JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II FLUID MECHANICS - I Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive an expression for the force exerted on a sub-merged vertical plane surface by the static liquid and locate the position of centre of pressure.
Answer
Consider a vertical plane surface of arbitrary shape submerged in a static liquid of density ρ. Let A be the total area of the surface, h̄ be the depth of the centroid of the area from the free liquid surface, and G be the centroid. Let the plane surface be inclined at 90° to the free surface.
Total Pressure Force (F): The force exerted on an elemental area dA at a depth h is dF = ρgh dA. Integrating over the entire area:
Since ∫ h dA = A × h̄, the total force is:
Center of Pressure (h*): The center of pressure is the point where the total force acts. Taking the moment of the total force about the free surface:
The term ∫ h² dA represents the moment of inertia of the area about the free surface (I₀). By the parallel axis theorem, I₀ = I_G + Ah̄², where I_G is the moment of inertia about the centroidal axis parallel to the free surface. Substituting this into the moment equation:
Solving for h*:
This expression shows that the center of pressure h* is always below the centroid h̄ by the distance I_G / Ah̄.
Explain the terms: (i) Dynamic viscosity, and (ii) Kinematic viscosity. Give their dimensions.
Answer
(i) Dynamic viscosity (μ) is the measure of a fluid's resistance to gradual deformation by shear stress or tensile stress. It relates the shear stress (τ) to the velocity gradient (du/dy) in a fluid: τ = μ(du/dy). Its SI unit is N·s/m² or Pa·s. Its dimensions are [M L⁻¹ T⁻¹].
(ii) Kinematic viscosity (ν) is defined as the ratio of dynamic viscosity to the density (ρ) of the fluid: ν = μ/ρ. It represents the momentum diffusivity of the fluid. Its SI unit is m²/s. Its dimensions are [L² T⁻¹].
A vertical gate closes a horizontal tunnel 5 m high and 3 m wide running full with water. The pressure at the bottom of the gate is 196.2 kN/m2. Determine the total pressure on the gate and position of the centre of pressure.
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Explain the three states of equilibrium of a floating body in terms of the magnitude and direction of righting couple acting on the body as a result of slight angular displacement.
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Derive, from first principles, the condition for irrotational flow. Prove that, for potential flow, both the stream function and velocity potential function satisfy the Laplace equation.
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Discuss the various empirical formulae for discharge over weirs.
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Find an expression for the discharge over a rectangular weir in terms of head of water.
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Derive an expression for the loss of head due to sudden contraction of a pipe.
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Air flows over a flat plate 1 m long at a velocity of 6 m/s. Determine (a) the boundary layer thickness at the end of the plate, (b) shear stress at the middle of the plate, (c) total drag per unit length on the sides of the plate. Take
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