JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year FLUID MECHANICS AND HEAT TRANSFER Previous Question Paper (March - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
What is velocity potential function? What is its use in fluid flow analysis?
Answer
The velocity potential function, denoted by φ, is a scalar function of space and time such that its negative partial derivative with respect to any coordinate direction gives the fluid velocity component in that direction. For a three-dimensional flow, it is defined as:
In fluid flow analysis, it is used to determine if a flow is irrotational. If a velocity potential exists, the flow must be irrotational, meaning the vorticity components are zero. Furthermore, for an incompressible flow, the velocity potential must satisfy the Laplace equation,
For the given three-dimensional flow field described by V = (x + y) i + (y + z) j + (x2 + y2 + z2) k, find the components of rotation at (1,1,1).
Answer
Given the velocity vector field
Calculating the partial derivatives:
- ∂w/∂y = 2y; ∂v/∂z = 1
- ∂u/∂z = 0; ∂w/∂x = 2x
- ∂v/∂x = 0; ∂u/∂y = 1
Substituting these into the rotation component formulas:
At the point (1, 1, 1):
The components of rotation at (1, 1, 1) are 0.5, -1, and -0.5 respectively.
Define fluid surface tension property. What are its examples?
Answer
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The velocity distribution in a viscous flow over a plate is given by u = 4y - y2. Where u is velocity at distance y from the plate. If the coefficient of dynamic viscosity is 1.5 Pa.sec, determine the shear stress at y=0 and y=2.
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Name the different forces present in a fluid flow. For the Euler’s equation of motion, which forces are taken into consideration.
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An oil of specific gravity 0.8 is flowing through a venturi meter having inlet diameter 20cm and throat diameter 10 cm. The oil – mercury differential manometer shows a reading of 25 cm. calculate the discharge of oil through the horizontal venturi meter. Take Cd = 0.98.
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Define orifice meter. Derive an expression for Co-efficient of discharge for orifice meter.
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An orifice meter with orifice diameter 10 cm is inserted in a pipe of 20 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter gives reading of 19.62 N/cm2 respectively. Co-efficient of discharge for the orifice meter is give as 0.6. Find the discharge of water through pipe.
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Derive an expression for the thermal resistance through a hollow spherical shell of inside radius ri and outside radius ro having conductivity k.
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It is desired to limit the heat loss through a boiler furnace wall to 200 W/m2. The wall is composed of a material having thermal conductivity of 1.125 W/mk. If the inner surface temperature is 100 °C and the outer surface temperature is 350 °C, find the thickness of the material to be used?
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Sheets of brass and steel, each of thickness 1 cm, are placed in contact. The outer surface of brass is kept at 100 °C and the outer surface of steel is kept at 0 °C. What is the temperature of the common interface? The thermal conductivities of brass and steel are in the ratio of 2:1.
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Define thermal conductivity and how it can be measured. What is the difference between the thermal conductivity and thermal conductance?
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Derive an expression for boundary layer thickness for free convection heat transfer on a vertical flat plate.
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Water at 1 Atm boils in a stainless-steel kitchen pan with ΔTx = 8 °C. Estimate the heat flux which will be obtained if the same pan operates as a pressure cooker at 0.17 MPa, what percentage increases in heat flux might be expected?
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What is Stefan-Boltzmann law? Explain the concept of total emissive power of a surface.
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Saturated steam at 2 bar condenses on a cylindrical vertical drum having an outside diameter of 25 cm and a temperature of 90 °C. Calculate how long must the drum be to condense 50 kg of steam per hour. Also estimate the thickness of condensate layer.
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