R09. d water surface. Prove that the depth of pressure is equal to p +.


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1 Code No:A R09 SET1 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal marks a) What is capillarity? Derive an expression for height of a capillary rise. b) What is the difference between cohesion and adhesion? c) Determine the minimum size of glass tube that can be used to measure water level, if the capillary rise in the tube is not to exceed 0.25 mm. Take surface tension of water in contact with air as N/m. [15] 2.a) Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface submerged in the liquid b) A rectangular sluice gate is situated on the vertical wall of a lock. The vertical side of the sluice is d metres in length and depth of centroid of the area is p metres below the 2 d water surface. Prove that the depth of pressure is equal to p p [15] 3.a) Explain Lagrangian and Eulerian methods of describing fluid flow. b) If the velocity potential function is given by ψ = 3x 4 y. Find the magnitude and direction of the velocity at any point? [15] 4.a) What is a pitot tube? Explain types of Pitot tubes? How is it used to measure velocity of flow at any point in a pipe or channel? b) A horizontal venturimeter with inlet and throat diameters 160 mm and 60 mm respectively is used to measure the flow of an oil of specific gravity 0.8. If the discharge of the oil is 0.05 m 3 / s, find the deflection of oil mercury gauge. Take venturimeter constant=1. [15] 5.a) Explain the characteristics of laminar and turbulent boundary layers. b) Prove that the momentum thickness and energy thickness for boundary layer flows are given by δ 2 u u θ = 1 dy U U u y y = 2 U δ δ. [15] 0
2 6.a) Derive HagenPoiseuilles equation and state the assumptions made. b) In a circular pipe of diameter 100 mm a fluid of viscosity 7 poise and specific gravity is flowing is 1.3. If the maximum shear stress at the wall of the pipe is N/m 2, find: i) The pressure gradient ii) The average velocity iii) Reynolds number of flow. [15] 7. A pipe of diameter 50 cm and length 5000 metres connects two reservoirs A and B. The difference of water levels of these reservoirs is 20 metres. Half way along the pipe there is a branch through which water can be discharged to a third reservoir C. Find the rate of flow to the reservoir B when i) No water is discharged to the reservoir C ii) The discharge to the reservoir C is 0.05 cumec. Take f= [15] 8.a) What do you mean by end contraction of a rectangular weir?. How the loss of discharging capacity due to end contractions can be compensated? b) The head of the water over a 3 metres long weir is 30 cm. Find the discharge by Francis formula. Allow for two end contractions. c) How does a Cippoletti weir differ from a rectangular sharp crested weir? [15] ********
3 Code No:A R09 SET2 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal marks a) Explain briefly the following terms: i) Mass density ii) Weight density iii) Specific volume iv) Specific gravity. b) State and explain the Newton s law of viscosity. c) A U tube is made up of two capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and is partially filled with liquid of surface tension 0.05 N/m and zero contact angle. Calculate the mass density of the liquid if the estimated difference in the level of two menisci is 12.5 mm. [15] 2.a) Derive expressions for total pressure and centre of pressure for the following two cases. (i) For a vertically immersed surface. (ii) For inclined immersed surface. b) The masonry dam of trapezoidal section has its upstream face vertical. The height is 10 m and top is 3 m wide. Find the minimum width of base if there is no tension at the base and water reaches the top of the dam. Take weight of water as 9.81 k N/m 3 and weight of mansonry is 22kN/m 3. What is then maximum compressive stress at the base? [15] 3.a) Write short notes on : i) Path line ii) Stream line iii) Streak line iv) Stream tube. b) 2 2 A stream function follows the law ψ = x y. Determine the velocity potential function. [15] 4.a) Describe an orifice meter and find an expression for measuring discharge of fluid through a pipe with this device. b) A Venturimeter is used for measuring the flow of petrol in a pipeline inclined at 35 0 to horizontal. The sp. Gravity of the petrol is 0.81 and throat area ratio is 4. If the difference in mercury levels in the gauge is 50 mm calculate the flow in m 3 /s if the pipe diameter is 300. Take venturimeter constant is [15]
