Mechanics Of Fluids Rr220301

Set No. 1

Code No: RR220301

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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 trapezoidal plate having its parallel sides equal to 2a and a at a distance h apart is immersed vertically in a liquid with 2a side uppermost and at a distance h below the surface of the liquid. Find the thrust on the surface and the depth of the centre of pressure. (b) A caisson for closing the entrance of a dry dock is of trapezoidal form 16m wide at the top and 12m wide at the bottom and 8m deep, Find the total pressure on the caisson if the water on the outside is 1 m below the top level of the caisson and dock is empty [8+8] 2. (a) What are the methods available for describing the fluid flow? and explain each method. (b) A circular pipe 10 cm in diameter has 2 m length which is porous, In this porous section the velocity of exit is known to be constant. If the velocities at the inlet and outlet of the porous section are 2.0 m/sec and 1.2 m/sec respectively, estimate (i) the discharge emitted out through the walls of the porous pipe and (ii) the average velocity of this emitted discharge. [8+8] 3. (a) State the momentum equation. How will you apply momentum equation for determining the force exerted by a flowing liquid on a pipe bend? (b) A nozzle at the end of a 80 mm hose produces a jet 40 mm in diameter. Determine the force on the joint at the base of the nozzle when it is discharging 1200 liters of water per minute. [8+8] 4. (a) What forces influences the motion of (i) a ship (ii) a sub marine (iii)an aeroplane flying at suspension speed. (b) Define and derive the expression for displacement thickness. (c) For laminar boundary layer on a flat plate held parallel to a stream of uniform velocity, determine the location of the section where drag up to that section is twice the drag on remaining region. [4+8+4] 5. (a) What is the relation between pressure and density of a compressible fluid for (i) Isothermal process (ii) adiabatic process. (b) A 100 mm diameter pipe reduces to 50 mm diameter through a sudden contraction. When it carries air at 20.160 under isothermal condition, the absolute pressure observed in the two pipes just before and after the contraction are 400KN/m2 and320KN/m2 respectively. Determine the densities and velocities at the two section. Take R = 290J/Kg 0 K [8+8] 1 of 2

Set No. 1

Code No: RR220301

6. (a) Sketch the Reynolds apparatus and explain how the laminar flow can be demonstrated with the help of this apparatus. (b) A viscous liquid was flowing in laminar regime in a 6 cm diameter circular pipe. A pitot tube at a radial distance of 2 cm from the axis indicated a velocity of 0.6 m/sec. Calculate the maximum velocity, the mean velocity and the discharge in the pipe. [8+8] 7. (a) Obtain an expression for the optimum exit diameter of a nozzle to be fitted at the service end of a pipe for maximum power transmission. (b) Find the loss of head when a pipe of diameter 20 cm is suddenly enlarged to a diameter of 40cm. The rate of flow of water through the pipe is 250lit/sec. [8+8] 8. (a) A venturimeter is used for measuring the flow of petrol (G = 0.81) in a pipeline inclined at 350 to the horizontal. The throat area ratio is 4. If the difference in mercury levels in the gage is 50 mm, calculate the flow if the pipe dia is 30 m. Take Cd = 0.975. Take specific gravity of mercury as 13.6. (b) Explain the working of Bourdon pressure gage with a sketch. ⋆⋆⋆⋆⋆

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[8+8]

Set No. 2

Code No: RR220301

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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) Give an example each where air can be treated as an incompressible fluid and water has to be treated as compressible fluid. Explain. (b) The bulk modulus of water is 210 KN/cm2 . What pressure is required to reduce its volume by 2%? Also prove that the increase in the mass density will be 2% only. [8+8] 2. (a) Define and distinguish between steady flow and uniform flow. Give two examples of each flow. (b) Derive continuity equation for 1-D flow.

