JNTU
JNTU B.Tech II MECHANICS OF FLUIDS Previous Question Paper (August/ September - 2022 - R13)
Answer any five questions. All questions carry equal marks.
Main
Explain the characteristic fluid properties to which the following phenomenon are attributable: (i) Rise of sap in a tree (ii) Spherical shape of a drop of a liquid (iii) Cavitation (iv) Flow of a jet of oil in an unbroken stream (v) Water hammer.
Answer
(i) Capillarity: The rise of sap is due to the combined effect of surface tension and adhesion between the liquid and the narrow capillary tubes (xylem) in the tree.
(ii) Surface Tension: A liquid drop assumes a spherical shape to minimize its surface area for a given volume, as the surface tension force acts to pull the surface inward.
(iii) Vapour Pressure: Cavitation occurs when the local pressure of a flowing liquid falls below its vapour pressure, causing the liquid to vaporize and form bubbles that collapse violently upon reaching higher pressure zones.
(iv) Cohesion and Viscosity: The unbroken stream is maintained by the cohesive forces between liquid molecules and the fluid's viscosity, which resists the separation of the jet.
(v) Compressibility and Inertia: Water hammer is caused by the sudden change in velocity of a fluid in a pipe, where the fluid's compressibility and inertia lead to high-pressure shock waves.
A rectangular plane surface 2 m wide and 3 m deep lies in water in such a way that its plane makes an angle of 30° with the free surface of water. Determine the total pressure and position of centre of pressure when the upper edge is 1.5 m below the free water surface.
Answer
Given: Width (b) = 2 m, Depth (d) = 3 m, Angle (θ) = 30°, Depth of upper edge (h1) = 1.5 m.
The depth of the centroid (hG) is:
Total pressure (F) is given by:
The moment of inertia (IG) for a rectangular plate is:
The centre of pressure (hP) is calculated using:
Define: (i) Steady flow (ii) Laminar flow (iii) Turbulent flow (iv) Uniform flow and (v) Compressible flow.
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The velocity vector in a fluid flow is given by V = 4x3i - 10x2yj + 2tk. Find the acceleration of fluid particle at (2,1,3) at time t = 1.
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Derive Euler’s equation of motion. How do you obtain Bernoulli’s equation from Euler’s equation.
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An oil of specific gravity 0.8 is flowing through a venturimeter having inlet diameter 20 cm and throat diameter 10 cm. The oil-mercury differential manometer shows a reading of 15 cm. Calculate the discharge of oil through the horizontal venturimeter. Take Cd = 0.98.
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With a neat sketch, explain the development of boundary layer over a horizontal flat plate which is kept in a flow field.
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For the velocity profile in a laminar flow Obtain the expression for boundary layer thickness, shear stress, drag force on one side of the plate and coefficient of drag in terms of Reynolds number.
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Derive Darcy-Weisbach equation and explain the salient points.
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A crude oil of viscosity 0.97 poise and relative density 0.9 is flowing through a horizontal circular pipe of diameter 100 mm and of length 15 m. Calculate the difference of pressure at the two ends of the pipe, if 100 kg of oil is collected in a tank in 25 seconds.
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Write the conditions for the equilibrium of floating and submerged bodies.
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In a 2D incompressible flow, the fluid velocity components are given by u = x - 4y and v = -y - 4x. Show that the velocity potential exists and determine its form. Find also the stream function.
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Explain similarity requirements between the model and prototype.
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The pressure drop ΔP in flow of incompressible fluid through rough pipes is found to depend on the length L, average velocity u, fluid density ρ, dynamic viscosity μ, diameter D and average roughness height e. Obtain a dimensionless expression using Π – theorem.
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Formulate Hagen-Poiseuille equation and discuss its importance.
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A plate 450 mm × 150 mm has been placed longitudinally in a stream of crude oil (Sp.gr = 0.925 and kinematic viscosity = 0.9 stoke) which flows with velocity of 6 m/s. Solve for (i) friction drag on the plate (ii) thickness of the boundary layer at the trailing edge (iii) shear stress at the trailing edge.
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