4 5.a) Define the following terms: i) Laminar boundary layer ii) Turbulent boundary layer iii) Laminar sub layer iv) Boundary layer thickness. b) For the velocity profile in laminar layer given asφ = log x. Find the thickness of y boundary layer at the end of the plate and the drag force on the side of the plate 1 m long and 0.8 m wide when placed in water flowing with a velocity of 0.15 m/s. Calculate the value of co efficient of drag also. Take μ for water is Ns/m 2. [15] 6.a) For a steady laminar flow through a circular pipe prove that the velocity distribution across the section is parabolic and the average velocity is half of the maximum local velocity. b) An oil of 8 poise and specific gravity 0.9 is flowing through a horizontal pipe of 50 mm diameter. If the pressure drop in 100 m length of the pipe is 2000 kn/m 2, determine: i) Rate of flow of oil ii) Centreline velocity iii) Total frictional drag over 100 m length of pipe iv) Power required to maintain the flow v) Velocity gradient at the pipe wall vi) Velocity and shear stress at 10 mm from the wall. [15] 7.a) Derive formulae for calculating loss of head due to i) Hydraulic gradient line (HGL) ii) Energy Gradient Line (EGL) b) A main pipe divides into two parallel pipes which again forms one pipe. The length and diameter for the first parallel pipe are 2000m and 1.0 m respectively, while the length and diameter of the second pipe are 2000 m and 0.8 meters respectively. If the total flow in the main is 3m3/sec and the coefficient of friction for each parallel pipe is same and equal to 0.005, find the rate of flow in each parallel pipe. [15] 8.a) How does the velocity of approach affect the expression for discharge over a weir? b) A rectangular weir 6 metres long discharges water at a head of 0.30 metre. If the available depth of the waterfall is 40 metres, find the H.P. Take C d = 0.6. c) Why is it necessary to ventilate a nappe? What is the arrangement for ventilating the nappe of a suppressed weir? [15] ********
5 Code No:A R09 SET3 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal marks a) Determine the mass density, specific volume and specific weight of a liquid whose specific gravity is b) A flat plate weighing 0.45 kn has a surface area of 0.1 m 2. It slides down an inclined plane at 30 0 to the horizontal, at a constant speed of 3 m/s. If the inclined plane is lubricated with an oil of viscosity 0.1 N.s/m 2, find the thickness of the oil film. [15] 2.a) Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface submerged in the liquid b) A rectangular door covering an opening 3m 1.75 high in a vertical wall is hinged about its vertical edge by two points placed symmetrically 0.4 m from either end. The door is locked by clamp placed at the centre of other vertical edge. Determine the reactions at the two hinges and the clamp, when the height of water is 1 m above the top edge of the opening. [15] 3.a) Obtain an equation of continuity for a threedimensional flow. b) A stream function follows the law ψ = a log x. State if the flow is continuous or not. y Also state if the flow is rotational or irrotational. c) In a twodimensional flow, show that the discharge per unit time across a line joining two points is equal to the difference between the stream function between the two points. [15] 4.a) Describe an orifice meter and find an expression for measuring discharge of fluid through a pipe with this device. b) A horizontal venturimeter 300 mm 150mm is used to measure the flow of oil through venturimeter is 0.5 m 3 /s. Find the reading of oil mercury differential manometer. Take venturimeter constant as [15]
6 5.a) How are the thickness of boundary layer, shear stress and the drag force along the flat plate determined by Von Karman momentum equation? b) A kite m weighing N assumes an angle of 12 0 to the horizontal. The string attached to the kite makes an angle of 45 0 to the horizontal. The pull on the string is N when the wind is flowing at a speed of 30km/h. Find the corresponding coefficient of drag and lift, Take ρ for air = 1.25 kg/m 3. [15] 6.a) Derive an expression for the velocity distribution for turbulent flow in smooth pipes. b) A pipeline carrying water has surface protrusions of average height of 0.15 mm. If the shear stress developed is 4.9 N/m 2 determine whether the pipe surface acts as smooth, rough or transition. The kinematic viscosity of water may be taken as 0.01 stokes. [15] 7.a) In a water supply scheme it was originally planned to provide 40 cm diameter pipe line. But it was later found that pipes of diameter more than 35 cm were not available. If it is now proposed to provide two parallel mains of the same diameter find the diameter of each parallel main pipe. b) Two reservoirs are connected by three pipes laid in parallel, their respective diameters being d, 2d and 3d. These are all of the same length l. If f is the same for all the pipes, find the discharge through the large pipes, if the discharge through the smallest is 0.05 cumec. [15] 8.a) The discharge over a rectangular weir is cumec when the head of water is 0.20 metre. What would be the discharge if the head of water is increased to 0.3 metre? b) Show that an error of 1% in the measurement of head produces an error of 2.5% in the discharge over a triangular notch. [15] ********