[8+8]

3. (a) Define the terms (i) Forced vertex flow (ii) Free vortex flow. Give suitable examples. (b) A rectangular duct of width 25 cm has a two dimensional irrotational flow. It has an elbow made up of circular arcs of radius 40 cm and 65 cm for the inner and outer walls respectively. Calculate the discharge per unit width of the duct when the difference in pressure between outer and inner walls in the elbow is 30 kPa. [8+8] 4. (a) Describe with the help of neat sketch, the variation of drag coefficient for a cylinder over a wide range of Reynolds number. (b) Oil with a free stream velocity of 3 m/s flows over a thin plate 1.25-m wide and 2 m long. Determine the boundary layer thickness and the shear stress at mid − length and calculate the total, double-sided resistance of the plate. Take Density = 860 kg/m3 andv = 10−3 . [8+8] 5. (a) What is the function of wind tunnel? (b) What is meant by stagnation point. Explain

[8+8]

6. (a) Sketch the velocity distribution of laminar flow in ideal and real fluid flow and explain it in detail. (b) A fluid of viscosity 0.883 pascal-sec and specific gravity 1.26 is pumped along a horizontal pipe of 65 m long and 10 cm diameter at a flow rate of 0.18m3 /sec. Determine the Reynolds Number and calculate the pressure loss in the pipe if the flow is laminar. [8+8] 7. (a) Obtain an expression for the optimum exit diameter of a nozzle to be fitted at the service end of a pipe for maximum power transmission. 1 of 2

Set No. 2

Code No: RR220301

(b) Find the loss of head when a pipe of diameter 20 cm is suddenly enlarged to a diameter of 40cm. The rate of flow of water through the pipe is 250lit/sec. [8+8] 8. (a) A venturimeter is used for measuring the flow of petrol (G = 0.81) in a pipeline inclined at 350 to the horizontal. The throat area ratio is 4. If the difference in mercury levels in the gage is 50 mm, calculate the flow if the pipe dia is 30 m. Take Cd = 0.975. Take specific gravity of mercury as 13.6. (b) Explain the working of Bourdon pressure gage with a sketch. ⋆⋆⋆⋆⋆

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[8+8]

Set No. 3

Code No: RR220301

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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) Define kinematic viscosity. How is this name attributed to this property? (b) Lateral stability of a long shaft 15cm diameter is obtained by means of a 25cm stationary bearing having an internal diameter of 15.025cm. If the space between bearing and shaft is filled with a lubricant having a viscosity 24 Pa-s, what power will be required to overcome the viscous resistance when the shaft is rotated at a constant rate of 180 r.p.m. [6+10] 2. (a) Define and distinguish between stream lines, streak lines and path line. When do these three lines coincide? (b) For the following velocity vectors, determine the magnitude of the velocity at A(x=2, y=-3,Z =1, t = 2) i. V = (10t + xy) i + ( - yz ?10t ) j + ( - yz + z2 /2) k ii. V = 4x i + ( - 4y + 3t) j

[8+8]

3. (a) State the momentum equation. How will you apply momentum equation for determining the force exerted by a flowing liquid on a pipe bend? (b) A nozzle at the end of a 80 mm hose produces a jet 40 mm in diameter. Determine the force on the joint at the base of the nozzle when it is discharging 1200 liters of water per minute. [8+8] 4. (a) Describe with the help of neat sketch, the variation of drag coefficient for a cylinder over a wide range of Reynolds number. (b) Oil with a free stream velocity of 3 m/s flows over a thin plate 1.25-m wide and 2 m long. Determine the boundary layer thickness and the shear stress at mid − length and calculate the total, double-sided resistance of the plate. Take Density = 860 kg/m3 andv = 10−3 . [8+8] 5. (a) What is the function of wind tunnel? (b) What is meant by stagnation point. Explain

[8+8]

6. (a) Derive an expression for mean velocity of flow for laminar flow through inclined pipes. (b) Derive the necessary condition for mean velocity for the laminar flow between parallel flat plates when both the plates are at rest. [8+8] 7. (a) How will you determine the loss of head due to friction in pipes using Darcy weisbach formula. 1 of 2

