A fluid flows through a horizontal pipe of diameter 0.1 m at a velocity of 3 m/s. If the pipe suddenly contracts to 0.05 m diameter, what is the velocity in the contracted section (assuming incompressible flow)?
The friction factor 'f' in the Darcy-Weisbach equation depends on Reynolds number and relative roughness. For laminar flow (Re < 2300), friction factor is given by:
Answer: A
For laminar flow in circular pipes, the Hagen-Poiseuille solution gives f = 64/Re. This is independent of roughness and applies for Re < 2300.
Q.83Medium
Water flows through a pipe at 15°C (ρ = 999 kg/m³, μ = 1.139×10⁻³ Pa·s). If flow rate is 0.05 m³/s through a 0.1 m diameter pipe, is the flow laminar or turbulent?
Answer: B
V = Q/A = 0.05/(π×0.1²/4) = 6.37 m/s. Re = ρVD/μ = 999×6.37×0.11.139×10⁻³ ≈ 558,000 (Turbulent)
Q.84Medium
In open channel flow, the Froude number (Fr) determines the type of flow. For a rectangular channel with depth 0.5 m and velocity 1.5 m/s, calculate the Froude number (g = 9.81 m/s²).
Answer: B
Fr = V/√(g×D_h) where D_h is hydraulic depth = 0.5 m for rectangular channel. Fr = 1.5/√(9.81×0.5) = 1.25.21 ≈ 0.68 (Subcritical flow)
Q.85Medium
For turbulent flow in smooth pipes, which equation is commonly used to estimate friction factor?
Answer: C
Blasius equation is specifically for smooth pipes with 4000 < Re < 100,000. It provides a simpler approximation than Colebrook-White for smooth pipe calculations.
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Q.86Medium
The minor losses in pipe fittings are expressed as K×(V²/2g) where K is the loss coefficient. For a 90° elbow with Re = 50,000, typical K value is:
Answer: B
For a 90° elbow at high Reynolds number, K typically ranges from 0.8-1.0. K = 0.9 is a standard value used in engineering calculations.
Q.87Easy
A manometer shows a pressure difference of 50 mm of mercury (ρ_Hg = 13,600 kg/m³). What is the equivalent pressure difference in Pa?
Answer: A
ΔP = ρ_Hg × g × h = 13,600 × 9.81 × 0.05 = 6,667 Pa
Q.88Medium
In boundary layer theory on a flat plate, the displacement thickness δ* represents:
Answer: B
Displacement thickness δ* = ∫₀^δ (1 - u/u∞)dy represents the distance by which streamlines are displaced outward due to the presence of the boundary layer.
Q.89Medium
For compressible flow through a nozzle, if pressure drops significantly and reaches sonic conditions, the Mach number at that point is:
Answer: C
Sonic condition occurs at critical pressure where Mach number equals 1.0. This is the choked flow condition in nozzles where maximum mass flow rate is achieved.
Q.90Medium
A hydraulic jump occurs in open channel flow when:
Answer: B
Hydraulic jump is an abrupt, turbulent transition from supercritical to subcritical flow. Energy is dissipated during this process, causing a sudden rise in water surface.
Q.91Medium
The Moody diagram is used to determine friction factor for pipe flow. It shows that friction factor increases with:
Answer: B
In the Moody diagram, friction factor decreases with increasing Re in laminar region. In turbulent region, f increases with relative roughness (ε/D) and slightly decreases with increasing Re for rough pipes.
Q.92Easy
For a fluid flowing over a submerged object, the drag force is given by F_D = (21)ρV²AC_D. If velocity doubles and drag coefficient remains constant, drag force increases by a factor of:
Answer: B
F_D ∝ V². When V doubles (V₂ = 2V₁), F_D increases by factor of (2)² = 4
Q.93Hard
In computational fluid dynamics (CFD), the Courant number (Co = U×Δt/Δx) is important for numerical stability. For explicit schemes, the Courant number should be:
Answer: A
The CFL (Courant-Friedrichs-Lewy) condition requires Co ≤ 1 for explicit numerical schemes to maintain stability. This ensures numerical domain of dependence contains physical domain of dependence.
Q.94Hard
For a reciprocating pump with bore diameter 0.08 m, stroke length 0.15 m, and operating at 60 RPM with 90% volumetric efficiency, the discharge is approximately:
In a convergent-divergent (de Laval) nozzle for compressible flow, the pressure reaches minimum (maximum acceleration) at:
Answer: B
In compressible flow through a C-D nozzle, pressure decreases through convergent section and reaches minimum at throat. This is where velocity is maximum and Mach number = 1 (sonic condition).
Q.96Hard
The Navier-Stokes equation for incompressible flow includes terms for pressure gradient, viscous forces, and inertial forces. Under creeping flow conditions (Re → 0), which term becomes negligible?
Answer: B
In creeping flow (Stokes flow), Reynolds number is very small (Re << 1), making inertial forces negligible compared to viscous and pressure forces. The simplified Stokes equation is: ∇p = μ∇²u
Q.97Medium
For a horizontal pipe with diameter variation from D₁ to D₂, if pressure difference is ΔP and ignoring losses, the velocity ratio V₁/V₂ is:
Answer: B
By continuity: A₁V₁ = A₂V₂. Since A = πD²/4, we get V₁/V₂ = A₂/A₁ = (D₂/D₁)². Pressure difference from Bernoulli validates this for incompressible flow.
