Part 1: Multiple choice
Fluids include:
Which statement is correct?
The SI unit of density is:
The dimensional formula of density is:
A liquid of mass 0.4 kg occupies 0.0005 m³. Its density is:
The mass of 2 m³ of oil of density 800 kg/m³ is:
Relative density:
Relative density of a substance is its density divided by the density of water at:
The density of mercury is 13 600 kg/m³. Its relative density is:
When a car battery discharges, the density of the electrolyte:
The normal density of human blood is about:
A blood density lower than normal may indicate:
Gold of 14 carat is less dense than pure gold because:
In laminar flow:
Streamlines in laminar flow:
Where streamlines are close together, the speed of the liquid is:
The tangent to a streamline at a point gives the direction of the:
Turbulent flow occurs when the speed of the liquid:
Which is NOT a condition of steady flow in a pipe?
The volume flow rate Qv is equal to:
The unit of mass flow rate is:
The continuity equation expresses the law of conservation of:
Water flows through a pipe of cross-section 8 cm² at 3 m/s into a section of 2 cm². The speed there is:
The radius of a pipe is halved. The speed of the water (same flow rate) becomes:
The diameter of a pipe is doubled. For the same flow rate, the speed becomes:
A volume flow rate of 0.004 m³/s passes through a section of area 2 cm². The speed of water is:
A pipe of cross-section 2 × 10⁻⁴ m² carries water at 3 m/s. The volume flowing in 10 s is:
The mass of water (1000 kg/m³) flowing in 10 s in the previous situation is:
In the narrowest part of a pipe carrying a steady flow, the liquid speed is:
Blood flows slowest in the capillaries mainly because:
According to Bernoulli's principle, where the speed of a fluid increases its pressure:
The air above an aeroplane wing moves faster than the air below it, so the pressure above is:
Viscosity is the property that causes:
Which of the following has the highest viscosity?
The SI unit of the coefficient of viscosity is:
The dimensional formula of the coefficient of viscosity is:
In the two-plate model, the force needed to keep the upper plate moving at constant speed is directly proportional to all EXCEPT:
If the distance between the plates is doubled (same A, v, η) the force becomes:
The coefficient of viscosity of a pure liquid depends on:
In anaemia the blood sedimentation rate is:
Part 2: Written questions and problems
1. [Give reasons] The density of the electrolyte of a car battery is measured regularly.
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It decreases on discharge (acid is consumed) and rises on charging, so it indicates the state of charge of the battery.
2. [Give reasons] Alloys of gold differ in density from pure gold.
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Gold is mixed with lighter metals such as copper, so the density of the alloy is lower.
3. [Give reasons] Gases have much smaller densities than liquids and solids.
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The distances between gas molecules are very large, so the mass per unit volume is small.
4. [Give reasons] Relative density has no unit.
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It is the ratio of two quantities of the same kind (two densities).
5. [Give reasons] Streamlines never intersect.
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A particle at an intersection point would have two different directions of velocity at the same instant, which is impossible.
6. [Give reasons] Streamlines are crowded together in a narrow part of a pipe.
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The speed is greater there, and the streamline density measures the speed.
7. [Give reasons] The speed of water increases when a finger is placed over the end of a hose.
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The exit area decreases, and A₁v₁ = A₂v₂ so the speed increases.
8. [Give reasons] The mass flow rate is the same at all cross-sections of a pipe carrying a steady flow of liquid.
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Conservation of mass: the liquid is incompressible and cannot accumulate or leak, so what enters equals what leaves.
9. [Give reasons] Blood flow in the capillaries is slow.
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The sum of the cross-sections of millions of capillaries is far larger than that of the aorta, so by continuity the speed is small; this gives time for exchange of gases and nutrients.
10. [Give reasons] An aeroplane wing is curved on top and flat underneath.
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Air passes faster over the top, so the pressure there is lower than below, giving an upward lift (Bernoulli's principle).
11. [Give reasons] Honey flows more slowly than water.
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Honey has a larger coefficient of viscosity (stronger resistance between layers).
12. [Give reasons] Engine parts are lubricated with oil of high viscosity rather than water.
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High-viscosity oil sticks to the parts and does not flow away; it reduces friction heat and wear. Water would run off quickly.
13. [Give reasons] A skilled driver does not exceed a moderate speed.
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At high speed air resistance becomes proportional to the square of the speed, so fuel consumption rises sharply.
14. [Give reasons] The sedimentation rate of blood increases in rheumatic fever.
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Red cells stick together to form clumps of larger radius, which settle faster.
15. [Give reasons] The layer of liquid in contact with a fixed plate does not move.
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Molecular attraction (adhesion) between the plate and the liquid molecules holds the layer in place.
Part C — Define / compare
16. [Define] Define a fluid and density.
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Fluid: a substance able to flow (a liquid or a gas). Density: mass of a unit volume of a substance, ρ = m/Vol, unit kg/m³.
17. [Define] Define relative density.
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The ratio between the density of a substance and the density of water at 4 °C (no unit).
18. [Compare] Compare laminar and turbulent flow.
