Chemical Engineering questions for GATE and PSU exams are built on a handful of core subjects applied in many ways. Practice spans fluid mechanics, heat transfer, mass transfer, chemical reaction engineering, thermodynamics, process control and instrumentation, and plant design economics. Numerical solutions carry the assumptions written out, because the assumption is usually what separates a correct answer from a plausible one.
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.
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.
