JNTU
JNTU B.Tech II FLUID MECHANICS – I Previous Question Paper (March – 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
A cylinder of 100 mm diameter and 300 mm length rotates about a vertical axis inside a fixed cylinder tube of 105 mm diameter and 300 mm length. If the space between the tube and cylinder is filled with liquid of dynamic viscosity of 0.125 N.s/m2, determine the speed of rotation of the cylinder which will be obtained if an external torque of 1 Nm is applied to it.
Answer
Given: Diameter of cylinder (D) = 0.1 m, Length (L) = 0.3 m, Diameter of tube (Do) = 0.105 m, Viscosity (μ) = 0.125 N.s/m2, Torque (T) = 1 Nm. The clearance (t) is (0.105 - 0.1)/2 = 0.0025 m. The shear stress (τ) is given by μ(du/dy), where du = ωR and dy = t. Thus, τ = μ(ωR/t). The shear force (F) = τ × Area = μ(ωR/t) × (2πRL). The torque (T) = F × R = μ(ωR/t) × (2πRL) × R = (2πμωR3L)/t. Substituting the values: 1 = (2 × π × 0.125 × ω × (0.05)3 × 0.3) / 0.0025. Solving for ω: ω = (1 × 0.0025) / (2 × π × 0.125 × 0.000125 × 0.3) = 106.1 rad/s. The speed of rotation (N) = (ω × 60) / (2π) = (106.1 × 60) / (2π) = 1013.2 rpm.
Enunciate Newton’s law of viscosity. Explain the importance of viscosity in fluid motion. What is effect of temperature on viscosity of water and air?
Answer
Newton's Law of Viscosity states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain (velocity gradient), expressed as τ = μ(du/dy), where μ is the coefficient of dynamic viscosity. Viscosity is critical in fluid motion as it dictates the internal resistance to flow, determines the Reynolds number, and governs the development of the boundary layer and energy losses due to friction. Regarding the effect of temperature: for liquids like water, viscosity decreases as temperature increases because the cohesive forces between molecules weaken; for gases like air, viscosity increases with temperature due to the increased rate of molecular momentum transfer between layers.
A circular plate 3 metre diameter is submerged in water in such a way that its greatest and least depth below the free surface are 4m and 1.5 m respectively. Determine the total pressure on one face of the plate and position of the centre of pressure.
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A log of wood in diameter and 5 m long is floating in river water. If the specific gravity of log is 0.7, what is depth of wooden log in water?
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What is meant by the potential function, Obtain the three dimensional continuity equation in terms of potential function. Explain the importance of potential function.
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A two dimensional flow is described by the velocity components: u = 5x3 and v = -15x2y. Determine the stream function, velocity and acceleration at P(x=1m, y=2m).
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A pipe line carrying oil (sp. gravity =0.87) changes in diameter from 200 mm diameter at position 1 to 500 mm diameter at position 2 which is 4 meters at a higher level. If the pressure at 1 and 2 are 100 kN/m2 and 60 kN/m2 respectively and the discharge is 0.2 m3/s, determine:
a) Loss of head
b) Direction of flow.
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State Bernoulli’s theorem for steady flow of an incompressible fluid. Derive an expression for Bernoulli’s theorem from first principle and state the assumptions made for such a derivation.
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Derive the Darcy-Wiesbach equation for finding out the energy loss of fluid flow through pipes. List out the reasons for minor loss of energy of fluid flow through pipes.
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Derive the expression of energy thickness of the boundary layer.
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The velocity distribution in a boundary layer is given by u/U = y/δ. Find out displacement, momentum and energy thickness.
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