Set No. 3

Code No: RR220301

(b) An oil pipe line 60cm in diameter and roughness height 0.00005m carries a flow of 0.55 cumecs across the country. The pumping stations are located at every 80km. If the pump efficiency is 85%, determine the power input required at each station when the kinematic viscosity and specific gravity of the oil are 2 × 10−6 m2 /sec and 0.88 respectively. [8+8] 8. (a) A venturimeter has its axis vertical, the inlet and throat diameters being 150 mm and 75 mm respectively. The throat is 225 mm above inlet and k = 0.96, petrol of specific gravity 0.78 flows up through the meter at a rate of 0.029 m3 /s. Find the pressure difference between the inlet and the throat. (b) Explain the working procedure of Bourdon pressure gauge. ⋆⋆⋆⋆⋆

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[8+8]

Set No. 4

Code No: RR220301

II B.Tech II Semester Supplimentary Examinations, Apr/May 2007 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) Write a note on viscosity and compressibility. (b) Calculate the velocity gradient at distances of 0,10,15 cm from the boundary if the velocity profile is a parabola given by u =Ay 2 + By + C and with the vertex 15cm from the boundary, where the velocity is 100 cm/sec. Also calculate the shear stress at these points if the fluid has a viscosity of 8.2 poise. [8+8] 2. (a) Derive three dimensional continuity equation. (b) The x and y components in a three dimensional flow are given by U = x2 + z 2 ϑ = y2 + z2 Find the simplest z − component of velocity that satisfies the continuity equation. [8+8] 3. (a) Define the terms (i) Forced vertex flow (ii) Free vortex flow. Give suitable examples. (b) A rectangular duct of width 25 cm has a two dimensional irrotational flow. It has an elbow made up of circular arcs of radius 40 cm and 65 cm for the inner and outer walls respectively. Calculate the discharge per unit width of the duct when the difference in pressure between outer and inner walls in the elbow is 30 kPa. [8+8] 4. (a) Draw and explain the approximate flow pattern and the pressure distribution around a flat plate placed normal to a stream. (b) A flat plate of 2.0 m width and 4.0 m length is kept parallel to air flowing at a velocity of 5 m/s. Determine the length of plate over which the boundary layer is laminar, shear at the location which boundary layer ceases to be laminar and total force on both sides on that portion of plate where the boundary layer is laminar. Take p = 1.2 kg/m3 and v = 1.47x10−5 m2 /s. [8+8] 5. (a) Differentiate between compressible and incompressible flows. (b) A large vessel fitted with a nozzle ,contains air at pressure of 2500 KN/m2 and a temperature of 200 C .If the pressure at the outlet of the nozzle is 1750 KN/m2 find the velocity of air flowing at the outlet of the nozzle? [8+8] 6. (a) Explain the velocity and shear stress distribution for laminar flow in a circular pipe with a neat sketch. 1 of 2

Set No. 4

Code No: RR220301

(b) A fluid of mass density 1790kg/m3 and viscosity of 2.1 pascal-sec flow at a velocity of 3 m/sec in a 6 cm diameter pipe. Estimate the head loss in a length of 12 m of pipe. [8+8] 7. (a) Define and explain the terms hydraulic gradient line and total energy line. (b) A pipe 20cm diameter and 1800 m long connects two reservoirs one being 30m below the other. The pipe line crosses a ridge whose summit is 7.5m above the upper reservoir. What will be the minimum depth of the pipe below the summit of the ridge in order that the pressure at the apex doesn’t fall below 7.5m vacuum. The length of the pipe from the upper reservoir to the apex is 300m. Taking f= 0.032 determine the rate of flow to the lower reservoir in lit/min. [8+8] 8. (a) Explain venturimeter in detail with diagram. Also derive an expression for finding out the actual discharge from a given venturimeter. (b) What is the purpose of Hot wire Anemometers. Explain the working procedure.. [8+8] ⋆⋆⋆⋆⋆

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