Code No:210106
Set No.
II B.Tech. I Semester Examination November/December 2002 FLUID MECHANICS (Civil Engineering)
Max. Marks: 80 Answer any Five questions All questions carry equal marks ---
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Time: 3 Hours
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1. a) Define surface Tension. Derive the relationship between surface Tension and pressure inside a droplet off liquid in excess of outside pressure. b) An oil of viscosity 5 poise is used for lubrication between a shaft and sleeve. The diameter of shaft is 0.5 m and it rotates at 200 rpm. Calculate the power lost in the oil for a sleeve length of 100 mm. The thickness of oil film is 1.0 mm. 2. a) Prove that the vertical component of the resultant pressure on a submerged curved surface is equal to the weight of the liquid supported by the curved surface. b) Find the total pressure and depth of center of pressure on a triangular plate of base 3 m and height 3 m which is immersed in water in such a way that plan of the plate makes an angle of 60 with the free surface. The base of the plate is parallel to water surface and at a depth of 2m from water surface.
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3. a) 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. b) A fluid flow is given by
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V = xy2i – 2yz2j – (zy2 – 2z3) k 3 Prove that it is a case of possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point [1,2,3]
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4. a) State Bernoulli’s theorem. Mention the assumptions made. How is it modified while applying in practice? List out its engineering application. b) A 45 reducing bend is connected in a pipe line, the diameters at the inlet and outlet of the hand being 40 cm and 20 cm respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet of bend is 21.58 N/cm2. The rate of flow of water is 500 lit/sec.
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Code No: 210106
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Set No. 1
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5. a) Explain the phenomenon of water hammer. Obtain an expression for the rise of pressure when the flowing water in a pipe is brought to rest by closing the value gradually. b) Three pipes of lengths 800m, 600m and 300m and of diameters 40cm, 30cm and 20cm respectively are connected in series. The ends off the compound pipe is connected to two tanks whose water surface levels are maintained at a difference off 15m. Determine the rate of flow of water through the pipes if f = 0.005 what will be diameter of a single pipe length 1700m and f = 0.005 which replaces the three pipes.
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6. a) Explain the principle and working of venturimeter with a neat sketch. b) State the different devices that can be used to measure the discharge through an open channel. Describe one of such devices with a neat sketch and explain how one can obtain the actual discharge with its help.
7. a) Define laminar boundary layer, turbulent boundary layer, displacement thickness and momentum thickness. b) Find the frictional drag on one side of the plate 20cm wide and 50cm long placed longitudinally in a stream of crude oil (specific gravity = 0.925 and kinematics’ viscosity 0.9 stoke) flowing with undisturbed velocity of 5 m/sec. Also find the thickness of boundary layer and the shear stress at the trailing edge of the plate. Write short notes an any four of the following.
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a) Pitot Static Tube d) Reynolds Number
b) Newton’s Law of Viscosity e) Boundary layer Separation
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c) Flow Net
Code No:210106
Set No.
II B.Tech. I Semester Examination November/December 2002 FLUID MECHANICS (Civil Engineering) Time: 3 Hours
2
Max. Marks: 80
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Answer any Five questions All questions carry equal marks --1. a) Explain kinematic viscosity and Dynamic viscosity. Give their diamensions in CGS and MKS systems. b) Calculate the capillary rise h in a glass tube of 3mm diameter when immersed in water at 20C. Take surface tension for water at 20C as 0.0075 kg/m. What will be the percentage increase in the value of h if the diameter of the glass tube is 2mm. 2. a) Obtain an expression for the pressure intensity at a point in a fluid. b) A pipe containing water at 1.75 kg/cm2 pressure is connected by a differential gauge to another pipe 1.5m lower than the first pipe and containing water at high pressure. If the difference in heights of the two mercury columns of the gauge is equal to 7.5cm, what is the pressure in the lower pipe? Specific gravity of mercury is 13.6.
