R05220302-mechanics-of-fluids

Set No. 1

Code No: R05220302

II B.Tech Supplimentary Examinations, Aug/Sep 2008 MECHANICS OF FLUIDS ( Common to Mechanical Engineering, Metallurgy & Material Technology and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) A lubricating oil of viscosity µ undergoes steady shear between a fixed lower plate and an upper plate moving at speed V. The clearance between the plates is t. Show that a linear velocity profile results if the fluid does not slip at either plate. (b) Describe with a neat sketch a micro-manometer used for very precise measurement of small pressure difference between two points. [8+8] 2. A two-dimensional flow field is given by φ = 3xy, determine: (a) The stream function (b) The velocity at L(2,6) and M (6,6) and the pressure difference between the points L and M. (c) The discharge between the streamlines passing through the points L and M. [16] 3. An open circuit wind tunnel draws air from the atmosphere through a well contoured nozzle. In the test section, where the flow is straight and nearly uniform, a static pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that the wall pressure within the tunnel is 45 mm of water below atmospheric. Assume that air is incompressible and at 250 C, pressure is 100 Kpa(absolute). Calculate the velocity in the wind tunnel section. Density of water is 999kg/m3 and characteristic gas constant for air is 287 J/Kg K. [16] 4. An Orifice meter is to be fitted in to a horizontal pipe 30cms diameter carrying oil of specific gravity 0.85 for the purpose of flow measurement that differential head is to be indicated by U tube manometer containing mercury. (Specific gravity = 13.6). If the Manometer meter is not to exceed 0.3 mts. When the flow is 17 Kg/Sec. What would be the diameter of the Orifice? Assume Cd = 0.62 [16] 5. (a) Explain with a neat sketch the boundary layer characteristics when a fluid is flowing over a flat plate. (b) A thin flat plate 0.3 m wide and 0.6 m long is suspended and exposed parallel to air flowing with a velocity of 3 m/sec. Calculate drag force on both sides of the plate when the 0.3 m edge is oriented parallel to free stream. Consider flow to be laminar and assume for air kinematic viscosity is 0.18 stokes and density is 1.2 kg/m3 . [10+6] 1 of 2

Set No. 1

Code No: R05220302

6. (a) Derive Darcy-Weisbach equation for loss of head in a pipe. (b) Two tanks are connected by a 300 mm diameter 1000 m long pipe. Find the rate of flow if the difference of water level in the tank is 10 m. Take 4f = 0.04 and ignore minor losses. [10+6] 7. (a) Derive an expression for the velocity distribution for viscous flow through a circular pipe. (b) An Oil of viscosity 0.1 Pascal - sec and specific gravity 0.9 is flowing through a circular pipe of diameter 50 mm and of length 300 m. The rate of flow of fluid through the pipe is 3.5 lit / sec. Find the pressure drop in a length of 300 m and also the shear stress at the pipe wall. [8+8] 8. (a) Write the importance of Mach number briefly. (b) Explain briefly the phenomenon of propagations of elastic waves. ⋆⋆⋆⋆⋆

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[8+8]

Set No. 2

Code No: R05220302

II B.Tech Supplimentary Examinations, Aug/Sep 2008 MECHANICS OF FLUIDS ( Common to Mechanical Engineering, Metallurgy & Material Technology and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) Expalin how the meta-centric height of a floating body can be detaermined experimentally? (b) How are manometers are classified?

[8+8]

2. (a) In a fluid, the velocity field is given by V=(3x+2y)i+(2z+3 x2 )j+(2t-3z)k Determine: i. The velocity components u,v,w at any point in the flow field ii. The speed at point (1,1,1); iii. The speed at time t = 2s at point (0,0,2). Also classify the velocity field as steady, or unsteady, uniform or nonuniform and one, two or three dimensional. (b) Define convectional and local accelerations.

