JNTU
JNTU B.Tech II CHEMICAL ENGINEERING FLUID MECHANICS Previous Question Paper (August/September - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
For the following situations of steady state flow, determine whether flow is laminar or turbulent: (i) water at 10°C flowing at an average velocity of 2 m/s in a 100-mm pipe; (ii) air at 2 atm pressure and 180°F flowing at 50 ft/s in a 12-in. duct; (iii) oil with a specific gravity of 0.78 and a viscosity of 20 cP flowing at 5 ft/s in a 2-in. pipe.
Answer
The flow regime is determined by the Reynolds number, Re = (ρvD) / μ, where Re < 2100 indicates laminar flow and Re > 4000 indicates turbulent flow.
(i) Water at 10°C: ρ ≈ 1000 kg/m³, μ ≈ 1.307 × 10⁻³ Pa·s, D = 0.1 m, v = 2 m/s. Re = (1000 × 2 × 0.1) / 0.001307 ≈ 153,022. Since Re > 4000, the flow is turbulent.
(ii) Air at 2 atm, 180°F (355 K): Using the ideal gas law, ρ = (PM) / (RT). With M ≈ 29 g/mol, P = 202,650 Pa, R = 8.314 J/mol·K, ρ ≈ 1.99 kg/m³. Viscosity μ ≈ 2.1 × 10⁻⁵ Pa·s, D = 1 ft = 0.3048 m, v = 50 ft/s = 15.24 m/s. Re = (1.99 × 15.24 × 0.3048) / 0.000021 ≈ 440,000. Since Re > 4000, the flow is turbulent.
(iii) Oil: ρ = 0.78 × 1000 = 780 kg/m³, μ = 20 cP = 0.02 Pa·s, D = 2 in = 0.0508 m, v = 5 ft/s = 1.524 m/s. Re = (780 × 1.524 × 0.0508) / 0.02 ≈ 3023. This falls in the transition region (2100 < Re < 4000), often treated as unstable or transition flow.
Explain the boundary layer formation for the flow of fluid parallel with a thin plate, giving a neat sketch.
Answer
When a fluid flows parallel to a thin flat plate, a boundary layer forms due to the no-slip condition at the surface. As the fluid contacts the leading edge, a thin layer of fluid is retarded by shear forces, creating a velocity gradient from zero at the wall to the free-stream velocity at the edge of the layer.
The boundary layer thickness (δ) increases with distance (x) from the leading edge. Initially, the flow is laminar (laminar boundary layer), characterized by smooth streamlines. As the distance increases, the boundary layer becomes unstable and transitions into a turbulent boundary layer, where eddies and fluctuations dominate. A thin viscous sublayer remains adjacent to the wall even in the turbulent region.
Sketch description: A flat plate is represented by a horizontal line. A velocity profile starts as a parabolic curve at the leading edge (laminar), gradually thickening as it moves downstream. Further along, the profile becomes fuller (turbulent), indicating higher velocity gradients near the wall. The boundary layer thickness δ(x) is shown as a curve growing from the leading edge.
Explain the Newtonian and Non-Newtonian fluids with neat sketches.
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Explain the following terms: (i) Steady and Unsteady flow (ii) Uniform and non-uniform flow (iii) Laminar and turbulent flow (iv) Rotational and irrotational flow.
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Two horizontal plates are placed 12.5 mm apart. The space between these plates is filled with an oil, having a viscosity of 14 P (poise). If the upper plate is moved with a velocity of 2.5 m/s, compute the shear stress in the oil.
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Derive the Hagen-Poiseuill’s equation for laminar flow of incompressible fluid in a pipe.
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Derive Bernoulli’s equation for the flow of incompressible, frictionless fluid from consideration of momentum and state the necessary assumptions made for the derivation of the same.
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A pipeline carrying oil of specific gravity 0.87 changes in diameter from 200 mm diameter at position A to 500 mm diameter at point B, which is 4m at a higher level. If the pressure at A and B are 1 Kgf/cm² and 0.6 Kgf/cm², respectively and the discharge is 200 lit/s. Determine the loss of head/energy and direction of flow.
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Derive the equation of continuity of compressible fluids. State the assumptions clearly.
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A pipe of 300 mm diameter conveying 0.30 m³/s of water has a right angled bend in a horizontal plane. Find the resultant force exerted on the bend if the pressure at inlet and outlet of the bend are 24.525 N/cm² and 23.544 N/cm².
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Methane gas is being pumped through a 305m length of 52.5mm diameter steel pipe at a rate of 41.0kg/m²-s. The inlet and outlet pressure is 345kPa abs and 298kPa. Assume isothermal flow at 288.8K. Calculate the maximum velocity that can be obtained at these conditions.
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What is stagnation pressure and temperature? Explain the significance of Mach number.
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What is minimum fluidization velocity? Write Ergun’s equation and comment on its applicability.
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Differentiate free and hindered settling.
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Water flows at the rate of 0.147 m³/s through a 150 mm diameter orifice inserted in a 300 mm diameter pipe. If pressure gauges fitted at the upstream and downstream of the orifice plate give readings of 176.58 kN/m² and 88.29 kN/m² respectively, find the coefficient of discharge of the orifice meter.
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A lube oil (specific gravity 0.8) is flowing through a 15 cm steel pipe at 1500 LPM. A 10 cm orifice attached to a mercury manometer is placed in the pipe line and the orifice coefficient may be taken as 0.62. If the manometer leg is inclined at an angle of 30° to the horizontal, what would be the manometer reading along the sloping leg?
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