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Fluid mechanics: board exam questions with solutions

On the REE exam under Engineering Sciences and Allied Subjects (ESAS). Try each question before you open its solution, then practise with fresh numbers below: 1 computed question type on this topic.

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Questions

1. What is the gauge pressure 10 m below the surface of fresh water? (ρ = 1000 kg/m³, g = 9.81 m/s²)

  1. 98.1 kPa
  2. 9.81 kPa
  3. 199.4 kPa
  4. 10.0 kPa
Show the answer and solution

Answer: A. 98.1 kPa

p = ρgh = 1000 × 9.81 × 10 = 98 100 Pa = 98.1 kPa. Adding 101.3 kPa atmospheric gives the absolute pressure, 199.4 kPa.

2. Water flows at 2 m/s in a 100 mm pipe that reduces to 50 mm. What is the velocity in the smaller pipe?

  1. 4 m/s
  2. 8 m/s
  3. 1 m/s
  4. 0.5 m/s
Show the answer and solution

Answer: B. 8 m/s

Continuity gives A₁v₁ = A₂v₂, so v₂ = v₁(D₁/D₂)² = 2 × (100/50)² = 8 m/s.

3. What is the buoyant force on a 0.2 m³ object fully submerged in seawater? (ρ = 1025 kg/m³)

  1. 1962 N
  2. 205 N
  3. 2011 N
  4. 4022 N
Show the answer and solution

Answer: C. 2011 N

F_B = ρgV = 1025 × 9.81 × 0.2 = 2011 N.

4. Water flows at 1.5 m/s through a 150 mm diameter pipe. What is the flow rate?

  1. 106.0 L/s
  2. 225.0 L/s
  3. 26.5 L/s
  4. 17.7 L/s
Show the answer and solution

Answer: C. 26.5 L/s

A = π(0.15)²/4 = 0.01767 m². Q = Av = 0.01767 × 1.5 = 0.0265 m³/s = 26.5 L/s.

5. A pump delivers 0.02 m³/s of water against a total head of 30 m with 75% efficiency. What shaft power does it require?

  1. 5.89 kW
  2. 4.41 kW
  3. 0.60 kW
  4. 7.85 kW
Show the answer and solution

Answer: D. 7.85 kW

Water power = ρgQH = 1000 × 9.81 × 0.02 × 30 = 5886 W. Shaft power = 5886/0.75 = 7848 W ≈ 7.85 kW.

6. Bernoulli's equation for ideal flow along a streamline is a statement of conservation of:

  1. Mass
  2. Energy
  3. Momentum
  4. Charge
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Answer: B. Energy

It balances pressure, kinetic and potential energy per unit volume. Mass conservation is the continuity equation.

7. Water discharges from a 50 mm orifice with C_d = 0.62 under a constant head of 5 m. Find the discharge. (g = 9.81 m/s²)

  1. 12.06 L/s
  2. 19.45 L/s
  3. 7.48 L/s
  4. 5.39 L/s
Show the answer and solution

Answer: A. 12.06 L/s

Theoretical velocity = √(2gh) = √98.1 = 9.905 m/s. A = π(0.05)²/4 = 1.963×10⁻³ m². Q = 0.62 × 1.963×10⁻³ × 9.905 = 0.01206 m³/s = 12.06 L/s.

8. Water (ν = 1×10⁻⁶ m²/s) flows at 1 m/s in a 50 mm pipe. What are the Reynolds number and flow regime?

  1. 50 000, laminar
  2. 500, laminar
  3. 5000, transitional
  4. 50 000, turbulent
Show the answer and solution

Answer: D. 50 000, turbulent

Re = vD/ν = 1 × 0.05/1×10⁻⁶ = 50 000. That is well above about 4000, so the flow is turbulent.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. What is the gauge pressure at a depth of 38 m in fresh water?

  1. 373 kPa
  2. 38 kPa
  3. 373 Pa
  4. 474 kPa
Show the answer and solution

Answer: A. 373 kPa

p = ρgh = 1000 × 9.81 × 38 = 373 kPa (gauge).

Other topics in the same subjects

Physics: mechanics · Physics: waves, electricity and magnetism · General chemistry · Thermodynamics · Strength of materials · Engineering materials · Engineering economics · Engineering management · Computer fundamentals and programming · RA 7920 and ethics (electrical) · PEC Part 1: general requirements

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