[10+6]

3. (a) In an inclined pipe of uniform diameter 20cm, a pressure of 40Kpa was observed at section I which was a elevation 18 m. At another section II at elevation 20m the pressure was 15Kpa and the velocity was 2m/s. Determine the direction of flow and the head loss between these sections. The fluid in the pipe is water. (b) Explain the concept of vertex flow. Name the different types of vertex flow. [9+7] 4. (a) Discuss the relative merits and demerits of venturimeter with respect to orifice meter (b) A rectangular channel 6mts wide carries 2800 lit/sec at the depth of 0.9mts. What height of a broad crested rectangular weir must be installed to double the depth? Assume a weir co coefficient as 0.86. [7+9] 5. (a) Explain with a neat sketch the boundary layer characteristics when a fluid is flowing over a flat plate. (b) A thin flat plate 0.3 m wide and 0.6 m long is suspended and exposed parallel to air flowing with a velocity of 3 m/sec. Calculate drag force on both sides of the plate when the 0.3 m edge is oriented parallel to free stream. Consider flow to be laminar and assume for air kinematic viscosity is 0.18 stokes and density is 1.2 kg/m3 . [10+6] 1 of 2

Set No. 2

Code No: R05220302

6. A pipeline ABC 180 m long is laid on an upward slope of 1 in 60. The length of portion AB is 90 m and its diameter is 0.15 m. At B the pipe section suddenly enlarges to 0.30 m diameter and remains so for the remainder of its length BC, 90 m. A flow of 50 litres per second is pumped into the pipe at its lower end A and is discharged at the upper end C into a closed tank. The pressure at the supply end A is 137.34 kN/m2 . Sketch [16] (a) the total energy line (b) the hydraulic gradient line and also find the pressure at discharge end C. Take lV 2 f = 0.02 in hf = f2gD 7. (a) Define the terms Kinetic energy correction factor and momentum correction factor. (b) The Radial clearance between a hydraulic plunger and the cylinder wall is 0.1 mm, the length of the plunger is 300 mm and diameter 100 mm. Find the velocity of leakage and rate of leakage past the plunger at an instant when the difference of the pressure between the two ends of the plunger is 9m of water. Take mu = 0.0127 Poise. [6+10] 8. (a) Derive an expression for velocity of sound for an adiabatic process. (b) Calculate Mach number at a point on a jet propeller aircraft, which is flying at 900 Km/hr at sea level where air temperature is 150 C. Take K=1.4 and R=287 J/Kg-K. [8+8] ⋆⋆⋆⋆⋆

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Set No. 3

Code No: R05220302

II B.Tech Supplimentary Examinations, Aug/Sep 2008 MECHANICS OF FLUIDS ( Common to Mechanical Engineering, Metallurgy & Material Technology and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) What do you mean by the term ‘Viscosity’ ? (b) What is the force of buoyancy? Is it a body force or surface force? (c) Show the center of pressure is always below the center of gravity.

[6+4+6]

2. A conical pipe diverges uniformly from 1200mm to 200mm diameter over a length of 1 meter. Determine the local and convective acceleration at the mid-section assuming (a) A study Rate of flow is 0.12 m3 /s (b) Rate of flow varies uniformly from 0.12 m3 /s to 0.24 m3 /s in 5 sec., at t = 2sec. [16] 3. (a) Prove that in case of forced vertex the rise of liquid level at the ends is equal to the fall of liquid level at the axis of rotation. (b) An open circular cylinder of 15 cm diameter and 100cm long contain water up to a height of 80cm. Find the maximum speed at which the cylinder is to be rotated about its vertical axis so that no water spills. [7+9] 4. (a) Explain and differentiate between Pitot tube and Pitot Static Tube. (b) Water flows through a rectangular channel 1m wide and 0.5m deep and then over a sharp crested cipolletti weir of crust length 0.6m. If the water level in the channel is 0.225m above the weir crest. Calculate the discharge over the weir. Take Cd = 0.6 and make correction for the velocity of approach. [7+9] 5. (a) Explain with a neat sketch the boundary layer characteristics when a fluid is flowing over a flat plate. (b) A thin flat plate 0.3 m wide and 0.6 m long is suspended and exposed parallel to air flowing with a velocity of 3 m/sec. Calculate drag force on both sides of the plate when the 0.3 m edge is oriented parallel to free stream. Consider flow to be laminar and assume for air kinematic viscosity is 0.18 stokes and density is 1.2 kg/m3 . [10+6] 6. (a) Derive Darcy-Weisbach equation for loss of head in a pipe. (b) Two tanks are connected by a 300 mm diameter 1000 m long pipe. Find the rate of flow if the difference of water level in the tank is 10 m. Take 4f = 0.04 and ignore minor losses. [10+6] 1 of 2

