A pump delivers 0.05 m³/s of water. If the pipe diameter is 0.1 m, the velocity of flow is:
Answer: A
Using Q = AV = (π/4)D²V, we get V = Q/A = 0.05/(π/4 × 0.1²) = 0.005.00785 = 6.37 m/s
Q.2Medium
The Darcy friction factor for fully developed laminar flow in a pipe depends on:
Answer: B
For laminar flow, friction factor f = 64/Re is independent of surface roughness. Roughness effects become significant only in turbulent flow.
Q.3Medium
Water flows through a horizontal pipe with diameter 0.05 m at a velocity of 2 m/s. The volumetric flow rate is:
Answer: A
Q = AV = (π/4)D² × V = (π/4) × 0.05² × 2 = 0.00393 m³/s
Q.4Medium
The Mach number is the ratio of:
Answer: B
Mach number M = V/a, where V is flow velocity and a is the speed of sound. It indicates whether flow is subsonic (M<1), sonic (M=1), or supersonic (M>1).
Q.5Medium
For turbulent flow in pipes, the Colebrook-White equation is used to find the friction factor. Which of the following is NOT an input parameter?
Answer: C
The Colebrook-White equation involves Reynolds number and relative roughness but not Mach number. Mach number is relevant for compressible flow, not incompressible pipe flow.
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Q.6Medium
A fluid element has shear stress τ = 0.5 Pa and velocity gradient du/dy = 10 s⁻¹. The dynamic viscosity of the fluid is:
Answer: A
From Newton's law of viscosity, τ = μ(du/dy), so μ = τ/(du/dy) = 0.105 = 0.05 N·s/m²
Q.7Medium
The Reynolds number for flow in a circular pipe is given by Re = ρVD/μ. If the flow transitions from laminar to turbulent at Re ≈ 2300, then for a pipe with D = 0.025 m and V = 1.5 m/s (ρ = 1000 kg/m³, μ = 0.001 N·s/m²), the flow regime is:
Answer: B
Re = (1000 × 1.5 × 0.025)/0.001 = 37,500, which is much greater than 2300, indicating turbulent flow.
Q.8Medium
Which of the following is a dimensionless number used in fluid mechanics that compares inertial forces to surface tension forces?
Answer: A
Weber number We = ρV²D/σ represents the ratio of inertial to surface tension forces. It's important in two-phase flows and atomization studies.
Q.9Medium
A venturi meter is used to measure fluid flow rate. The principle it operates on is:
Answer: B
Venturi meter uses both continuity equation (conservation of mass) and Bernoulli's equation (energy conservation) to relate pressure difference to flow velocity.
Q.10Medium
The major loss in pipe flow (Darcy-Weisbach equation: hf = f(L/D)(V²/2g)) is primarily due to:
Answer: C
Major losses or friction losses occur due to wall shear stress and account for the majority of energy dissipation in long straight pipe sections. This is captured by the Darcy friction factor.
Q.11Medium
In a pitot tube, the stagnation pressure and static pressure are measured. The velocity at the measurement point is:
Answer: A
From Bernoulli's equation applied between static and stagnation points: v = √(2ΔP/ρ)
Q.12Medium
A jet of water impinges on a flat plate perpendicular to its surface. If jet velocity is 10 m/s and jet area is 0.01 m², the force on the plate is approximately:
Answer: C
Force F = ρAv² = 1000 × 0.01 × 10² = 1000 N (using ρ = 1000 kg/m³ for water)
Q.13Medium
In a U-tube manometer with mercury, if one leg shows 50 mm height difference, the pressure difference is:
Answer: B
ΔP = ρgh = ρ_mercury × 9.81 × 0.05 ≈ 50 × ρ_mercury × g Pa (approximately)
Q.14Medium
For a turbulent flow in pipes, the friction factor f in the Darcy-Weisbach equation depends primarily on:
Answer: B
Friction factor for turbulent flow depends on Re and roughness (ε/d) as shown in Moody diagram.
Q.15Medium
A convergent-divergent nozzle (De Laval nozzle) accelerates gas to supersonic speeds. The throat area compared to exit area is:
Answer: B
In a convergent-divergent nozzle, throat area is smallest and exit area is larger for supersonic flow.
Q.16Medium
The Froude number characterizes the relative importance of:
A pipeline carrying oil (ν = 2 × 10⁻⁴ m²/s) has diameter 0.5 m and velocity 2 m/s. The flow regime is:
Answer: C
Re = vd/ν = (2 × 0.5)/(2 × 10⁻⁴) = 5000 > 4000, so turbulent
Q.18Medium
The Mach number M = 0.3 indicates:
Answer: B
M < 0.3 indicates incompressible flow approximation is valid; compressibility effects are negligible.
Q.19Medium
For water flow in a pump system, cavitation occurs when:
Answer: B
Cavitation occurs when local pressure drops below fluid vapor pressure, causing vapor bubbles to form.
Q.20Medium
A horizontal pipe of diameter 50 mm carries water at 2 m/s. If the pipe length is 100 m and friction factor f = 0.04, calculate the head loss using Darcy-Weisbach equation.
