Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II Year FLUID MECHANICS AND OPEN CHANNEL HYDRAULICS Previous Question Paper (May/June - 2019 - R13)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.
Part A
(25 Marks)
A cylindrical plug of 120mm diameter and 200mm length slides concentrically in a stationary cylinder of 120.2mm internal diameter. The clearance is filled with oil of viscosity 0.25 Ns/m². Find the force required to slide the plug along the cylinder at a speed of 3.5 m/s.
Answer
The force required is calculated using Newton's law of viscosity, where the shear force F is given by F = μ A (du/dy). The clearance thickness dy is half the difference in diameters: dy = (120.2 mm - 120 mm) / 2 = 0.1 mm = 0.0001 m. The surface area of the plug is A = π D L = π × 0.12 m × 0.2 m = 0.0754 m². Given the velocity u = 3.5 m/s and viscosity μ = 0.25 Ns/m², the force is F = 0.25 × 0.0754 × (3.5 / 0.0001) = 659.75 N.
Prove that the pressure is the same in all directions at a point in a static fluid.
Answer
Consider an infinitesimal wedge-shaped fluid element of unit thickness (perpendicular to the plane) with sides dx, dy, and ds, where ds is the hypotenuse. Let px, py, and ps be the pressures acting on the faces dy, dx, and ds respectively, and let θ be the angle between the hypotenuse and the vertical face.
The forces acting on the element are the pressure forces normal to the faces and the weight of the element acting vertically downwards. The weight is given by W = ρg(0.5 × dx × dy × 1).
Resolving the forces in the x-direction (horizontal):
Since sin(θ) = dy/ds, this simplifies to px = ps.
Resolving the forces in the y-direction (vertical):
Since cos(θ) = dx/ds and W is a third-order differential term (dx × dy), it vanishes as the element size approaches zero. Thus, py = ps. Combining these results, px = py = ps, proving that pressure at a point in a static fluid is independent of direction.
Name any two devices for each of the following: i) Measuring of discharge. ii) Measuring of velocity.
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How does a boundary layer produce momentum change? How is this related to boundary resistance?
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What is a notch? How are they classified?
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Define Vena contracta. How is it developed?
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Explain three kinds of similitude.
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Explain the significance of hydraulic jump in open channel flow.
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State the conditions for rectangular channel to have most economical cross-section.
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Show that for critical flow at a section the Froude’s number is equal to unity.
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Part B
(50 Marks)
In a two dimensional flow, show that the continuity equation is satisfied. Find the stream function and velocity potential function and find the equation to the stream function passing through the point (3, 5).
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Derive the equation for variation of pressure in a fluid in Cartesian coordinates.
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If a potential function is given, calculate the velocity components at a point (3,4).
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Derive the equation to determine the pressure head in a differential manometer at different levels containing three liquids of specific gravities S1, S2 and S3.
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Describe the working principle of venturimeter. Derive the discharge equation.
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A vertical Venturimeter has its inlet and throat diameters as 300 mm and 150 mm respectively. A differential mercury manometer connected to the inlet and throat points gives a reading of 300 mm. Find the rate of flow in lt/min. Take Cd = 0.98.
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Mention few practical applications of Boundary layer flows over a flat plate. Also state the effects of boundary layer.
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A cylindrical boiler, diameter 2m and length 10m is lying horizontally and is half full of water. It is to be emptied by an external cylindrical mouthpiece of diameter 75mm fixed at the bottom. Calculate time required.
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The maximum flow through a rectangular flume 1.8m wide and 1.2m deep is 1.65 cumec. Find the maximum height at which the weir crest can be placed in order that water may not overflow the sides. Assume Cd = 0.6.
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What is meant by stability of a floating body? Explain with reference to its metacentric height.
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Find the time required to empty a swimming pool through an opening provided in the bottom of the deep end.
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Three pipes were connected between two points A and B to carry 0.5 cumec. Determine the flow in each pipe and the pressure at B.
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Outline the procedure when the dimensional analysis is to be carried out using Buckingham method.
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Derive Darcy’s Weisbach formula for the loss of head due to friction in a pipe system.
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Classify the open channels and write the definitions.
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Differentiate between open channel flow and pipe flow. Which is complicated and why?
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Enumerate the characteristics of hydraulic jump.
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Show the velocity and pressure distribution profiles for different channel cross-sections.
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A trapezoidal channel is 3.0m wide at the bottom provided with side slopes of 1.5H:1V. Construct the specific-force diagram for a discharge of 17.5 cumec.
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