JNTU
JNTU B.Tech II FLUID MECHANICS AND HEAT TRANSFER Previous Question Paper (November/December - 2020 - R13)
Answer any five questions. All questions carry equal marks.
Main
Explain the importance of these terms in understanding the flow behavior.
Velocity Potential
Answer
The Velocity Potential (denoted by φ) is a scalar function of space and time such that its negative gradient with respect to any direction gives the fluid velocity in that direction. Mathematically, for a three-dimensional flow, the velocity components are defined as u = -∂φ/∂x, v = -∂φ/∂y, and w = -∂φ/∂z.
Its importance in flow behavior includes:
- It exists only for irrotational flow, serving as a mathematical criterion to identify if a flow field is irrotational.
- For an incompressible fluid, the continuity equation reduces to the Laplace equation, ∇²φ = 0, which allows for the use of potential flow theory to solve complex flow problems.
- It simplifies the analysis of fluid motion by reducing a vector field problem to a scalar field problem, making it easier to determine velocity distributions in ideal fluid flows.
Stream function
Answer
The Stream function (denoted by ψ) is a scalar function defined for two-dimensional incompressible flow such that its partial derivatives represent the velocity components. Specifically, u = ∂ψ/∂y and v = -∂ψ/∂x.
Its importance in flow behavior includes:
- The value of the stream function is constant along a streamline, which allows for the direct visualization of flow patterns and paths of fluid particles.
- The difference in the value of the stream function between two streamlines represents the volume flow rate per unit depth between those two streamlines.
- It is applicable to both rotational and irrotational flows, making it a more versatile tool than velocity potential for general two-dimensional flow analysis.
- It automatically satisfies the continuity equation for two-dimensional incompressible flow, as ∂u/∂x + ∂v/∂y = ∂²ψ/∂x∂y - ∂²ψ/∂y∂x = 0.
A square aperture in the vertical side of a tank has one diagonal vertical and is completely covered by a plane plate hinged along one of the upper sides of the aperture. The diagonals of the aperture are 2 m long and the tank contains a liquid of relative density 1.15. The centre of aperture is 1.5 m below the free surface. Calculate the thrust exerted on the plate by the liquid and position of the centre of pressure.
Answer
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A 100 mm diameter pipe carries oil of specific gravity 0.8 which flows with a velocity of 2 m/s. At another section of the pipe, the diameter is 50 mm. Determine the mass flow rate of oil through the pipe and velocity of oil at the smaller section.
Answer
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Explain the principle of Venturimeter with a neat sketch. Derive the expression for the rate of flow of fluid through it.
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A composite cylinder is made of 6 mm thick layers each of two materials of thermal conductivities of 30 W/m.K and 45 W/m.K. The inside is exposed to a fluid at 500oC with a convection coefficient of 40 W/m2.K and the outside is exposed to air at 35oC with a convection coefficient of 25 W/m2.K Determine the heat loss for a length of 2 m. The inside diameter = 20 mm.
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One side of a plane wall is maintained at 100oC, while the other side is exposed to a convection environment having T=10oC and h= 11 W/m2K. The wall has k = 1.6 W/mK and is 40 cm thick. Calculate the heat transfer rate through the wall.
Answer
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Derive an expression for forced convective heat transfer through a conduit using dimensional analysis.
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Explain shape factor and calculate the shape factor for a cylindrical cavity of diameter D and height L with respect to itself.
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