculate density and pressure, apply Pascal's principle and buoyancy, and use continuity and Bernoulli's equation to analyse fluid flow.Density — ρ = m/V, the mass per unit volume, in kg/m3.Example — a block 0.20 m × 0.10 m × 0.050 m of mass 2.7 k…

  • Temperature
  • Smaller area
  • Pressure at depth
  • Mercury barometer
  • Buoyant force
  • Vdisplaced

Section 1 of 7Density

Density
  • ρ = m/V, the mass per unit volume, in kg/m3.
Example
  • Example a block 0.20 m × 0.10 m × 0.050 m of mass 2.7 kg has V = 1.0 × 10−3 m3 and ρ = 2.7 × 103 kg/m3 (aluminium).
Mixtures
  • Mixtures mixture density is total mass divided by total volume (200 mL water + 100 mL oil of 0.80 g/cm3 gives 280 g in 300 cm3, 0.93 g/cm3).
Temperature
  • Temperature heating expands a liquid and lowers its density, driving convection.
Water
  • Water densest near 4 °C, which is why ice floats and lakes freeze from the top.
Gases
  • Gases density depends strongly on pressure and temperature.
Floating
  • Floating a liquid with density below 1000 kg/m3 floats on water.

Section 2 of 7Pressure

P = F/A
  • P = F/A perpendicular force per unit area, in pascals (1 Pa = 1 N/m2); a scalar.
    What the symbols mean: p = pressure (Pa = N m−2) · F = force acting at right angles to the surface (N) · A = area (m2)
Smaller area
  • Smaller area the same force gives more pressure.
    • (stiletto heel, drawing-pin point)
Net force
  • Net force a pressure difference gives Fnet = ΔP × A.
Pascal's principle
  • Pascal's principle a pressure change applied to an enclosed fluid is transmitted undiminished everywhere, the basis of hydraulic lifts, F1/A1 = F2/A2.
Pressure at depth
  • P = P0 + ρgh;
    • for immiscible layers add each term, the denser fluid at the bottom, and every interface is a surface of constant pressure.
U-tube
  • U-tube equate pressures at the same level in the same liquid.
Mercury barometer
  • Patm = ρHggh, so h = 1.01 × 105/(13 600 × 9.8) = 0.76 m.

Section 3 of 7Buoyancy

Buoyant force
  • FB = ρfluidVdisplacedg, the weight of fluid displaced.
ρ
ρ is the density of the fluid, not of the object.
Vdisplaced
  • Vdisplaced the whole volume if fully submerged, only the submerged part if floating.
Direction
  • Direction upward, through the centre of the displaced fluid.
Apparent weight
  • Apparent weight buoyancy does not change the object's weight but reduces its apparent weight in the fluid.

Section 4 of 7Continuity

1Volume flow rate
  • Q = Av is the same everywhere for steady flow of an ideal fluid, so A1v1 = A2v2.
    • (incompressible, non-viscous)
2Mass flow rate
  • ρQ.
3Narrowing
  • Narrowing halving the diameter quarters the area and quadruples the speed;
    • a thumb over a hose end sends the spray farther.
4Narrow pipes
  • Narrow pipes do not carry less fluid per second in steady flow.
5Junctions
  • Junctions add flow rates, not speeds.
6Limit
  • Limit continuity says nothing about pressure.

Section 5 of 7Bernoulli's equation

Bernoulli's equation
P + ½ρv2 + ρgy
  • P + ½ρv2 + ρgy is constant along a streamline.
Narrow section
  • Narrow section fluid is faster and the pressure lower.
Rising pipe at same speed
  • Rising pipe at same speed pressure falls by ρgΔy.
Hole at depth h in a tank
  • Hole at depth h in a tank exit speed v = √(2gh) (Torricelli).
Wing
  • Wing lift comes from lower pressure over the faster-moving upper surface.

Section 6 of 7Key terms

TermMeaning
DensityMass per unit volume.
PressurePerpendicular force per unit area.
Pascal's principlePressure change in an enclosed fluid transmits undiminished.
Buoyant forceUpward force equal to the weight of displaced fluid.
Continuity equationA1v1 = A2v2 for incompressible flow.
Bernoulli's equationP + ½ρv2 + ρgy constant along a streamline.
Volume flow rateVolume passing a point per second, Q = Av.

Section 7 of 7Exam technique

1
Using the object's density instead of the fluid's in the buoyant force.
2
Concluding a narrower pipe carries less fluid per second.
3
Using diameters instead of areas in continuity.
4
Assuming faster fluid means higher pressure — Bernoulli gives lower.
5
Adding speeds instead of flow rates at a junction.

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