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- Laminar: smooth sliding layers, non-intersecting streamlines, quiet, can be steady.
- Turbulent: eddies, irregular, occurs above a certain speed, noisy.
19. [Define] What is meant by steady flow? State its three conditions.
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- Flow in which the velocity at each point does not change with time.
- Conditions: the tube is full; the amount entering equals the amount leaving in the same time; constant velocity at each point.
20. [Define] Define volume flow rate and mass flow rate, giving formulae and units.
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Volume flow rate Qv = Av (m³/s); mass flow rate Qm = ρAv (kg/s).
21. [Define] State the continuity equation and the physical law it is based on.
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A₁v₁ = A₂v₂ (speed inversely proportional to cross-sectional area); based on conservation of mass.
22. [Define] Define viscosity.
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The property that causes resistance or friction between the layers of a fluid, hindering their sliding over each other.
23. [Define] Define the coefficient of viscosity and give its unit.
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The tangential force on unit area that produces a velocity difference of one unit between two layers one unit apart. Unit: N·s/m² (kg/m·s).
24. [Compare] Compare high-viscosity and low-viscosity liquids with examples and uses.
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- Low: water, alcohol; flow easily, little resistance to moving objects.
- High: honey, glycerin, engine oil; flow with difficulty, high resistance; used for lubrication.
25. [Compare] Compare density and relative density (definition, unit).
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Density: mass per unit volume, kg/m³. Relative density: density of substance ÷ density of water at 4 °C; no unit.
Part D — Problems
26. [Problem] Water flows at a steady 0.002 m³/s through a pipe of cross-section 4 cm². Find the speed.
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5 m/s
v = Q/A = 0.002/(4 × 10⁻⁴).
27. [Problem] Water leaves a rubber pipe of inner diameter 3 cm at 2 m/s through an outlet at 18 m/s. Find the diameter of the outlet.
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1 cm
d₂ = d₁√(v₁/v₂) = 3 × √(2/18) = 3 × 1/3 = 1 cm.
28. [Problem] A main artery of radius 0.3 cm carries blood at 0.04 m/s and branches into 60 smaller vessels each of radius 0.05 cm. Find the speed in each.
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0.024 m/s
A₁ = π(0.3)² = 0.09π; A₂ = 60π(0.05)² = 0.15π; v₂ = 0.09 × 0.04/0.15.
29. [Problem] Water flows at 5 m/s through a pipe of cross-section 3 cm². Find the volume and the mass flowing in 2 minutes.
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0.18 m³; 180 kg
Qv = 3 × 10⁻⁴ × 5 = 1.5 × 10⁻³ m³/s; × 120 s = 0.18 m³; mass = 180 kg.
30. [Problem] A pipe has cross-section 12 cm² at A and 3 cm² at B. Water flows at 1.5 m/s at A. Find the speed at B.
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6 m/s
vB = 12 × 1.5/3.
31. [Problem] A mass flow of 0.72 kg/s of oil passes along a pipe of cross-section 2 cm² at a speed of 4 m/s. Find the density of the oil.
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900 kg/m³
ρ = Qm/(Av) = 0.72/(2 × 10⁻⁴ × 4).
32. [Problem] A tank of 120 litres is filled by a tap at 0.4 litre per second. How long does it take?
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300 s
t = 120/0.4.
33. [Problem] The speed of water in a pipe is 1 m/s at a section of radius 3 cm and 9 m/s at another section. Find the radius of the second section.
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1 cm
r₂ = r₁√(v₁/v₂) = 3 × 1/3.
34. [Problem] A stone has mass 270 g and volume 100 cm³. Find its density in kg/m³ and its relative density.
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2700 kg/m³; 2.7
270/100 = 2.7 g/cm³.
35. [Problem] Find the mass of 5 litres of sea water of density 1030 kg/m³.
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5.15 kg
1030 × 5 × 10⁻³.
36. [Problem] 200 mL of a liquid has a mass of 160 g. Find its density and relative density.
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800 kg/m³; 0.8
160/200 = 0.8 g/cm³.
37. [Problem] Ethanol has relative density 0.79. Find the mass of 2.5 litres of it.
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1.975 kg
ρ = 790 kg/m³; m = 790 × 2.5 × 10⁻³.
38. [Problem] A plate of area 0.04 m² moves at 0.1 m/s over a layer of oil 2 mm thick when a force of 0.5 N is applied. Find the coefficient of viscosity.
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0.25 N·s/m²
η = Fd/(Av) = 0.5 × 0.002/(0.04 × 0.1).
39. [Problem] Find the force needed to move a plate of area 0.1 m² at 0.4 m/s over a layer of liquid of η = 0.5 N·s/m² and thickness 1 cm.
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2 N
F = ηAv/d = 0.5 × 0.1 × 0.4/0.01.
40. [Problem] A force of 0.3 N moves a plate at a given velocity over oil A and 1.2 N over oil B (same plate, same distance and speed). Compare the viscosity coefficients.
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ηB = 4 ηA
η ∝ F when A, v and d are the same.