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.42Medium
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.43Medium
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.44Medium
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.45Medium
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.
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Q.46Medium
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.47Medium
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.48Medium
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.49Medium
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.