7 Code No:A R09 SET4 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal marks a) Explain briefly the following mechanical gauges: i) Bourdon tube pressure gauge. ii) Diaphragm gauge. b) A cylinder of 100 mm diameter and 300 mm length rotates about a vertical axis inside a fixed cylindrical tube of 105 mm diameter and 300 mm length. If the space between the tube and the cylinder is filled with liquid of dynamic viscosity of N.s/m 2, determine the speed of rotation of the cylinder which will be obtained, if an external torque of 1 Nm is applied to it. [15] 2.a) A gate which is 2 m wide and 1.2 m high lies in vertical plane and is hinged at the bottom. There is a liquid on upstream side of the gate which extends 1.5 m above the top of the gate has a specific gravity of On the downstream side of the gate there is water upto the top of the gate. Find: i) The resultant force acting on the gate ii) The position of the centre of pressure iii) The least force acting horizontally on the top of the gate which is capable of opening it. b) A rectangular plane surface 1 m wide and 3 m deep lies in water in such a way that its plane makes an angle of 30 0 with the free water surface. Determine the total pressure and position of centre of pressure when the upper edge is 2 m below the free surface. [15] 3.a) Write short notes on i) Pure translation ii) Linear deformation iii) Rotation iv) Angular deformation of a fluid mass. b) In a two dimensional flow, show the line integral from one point to another point is equal to the difference between the velocity potential functions between the two points. c) Calculate the velocity components if the velocity potential function follows the lawφ = log x. [15] y
8 4.a) Derive Euler s equation of motion along with assumptions. b) A venturimeter with inlet and throat diameters 300 mm and 150 mm respectively is attached in a vertical pipe in which flow occurs from bottom to top. The distance between the point of entrance and to the point of throat of the venturimeter is 750 mm. If the difference of mercury levels in the two limbs of differential gauge is 220 mm, find the discharge passing through the vertical pipe. Take coefficient of discharge, C d = [15] 5.a) Define the following terms for an airfoil. i) Chord line ii) Angle of attack iii) Camber iv) Profile centre line. b) A kite weighing 7.85 N has an effective area of 0.8 m 2. It is maintained in air at an angle of 10 0 to the horizontal. The string attached to the kite makes an angle of 45 0 to the horizontal and at this position the values of coefficient of drag and lift are 0.6 and 0.8 respectively. Determine: i) The speed of wind ii) The tension in the string. Take ρ for air = 1.25 kg/m 3 [15] 6.a) Derive expressions for velocity distribution in terms of average velocity for i) Smooth pipe ii) Rough pipe. b) The velocity of flow in a badly corroded 8 cm pipe is found to increase 30 percent as a pitot tube is moved from a point 1 cm from the wall to 3 cm from the wall. Estimate the height of the roughness elements. [15] 7.a) Two reservoirs are connected by a 30 cm diameter pipe, 4000 metres long. The difference in levels of water surfaces of the two reservoirs is 25 metres. Find the discharge to the lower reservoir. If a 30 cm diameter additional pipe is attached to the last 2000 metres length of the existing pipe, find the new discharge to the lower reservoir. Neglect secondary losses. Take f = b) Two reservoirs have a difference of level of 12 metres and are connected by a pipe line 60 cm diameter 2500 metres long feeding a junction from which two pipes of 30 cm diameter and 2500 metres long lead in parallel to the lower reservoirs. Taking f = Calculate the total discharge. [15] 8.a) What are the various ways in which weirs are classified? b) Show that an error of 1% in the measurement of head produces an error of 1.5 % in the discharge over a rectangular weir. c) Find the discharge over a broad crested weir 25 metre long for a head of 0.60 metre. Take C d =0.85 and allow for two end contractions. Neglect velocity of approach. [15] ********
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