Fluid Properties and Hydrostatics
Q1. A Newtonian fluid has a dynamic viscosity of 0.5 Pa·s and a shear rate of 20 s⁻¹ at a point. What is the shear stress at that point?
(a) 5 Pa (b) 10 Pa (c) 15 Pa (d) 25 Pa
Answer: (b) 10 Pa — Shear stress = μ × (du/dy) = 0.5 × 20 = 10 Pa, following Newton’s law of viscosity.
Q2. The pressure at a depth of 5 m below the free surface of water (density 1000 kg/m³) is approximately:
(a) 5 kPa (b) 49 kPa (c) 98 kPa (d) 500 kPa
Answer: (b) 49 kPa — Using , Pa ≈ 49 kPa.
Q3. A cube of density 800 kg/m³ floats in water of density 1000 kg/m³. What fraction of the cube’s volume is submerged?
(a) 0.6 (b) 0.7 (c) 0.8 (d) 0.9
Answer: (c) 0.8 — By Archimedes’ principle, submerged fraction = ρ_body/ρ_fluid = 800/1000 = 0.8.
Q4. The excess pressure inside a spherical air bubble of radius r immersed in a liquid with surface tension σ is given by:
(a) σ/r (b) 2σ/r (c) 4σ/r (d) σ/2r
Answer: (c) 4σ/r — A bubble has two liquid-gas interfaces (inner and outer film), so , unlike a single droplet which has(look below :) .
Q5. Which non-dimensional number represents the ratio of inertia forces to viscous forces in a flow?
(a) Froude number (b) Mach number (c) Reynolds number (d) Weber number
Answer: (c) Reynolds number — Reynolds number (look below) governs the transition between laminar and turbulent flow regimes.
Fluid Kinematics and Dimensional Analysis
Q6. In a steady flow, which of the following statements is true regarding streamlines, pathlines, and streaklines?
(a) They are always different (b) They coincide only in unsteady flow (c) They coincide in steady flow (d) They never coincide
Answer: (c) They coincide in steady flow — In steady flow, the flow pattern does not change with time, so streamlines, pathlines, and streaklines are identical.
Q7. The continuity equation for an incompressible, steady flow in differential form is:
(a) (b) (c) (d) Look below for the equations :
Answer: (b) — For incompressible flow, density is constant, so the continuity equation reduces to divergence of velocity equal to zero.
Q8. According to the Buckingham Pi theorem, if a physical phenomenon depends on n variables and there are m fundamental dimensions, the number of independent dimensionless groups is:
(a) n + m (b) n − m (c) n × m (d) m − n
Answer: (b) n − m — This is the core statement of the Buckingham Pi theorem used to reduce variables into dimensionless groups for model studies.
Q9. Two geometrically similar pumps are operating under dynamically similar conditions. Which dimensionless number must match for dynamic similarity in pump flows?
(a) Froude number (b) Reynolds number (c) Mach number (d) Weber number
Answer: (b) Reynolds number — For internal, viscous-dominated flows such as pump and pipe flows, Reynolds number similarity is the governing criterion.
Q10. The velocity potential function exists only for flows that are:
(a) Rotational (b) Irrotational (c) Viscous (d) Compressible
Answer: (b) Irrotational — A velocity potential function can be defined only when the flow field is irrotational, i.e., .
Bernoulli’s Equation, Flow Measurement, and Pipe Flow
Q11. Bernoulli’s equation is derived by integrating which of the following along a streamline?
(a) Continuity equation (b) Euler’s equation (c) Navier-Stokes equation (d) Momentum integral equation
Answer: (b) Euler’s equation — Bernoulli’s equation results from integrating Euler’s equation of motion along a streamline for steady, inviscid, incompressible flow.
Q12. A venturimeter is used to measure flow rate in a pipe based on the principle of:
(a) Conservation of mass only (b) Conservation of mass and Bernoulli’s principle (c) Momentum conservation only (d) Dimensional analysis
Answer: (b) Conservation of mass and Bernoulli’s principle — The venturimeter combines the continuity equation and Bernoulli’s equation to relate the pressure difference to flow velocity between the throat and inlet sections.
Q13. For fully developed laminar flow in a circular pipe (Hagen-Poiseuille flow), the velocity profile across the cross section is:
(a) Linear (b) Logarithmic (c) Parabolic (d) Uniform
Answer: (c) Parabolic — Solving the Navier-Stokes equation for laminar pipe flow yields a parabolic velocity distribution, with maximum velocity at the centerline.
Q14. In the Darcy-Weisbach equation for head loss due to friction in a pipe, the friction factor for laminar flow is given by:
(a) 64/Re (b) 16/Re (c) 0.316/Re^0.25 (d) 32/Re
Answer: (a) 64/Re — For laminar flow in pipes, the Darcy friction factor f = 64/Re, derived analytically from the Hagen-Poiseuille solution.
Q15. The critical Reynolds number below which pipe flow is generally considered laminar is approximately:
(a) 500 (b) 2000 (c) 4000 (d) 10000
Answer: (b) 2000 — Flow in pipes is typically laminar for Re < 2000, transitional between 2000 and 4000, and turbulent above 4000.
Boundary Layer Theory and External Flows
Q16. The boundary layer thickness is defined as the distance from the solid surface where the velocity reaches:
(a) The free stream velocity exactly (b) 99% of the free stream velocity (c) 50% of the free stream velocity (d) Zero velocity
Answer: (b) 99% of the free stream velocity — By convention, the boundary layer thickness δ is where local velocity equals 99% of the free stream velocity, since it asymptotically approaches U∞.