Set No. 3

Code No: R05220302

7. (a) What do you meant by viscous flow? Mention various forces to be considered in Navier Stroke’s equation. (b) Through a horizontal circular pipe of diameter 100 mm and of length 10m, an oil of dynamic 0.097 poise and relative density 0.9 is flowing. Calculate the difference of pressure at the two ends of the pipe, if 100 Kg. of the oil is collected in a tank in 30 seconds. [10+6] 8. (a) Obtain the expression for the sound wave in a compressible fluid in terms of change of pressure and change of density. (b) Air at 300 C at a pressure of 294.3 KN/m2 absolute flows into another reservoir through an office 50 ×10−4 m2 in area. If the pressure in the reservoir is 147.15 N/m2 absolute, what is the discharge? Given R = 287.14 J/KgK, K = 1.4 and coefficient of discharge Cd = 0.65. [8+8] ⋆⋆⋆⋆⋆

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Set No. 4

Code No: R05220302

II B.Tech Supplimentary Examinations, Aug/Sep 2008 MECHANICS OF FLUIDS ( Common to Mechanical Engineering, Metallurgy & Material Technology and Automobile Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ⋆⋆⋆⋆⋆ 1. (a) A plate 0.05 mm distant from a fixed plate moves at 1.2 m/s and requires a force of 2.2 N/ m2 to maintain this speed. Find the viscosity of the fluid between the plates. (b) Expalin how vacuum pressure can be measure with the help of a U-tube manometer. [8+8] 2. (a) Velocity for a two dimensional flow field is given by V = (3+2xy+4 t2 )i+(x y 2 +3t)j Find the velocity and acceleration at a point(1,2) after 2 sec (b) Define tangential and local accelerations

[10+6]

3. (a) Derive kinetic energy correction factor? (b) A pipe through which water is flowing is having diameter 40cm and 20cm at the cross sections 1 and 2 respectively. The velocity of water at section 1is given 5m/s. Find the velocity head at the section 1 and 2 and also rate of discharge [7+9] 4. Explain Venturimeter principle with neat sketch and also derive and expression for finding out actual discharge from a given venturimeter. [16] 5. (a) What are different types of drag? What is streamlining? What is its effect on the Different types of drag? (b) A cylinder 15 cm in diameter and 10 m long, is made to turn 1500 revolutions per minute with its axis perpendicular in a stream of air having uniform velocity of 25 m/sec. Assuming ideal fluid flow, find [8+8] i. Circulation ii. Lift force experienced by the cylinder and iii. The position of stagnation points Take density of air as 1.2 kg/m3 . 6. (a) How the loss of energy at the entrance to the pipe and exit from the pipe is to be determined? (b) A horizontal pipeline 50 m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 30 m of its length from the tank, the pipe is 100 mm diameter and its diameter suddenly enlarged to 200 mm. The height of the water level in the tank is 10 m above the centre of the pipe. Determine the rate of flow. Take 4f = 0.04 for both sections of the pipe and consider minor losses. [6+10] 1 of 2

Set No. 4

Code No: R05220302

7. (a) Sketch the Reynolds apparatus and explain how the laminar flow can be demonstrated with the help of this apparatus? (b) Oil of absolute viscosity 1.5 poise and relative density 0.85 flows through a 30cm diameter pipe .If the head losses in a 3000M length of a pipe is 20M.estimate the friction factor by assuming the flow to be laminar. [8+8] 8. Find the mass flow rate of air through venturimeter having inlet diameter as 400 mm and through diameter 200mm. The pressure at the inlet of the venturimeter is 27.468 N/ cm2 (abs) and temperature of a air at inlet is 200 C. The pressure at the throat is given as 25.506 N/ cm2 (abs ).Take R=287 J/Kg-K and K=1.4. [16] ⋆⋆⋆⋆⋆

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