JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year I Semester FLUID MECHANICS - I Previous Question Paper (August/September - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
A Circular plate 4 m in diameter is placed in such a way that its top vertex is at 2 m below free water surface and bottom vertex is 5 m below the free water surface. Find out the total pressure acting on the plate.
Answer
The total pressure force F acting on a submerged plane surface is given by:
Where:
- ρ (density of water) = 1000 kg/m3
- g (acceleration due to gravity) = 9.81 m/s2
- D (diameter) = 4 m, so R (radius) = 2 m
- A (Area) = π × R2 = π × 22 = 4π m2 ≈ 12.566 m2
- h̅ (depth of centroid) = (depth of top + depth of bottom) / 2 = (2 + 5) / 2 = 3.5 m
Substituting the values:
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
The torque T required to rotate the cylinder is given by the product of the shear force and the radius of the cylinder:
Where τ is the shear stress, A is the surface area of the cylinder, and R is the radius.
- R (cylinder radius) = 0.05 m
- L (length) = 0.3 m
- A (surface area) = 2 × π × R × L = 2 × π × 0.05 × 0.3 = 0.03π m2
- dy (gap width) = (105 mm - 100 mm) / 2 = 2.5 mm = 0.0025 m
- μ (viscosity) = 0.125 N.s/m2
Using Newton's Law of Viscosity, τ = μ × (du / dy), where du = ω × R:
Rearranging for angular velocity ω:
Plugging in the values:
The rotational speed N in rpm is:
Explain the different manometers to measure the pressure in the fluid flow.
Answer
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An oil film of thickness 2 mm is used for lubrication between a square plate of size 0.8 m × 0.8 m and an inclined plane having an angle of inclination 30°. The weight of the square plate is 400 N and it slides down the plane with a uniform velocity of 0.3 m/s. Find the dynamic viscosity of the oil.
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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).
Answer
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What is meant by Velocity Potential function? What are the different characteristics of Potential function?
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Define the equation of continuity. Obtain an expression for continuity equation for three dimensional flow.
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In an incompressible flow field, the velocity vector is given by V = (6xt+yz2) i + (3t+xy2) j + (xy-2xyz – 6tz) k. Verify whether the flow exists or not? If so, then find the acceleration vector at a point P(1,2,3) at t = 2.
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The diameters of pipe bend at the inlet and outlet are 30 cm and 15 cm and turned through 120° right in the vertical plane. The axis at the inlet is horizontal. The outlet is 1.5 cm below the inlet. The volume of water in the bend is 900 liters. Find the force acting on the bend when the water flow is 250 liters/second. And inlet pressure is 1.5 bar.
Answer
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Derive the Bernoulli’s equation for one dimensional flow along the stream line.
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Derive the expression for the discharge of fluid flow rectangular notch.
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A pipe line 30 cm in diameter 1500 m long is used to connect two tanks and has a slope of 1 in 100. The water level in the first tank is 10 m above inlet of the pipe and water level in the second tank is 2 m above the outlet of the pipe. Find the flow rate through the pipe:
- a) Considering only frictional losses
- b) Considering all minor losses. Take friction factor as 0.005.
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Explain the boundary layer formation along the flat plate and explain the characteristics of boundary layer.
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What are the methods to be adopted to prevent the separation of boundary layer?
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