QUESTION PAPER 1

Chapter 9: Mechanical Properties of Fluids

Original chapter-specific practice paper

Maximum Marks: 40Suggested time: 60 minutes

Instructions: Answer all 20 questions. Marks are shown in brackets. Show calculation steps and units. These are original practice questions, not an official examination paper.

Section A · 1-mark questions — 8 × 1 = 8 marks

Define pressure.[1]
SI unit of dynamic viscosity?[1]
Continuity relation for incompressible flow?[1]
Bernoulli relation?[1]
Surface tension unit?[1]
Pressure rise at depth h?[1]
Stokes drag?[1]
Excess pressure in a liquid drop?[1]

Section B · 2-mark questions — 6 × 2 = 12 marks

Water at 3m depth, ρ=1000,g=10: gauge pressure?[2]
If pipe area halves, incompressible speed?[2]
Under Bernoulli assumptions, faster horizontal flow means pressure?[2]
Force from p=5000 Pa over area .02 m²?[2]
Drop S=.06 N/m,r=.003 m: excess pressure?[2]
Why is a soap bubble pressure difference twice a drop's?[2]

Section C · 3-mark questions — 4 × 3 = 12 marks

Pipe area 4 cm² at 2 m/s narrows to 1 cm². New speed?[3]
Horizontal water speeds 2 and 6 m/s, ρ=1000. Find p₁−p₂.[3]
Stokes drag for r=.5 mm,η=1 Pa s,v=.02 m/s?[3]
Explain why pressure rises with depth.[3]

Section D · 4-mark questions — 2 × 4 = 8 marks

Areas 6 cm² and 2 cm²; inlet speed 1.5 m/s. Find outlet speed.[4]
Soap bubble r=2mm,S=.03N/m: excess pressure?[4]

End of paper — review signs, units and working.

Open marking scheme and model answers

Attempt the paper before opening the key. Model answers show the expected facts and results; mark allocation is a suggested guide and equivalent correct methods should receive credit.

Q1 · 1 mark
Normal force per unit area.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q2 · 1 mark
Pa s.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q3 · 1 mark
A₁v₁=A₂v₂.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q4 · 1 mark
p+½ρv²+ρgh=constant.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q5 · 1 mark
N/m.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q6 · 1 mark
ρgh.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q7 · 1 mark
6πηrv.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q8 · 1 mark
2S/r.
1 mark for the correct fact, unit or formula. Accept an equivalent correct method.

Q9 · 2 marks
30,000 Pa.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q10 · 2 marks
Doubles.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q11 · 2 marks
Lower.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q12 · 2 marks
100 N.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q13 · 2 marks
40 Pa.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q14 · 2 marks
Bubble has two liquid-air surfaces; Δp=4S/r.
Suggested split: 1 mark for the principle/formula and 1 for the answer or explanation. Accept an equivalent correct method.

Q15 · 3 marks
8 m/s.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q16 · 3 marks
16,000 Pa.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q17 · 3 marks
≈1.88×10⁻⁴ N.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q18 · 3 marks
Hydrostatic balance gives p=p₀+ρgh due to weight of fluid above.
Suggested split: 1 for the relation, 1 for working/reasoning and 1 for result with unit. Accept an equivalent correct method.

Q19 · 4 marks
4.5 m/s.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.

Q20 · 4 marks
Δp=4S/r=60 Pa.
Suggested split: 1 for principle, 1 for equation, 1 for working and 1 for result/explanation. Accept an equivalent correct method.