JNTU
JNTU B.Tech II Year FLUID MECHANICS AND HEAT TRANSFER Previous Question Paper (August/September - 2022 - R16)
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Main
If the velocity profile of a fluid over a plate is a parabolic with the vertex 20 cm from the plate where the velocity is 120 cm/sec. Calculate the velocity gradients and shear stresses at a distance of 0, 10 cm and 20 cm from the plate, if the viscosity of the fluid is 8.5 poise.
Answer
The velocity profile is parabolic, given by the equation u = ay² + by + c. Given conditions: at y = 0, u = 0 (no-slip condition), so c = 0. At y = 20 cm, u = 120 cm/s, and du/dy = 0 (vertex of parabola). Substituting these into the derivative du/dy = 2ay + b, we get 0 = 2a(20) + b, so b = -40a. Substituting into the velocity equation: 120 = a(20)² - 40a(20) = 400a - 800a = -400a. Thus, a = -0.3 and b = 12. The velocity profile is u = -0.3y² + 12y.
The velocity gradient is du/dy = -0.6y + 12. Shear stress is τ = μ(du/dy), where μ = 8.5 poise = 0.85 Ns/m². Converting units: y in meters, u in m/s, τ in N/m².
- At y = 0 cm: du/dy = 12 s⁻¹; τ = 0.85 × 12 = 10.2 N/m².
- At y = 10 cm: du/dy = -0.6(10) + 12 = 6 s⁻¹; τ = 0.85 × 6 = 5.1 N/m².
- At y = 20 cm: du/dy = -0.6(20) + 12 = 0 s⁻¹; τ = 0.85 × 0 = 0 N/m².
Define steady, unsteady, uniform and non-uniform flows with suitable examples.
Answer
Steady Flow: Fluid properties at any point do not change with time (∂/∂t = 0). Example: Flow through a pipe at a constant discharge.
Unsteady Flow: Fluid properties at a point change with time (∂/∂t ≠ 0). Example: Flow in a pipe during the starting or stopping of a pump.
Uniform Flow: Velocity does not change along the direction of flow (∂v/∂s = 0). Example: Flow through a long pipe of constant diameter at constant velocity.
Non-uniform Flow: Velocity changes along the direction of flow (∂v/∂s ≠ 0). Example: Flow through a tapering pipe or a nozzle.
A shaft of diameter 100 mm is rotating inside a journal bearing of diameter 102 mm at a speed of 360 rpm. The space between the shaft and bearing is filled with a lubricating oil of viscosity 5 Poise. The length of the bearing is 200 mm. Find the power absorbed in the lubricating oil?
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State and explain about velocity potential function and stream function.
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The water is flowing through a taper pipe of length 100 m having diameters 600 mm at the upper end and 300 mm at the lower end at the rate of 50 litres/sec. The pipe has a slope of 1 in 30. Find the pressure at the lower end if the pressure at the higher level is 19.62 N/cm2.
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Explain the principle of venturimeter with a neat sketch and derive an expression for the rate of flow of fluid through it.
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An orifice meter with orifice diameter 15 cm is inserted in a pipe of 30 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter readings are 14.715 N/cm2 and 9.81 N/cm2 respectively. Find the rate of flow of water through the pipe in litres/sec assuming the cd=0.6?
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State the momentum equation and how will you apply the momentum equation for determining the force exerted by a flowing liquid on a pipe bend?
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State and explain Fourier law of heat conduction for 1 D problems.
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A 30 cm thick wall of reactor is made up of an inner layer of fire brick k1= 0.85 W/m K covered with a layer of insulation k2= 0.15 W/m K. The reactor operates at a temperature of 1600 K while the ambient temperature is 295 K. Calculate the thickness of the fire brick and insulation which gives a minimum heat loss presuming that the insulating material has a maximum temperature of 1475 K.
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Derive an expression to determine heat transfer rate assuming conduction through a composite wall.
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State and explain the different types of boundary conditions applied to heat conduction problems.
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Derive an expression for heat flow through a composite cylinder taking in to account the film heat transfer coefficients on the inside and outside surface of a cylinder.
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Atmospheric air at 30°C temperature and free stream velocity of 2.5 m/sec flows along the length of a flat plate maintained at a uniform surface temperature of 90°C. The length, width and thickness of a plate are 100 cm, 50 cm and 2.5 cm respectively. If the thermal conductivity of the plate material is 25 w/m K. Calculate heat loss by the plate and the temperature of the bottom surface of the plate for steady state conditions.
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Explain the terms absorptivity, reflectivity and transmissivity of radiant energy. How they are related to each other for a black body and an opaque body?
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A tubular heat exchanger is to be designed for cooling oil from a temperature of 80°C to 30°C by large stagnant water which may be assumed to remain constant at a temperature of 20°C. The heat transfer surface consists of 30 m long straight tube of 20 mm inside diameter. The oil specific heat is 2.5 kJ/kg K and specific gravity is 0.8 flows through the cylindrical tube with an average velocity of 50 cm/s. calculate the overall heat transfer coefficient for the oil cooler.
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