Define and distinguish between a) a steady and unsteady flow uniform and non-uniform flow Rotational and irrotational flow. b) In a free cylindrical vortex of water, the tangential velocity at a radius of 10 cm from the axis of rotation is found to be 10m/sec and the intensity of pressure is 2 kg/cm2. Find the intensity of pressure at a radius of 20cm from the axis.
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3. a) Show that the center of pressure of any lamina immersed under liquid is always below its centroid. b) A triangular gate which has a base of 1.5m and an altitude of 2m lies in a vertical plane. The vertex of the gate is 1m below the surface in a tank which contains oil of specific gravity 0.8. Find the force exerted by the oil on the gate and the position of the center of pressure.
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Code No: 210106
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Set No. 2
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5. a) Starting with Eulers equation of motion along a streamline, obtain Bernoulli’s equation by its integration. List all the assumptions made. b) A 30cm x 15cm venturimeter is inserted in a vertical pipe carrying water flowing in the upward direction. A differential mercury manometer connected to the inlet and the throat gives a reading of 30cm. Find the discharge taking cd as 0.98. Instead of water, oil of specific gravity 0.8 is flowing through venturimeter determine the rate of flow of oil in lit/sec. 6. a) Define vena-contracte obtain an expression for discharge through a large rectangular orifice. b) Water is flowing in a rectangular channel of 1.2m wide and 0.8m deep. Find the discharge over a rectangular weir of crest length 70cm if the head of water over the crest of weir is 25 cm and water from channel flows over the weir. Take cd = 0.60. Neglect end contractions but consider velocity of approach.
7. a) Derive an expression for head loss due to friction in pipe flow, b) Two sharpended pipes of diameters 60mm and 100mm respectively, each of length 150m are connected in parallel between two reservoirs which have a difference of level off 15m. If coefficient of friction for each pipe is 0.08 calculate the rate of flow for each pipe and also the diameter of a single pipe 150m long which would give the same discharge if it were substituted for the original two pipes. Write short notes on any four of the following a) Surface Tension b) Hydrostatic force on curved surfaces. c) Orifice meter. d) Stream lines and equipotential lines e) Broad crested weirs.
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Code No:210106
Set No.
II B.Tech. I Semester Examination November/December 2002 FLUID MECHANICS (Civil Engineering)
Max. Marks: 80 Answer any Five questions All questions carry equal marks ---
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Time: 3 Hours
3
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1. a) Explain (i) ideal fluid (ii) Newtonian fluid (iii) dilatants and (iv) shear thinning fluid and give an example for each. b) Derive the expression for capillary rise. c) A soap bubble of 60mm in diameter contains a pressure in excess of atmospheric pressure of 15 N/m2. Calculate the tension in the soap film. 2. a) Define rotational component b) What is a flow net? What are its characteristics? c) A fluid flow field is given by V = x2yi + y2zj – (2xyz + yz2)k Prove that it is the case of a possible steady incompressible fluid flow. Calculate the velocity and acceleration at a point (2,1,3).
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3. a) State and prove Euless equation for one dimensional flow and hence obtain Bernoulli’s equation. Mention the assumptions. b) A nozzle of 30mm diameter is fitted in a pipe of 50mm diameter. Find the force exerted by the nozzle on the water flowing through the pipe if the rate of flow is 1.5 m3/minute.
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4. a) Define the terms lift and drag and give expressions for coefficients of lift and drag. b) A rectangular plate 1m wide and 2.5m long is held in a stream of water moving at 2m/s parallel to its length. Assuming laminar conditions at the leading edge of the plate, determine where the boundary layer changer from laminar to turbulent. Calculate the thickness of boundary layer at this point and to computer the friction drag on the plate given the kinematic viscosity of water to be 0.012 cm2/sec.
