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GATE fluid mechanics: 5 practice questions with answers
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Fluid mechanics is tested in GATE ME inside Fluid Mechanics and Thermal Sciences, and in GATE CE inside Water Resources Engineering, which also covers hydraulics, hydrology and irrigation. It is also an option (XE1) in Engineering Sciences. The questions repeat a small set of ideas: pressure and force in a static fluid, the Bernoulli and momentum equations, pipe flow, and similarity. The five original questions below practise one of each.
What GATE tests in fluid mechanics
Fluid properties, statics and the control-volume equations are common ground. ME papers have typically added dimensional analysis, viscous flow, boundary layers, turbulent pipe flow and turbomachinery, while CE shifts towards open-channel flow, hydraulics and hydrology. The 2027 syllabi were revised, so check your own list on the official syllabus page. The real paper also has MSQ and NAT questions; all five below are MCQ.
Practice questions
Question 1
A horizontal venturimeter has an inlet diameter of 200 mm and a throat diameter of 100 mm. The pressure difference between inlet and throat is 15 kPa, and the fluid is water (1000 kg/m³). Taking the coefficient of discharge as 1, the discharge in litres per second is:
- A. 22.2
- B. 31.4
- C. 44.4
- D. 62.8
Question 2
A vertical rectangular gate, 2 m wide and 3 m high, is submerged in water with its top edge at the free surface. Taking g = 9.81 m/s² and the density of water as 1000 kg/m³, the hydrostatic force on one side of the gate is:
- A. 88.3 kN
- B. 117.7 kN
- C. 176.6 kN
- D. 264.9 kN
Question 3
Oil of kinematic viscosity 1 × 10⁻⁴ m²/s flows through a pipe of diameter 100 mm and length 100 m with a mean velocity of 0.5 m/s. Use g = 9.81 m/s². The head loss due to friction is closest to:
- A. 0.82 m
- B. 1.63 m
- C. 3.26 m
- D. 6.52 m
Question 4
A spillway model is built to a geometric scale of 1:16 and passes a discharge of 0.05 m³/s. For dynamic similarity based on the Froude number, the corresponding discharge of the prototype is:
- A. 3.2 m³/s
- B. 12.8 m³/s
- C. 51.2 m³/s
- D. 204.8 m³/s
Question 5
A jet of water, 50 mm in diameter and moving at 20 m/s, strikes a stationary flat plate held normal to the jet. The water density is 1000 kg/m³. The force exerted by the jet on the plate is closest to:
- A. 393 N
- B. 1571 N
- C. 3142 N
- D. 785 N
Answers and explanations
- C. The area ratio is (100/200)² = 0.25. The throat velocity is v2 = √[2 Δp / ρ / (1 − 0.25²)] = √[30 / 0.9375] = √32 = 5.657 m/s. The throat area is (π/4)(0.1)² = 7.854 × 10⁻³ m², so Q = 7.854 × 10⁻³ × 5.657 = 0.0444 m³/s = 44.4 L/s. Skipping the area-ratio term in the formula gives the wrong answer.
- A. The force is ρ g h̄ A, where h̄ is the depth of the centroid, 1.5 m, and A = 2 × 3 = 6 m². F = 1000 × 9.81 × 1.5 × 6 = 88 290 N = 88.3 kN. Option B uses the depth of the centre of pressure (2 m), which locates the force and does not give its size. Option C uses the full depth of 3 m.
- B. The Reynolds number is Re = V D / ν = 0.5 × 0.1 / 10⁻⁴ = 500, which is laminar. The Darcy friction factor is f = 64 / Re = 0.128. The head loss is hf = f (L / D) V² / 2g = 0.128 × (100 / 0.1) × 0.25 / 19.62 = 1.63 m.
- C. For Froude similarity the discharge scales as L^2.5, where L is the length scale. With L = 16, 16^2.5 = 1024, so Qp = 1024 × 0.05 = 51.2 m³/s. The other options use exponents 1.5, 2 and 3.
- D. For a plate normal to the jet, the force is F = ρ A V² = 1000 × (π/4)(0.05)² × 20² = 1000 × 1.9635 × 10⁻³ × 400 = 785 N. Option B (1571 N) would apply to a jet turned back through 180 degrees, as in a hemispherical cup vane, where the momentum change is doubled.
How to prepare fluid mechanics
- Learn the three control-volume equations: continuity, Bernoulli (with its conditions) and momentum. Most numerical problems apply one or two of them in sequence.
- For statics, memorise the force and centre-of-pressure formulas for plane surfaces, plus the buoyancy and stability criteria. Questions often differ from a standard case only by a changed depth.
- Separate laminar and turbulent pipe flow by the Reynolds number, then use f = 64 / Re for laminar flow and the Moody chart or a given correlation for turbulent flow.
- Master dimensional analysis and similarity: the Buckingham pi theorem, and which dimensionless number governs which flow (Reynolds for pipes, Froude for free surfaces, Mach for compressibility).
- Practise jet and vane problems, and for CE add open-channel flow: Manning's and Chezy's equations, specific energy and the hydraulic jump.
For the thermal half of the ME section, use thermodynamics. Strength of materials covers the solid-mechanics side, and civil aspirants will find a soil-water link in geotechnical engineering. The GATE mechanical preparation guide and GATE civil preparation guide cover the plan around this section.
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