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5. a) State and derive Hagen – Poiseullis equation. b) A flat plate 1m x 1m is pulled over a flat horizontal surface at 1.5m/s. The oil flowing between the two surfaces is 1cm thick and has an absolute viscosity of 0.06 Pa. S and density of 900 kg/m3. Calculate (i) the force required to maintain the speed against a pressure difference of 10 N/m2/m and the discharge rates of oil. Contd……2
Code No: 210106
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Set No. 3
6. a) Explain with a neat sketch Reynolds experiments and the inference made. b) A pipe line is 0.5m diameter and 1km long. To augment the discharge another pipe line of the same diameter in introduced parallel to the first one in the second half of the length. Neglective in minor losses, find the increase in discharge given the friction factor ‘4f’ is 0.04 and the head of water above the outlet is 25m.
Write short notes on the following a) Micro manometer b) Flow net c) Boundary layer separations.
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7. a) With a neat sketch explain the principle of pitot tube. b) An orifice meter with an orifice of diameter 7.5cm is installed in a pipeline 15cm in diameter. The pressure on one side of orifice enter is 7 N/cm2 gauge and that on the other side is 5 N/cm2 absolute. Determine the discharge of water assuming Cd of the meter to be 0.7. Atmospheric pressure is 9.81 N/cm2.
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Code No:210106
Set No.
II B.Tech. I Semester Examination November/December 2002 FLUID MECHANICS (Civil Engineering) Time: 3 Hours
4
Max. Marks: 80
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Answer any Five questions All questions carry equal marks --1. a) Explain the phenomenon of capillarity. Obtain an expression for capillary rise of a liquid. b) Two plates are placed at a distance of 0.15 mm apart. The lower plate is fixed while the upper plate is having surface area of 1.0m2 is pulled at 0.3 m/sec. Find the force and power required to maintain this speed if the fluid separating them is having viscosity of 1.5 poise.
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2. a) Derive an expression for the depth of center of pressure from free surface of liquid on an inclined plane surface submerged in the liquid. b) A circular plate 3.0 m diameter is immersed in water in such away that the plane of the plate makes an angle of 60 with the free surface of water. Determine the total pressure and position of center of pressure when the upper edge of the plate is 2m below the free water surface.
3. a) Define the education of continuity. Obtain an expression for continuity education for a three dimensional flow. b) If for a two dimensional potential flow the velocity potential is given by = 4x (3y-4). Determine the velocity at the point (2,3). Determine also the value of stream function at the point (2,3).
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4. a) Derive Bernoulli’s education for the flow of an incompressible frictionless fluid from consideration of momentum. b) A 45 reducing bend is connected in a pipeline. The diameters at the inlet and outlet of the bend being 40cm and 20cm respectively. Find the force exerted by water on the bend if the intensity of pressure at inlet of bend is 21.58 N/cm2. The rate of flow of water is 500 lit/sec.
Contd……2
Code No: 210106
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Set No. 4
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5. a) Define coefficient of velocity (Cv) coefficient of contraction (Cc) Derive an expression. C d = Cc x Cv Where Cd is coefficient of discharge. b) Prove that the error in discharge due to the error in measurement of head over a rectangular notch is given by dQ = 3 dH Q 2 H Q = Discharge through rectangular notch H = Head over the rectangular notch.
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6. a) Explain Hydraulic Gradient Line, Total energy line, equivalent pipe and compound pipe. b) The rate of flow of water through a horizontal pipe is 0.3 m3/sec. The diameter of the pipe is suddenly enlarged from 25 cm to 50cm. The pressure intensity in the smaller pipe is 1.4 kgf/cm2. Determine loss of head due to sudden enlargement, pressure intensity in the large pipe and power lost due to enlargement.
Write short notes on any four of the following . a) Drag and Lift b) Free Vortex and Force Vortex c) Pitot Tube. d) Venturi meter e) Flow net
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7. a) Explain the different methods of preventing the separation of boundary layers. b) A thin plate is moving in still atmospheric air at a velocity of 4 m/sec. The length of plate is 0.5m and width is 0.4m calculate the thickness of boundary layer at the end of the plate and drag force on one side of the plate. Take density of air as 1.25 kg/m3 and kinematic viscosity as 0.15 stokes.
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