Rr220301-mechanics-of-fluids

Set No. 1

Code No: RR220301

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) 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) 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) What is the physical significance of displacement thickness of boundary layer theory? (b) What boundary conditions must be satisfied by the velocity distribution in laminar boundary layer over a flat plate. (c) The velocity distribution in the boundary layer was found to fit the equation (u/U ) = (y/d)1/7 . Find the displacement thickness. [4+4+8] 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]

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Set No. 1

Code No: RR220301

6. (a) Explain Reynolds number and its significance in detail? What is the significance of upper and lower critical Reynolds numbers. (b) A viscous fluid of viscosity 2.2 poise and specific gravity 1.4 flows through a 40 cm diameter pipe. If the loss of head is 3 m in 100 m length, determine the shear stress at the wall pipe and velocity of flow assuming the flow to be laminar. [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) Derive an expression for discharge of liquids through a rectangular notch. Explain how it is modified to take into account the effect of end contractions and velocity of approach. (b) Explain the working of Viscometers ⋆⋆⋆⋆⋆

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[8+8].

Set No. 2

Code No: RR220301

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) The weight of 8 m3 of a certain oil is 64 KN. Calculate its specific weight, mass density and specific gravity (b) The weight of an object measured on ground level where g = 9.81 m/sec2 is 35,000 N. Calculate its weight at the following locations (i) Moon gm = 1.62 m/sec2 ,(ii) Sun , gs =274.68 m/sec2 (iii) Mercury, gme = 3.53 m/ sec2 (iv) Jupiter, gj = 26.0 m/sec2 (v) Saturn, gsa = 11.2 m/sec2 and (vi) Venus, gv = 8.54 m/sec2 . Also find the mass density of the object on these planets [8+8] 2. (a) State the basic principle of continuity equation. Obtain an expression of continuity equation for a three dimensional - steady - incompressible fluid flow. √ (b) A flow is described by the stream function ψ= 2 3XY . Locate the point at which the velocity vector has a magnitude of 4 units and makes an angle of 150o with the x- axis. [8+8] 3. (a) Derive an expression for the difference of pressure between two points in a free vortex flow. (b) An open circular cylinder of 15 cm diameter and 100 cm long contains water up to a height of 70 cm. Find the speed at which the cylinder is to be rotated about its axis so that the axial depth becomes zero. [8+8] 4. (a) Why is it necessary to control the growth of boundary layer on most of the bodies? What methods are used for such a control? (b) A sphere has a projected area of 1m2 . Compare the drag force in water and in air when travelling at a speed of 30 km/hr. [8+8] 5. (a) What is the relation between pressure and density of a compressible fluid for (i) Isothermal (ii) adiabatic process (b) Air ,thermodynamic state of which given by pressure P = 230 kN/m2 and temperature = 300 K is moving at a velocity V= 250 m/s .Calculate the stagnation pressure if (i) compressibility is neglected (ii) compressibility account for.

[8+8]

6. (a) Obtain an expression for the head loss in laminar flow in a circular pipe. Also write down the equation for head loss due to laminar flow between parallel plates and for flow down an inclined plane. Give the Reynolds numbers up to which these equations are valid. 1 of 2

Set No. 2

Code No: RR220301

(b) An oil of specific gravity 0.9 flow at a rate of 0.2m3 /sec through a horizontal pipe of 7.5 cm diameter. The pressure drop is 400KN/m2 over 300m length of pipe. Find the viscosity of the oil. [8+8] 7. (a) ) What is siphon? On what principle it works? Under what conditions would it stop functioning? (b) A horizontal pipe of diameter 50cm is suddenly contracted to a diameter of 25cm. The pressure intensities in the large and smaller pipe are given as 13.734N/cm2 and 11.772N/cm2 respectively. If the rate of flow of water is 300lit/sec, find the value of coefficient of contraction [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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Set No. 3

Code No: RR220301

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) 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) State and explain the four types of displacements of a fluid particle that undergoes as it moves in a flow field. (b) For the following flows, determine the components of rotation about the various axes: i. u = xy 3 z, v = −y 2 z 2 , w = yz 2 − ii. u = 3xy, v = 32 x2 − 23 y 2 iii. u = y 2 , v = −3x

y2 z2 2

[8+8]

3. (a) Derive Euler’s equation of motion for a fluid flow.. (b) A jet of water issues from 20 mm dia fire hose at the end of which a 5.0 mm diameter nozzle is fixed. If pressure at inlet of the nozzle is 200 kN/m2 , determine force exerted by nozzle on the flow. [8+8] 4. (a) Give four examples in every day life where separation takes place. Draw flow pattern in each case. (b) A jet plane, which weighs 30 kN and has a wing area of 20 m2 flies at a velocity of 1000 km/hr when the engine delivers 7350 kN. 65% Of the power is used to overcome the drag resistance of the wing, Calculate coefficient of lift and drag for the wing. The mass density of air is 1.2 kg/m3 . [8+8] 5. (a) What is meant by co-efficient of compressibility? (b) A diffuser of area ratio 2 :1 operates at the inlet condition P1 = 500KN/m2 , T1 = 500 K , M1 = 0.6, γ = 1.4 .Estimate the following at the exit (i) velocity (ii) pressure (iii) Temperature (iv) Mach number [6+10] 6. (a) Sketch the Reynolds apparatus and explain how the laminar flow can be demonstrated with the help of this apparatus.

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Set No. 3

Code No: RR220301

(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) 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 a concentric - cylinder viscometer in detail with Diagram. Also derive the expression to find the value of viscosity of a given fluid. (b) What is meant by hot wire Anemometer. ⋆⋆⋆⋆⋆

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[8+8]

Set No. 4

Code No: RR220301

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 is meant by Newtonian and non-Newtonian fluids. Explain with the help of examples. (b) A circular gate in a vertical wall has a diameter of 4m. The water surface on the upstream side is 8m above the top of the gate and on the downstream side 1m above the top of the gate. Find the forces acting on the two sides of the gate and the resultant force acting on the gate and its location. [8+8] 2. (a) Define equipotential line and a line of constant stream function, Show that these lines intersect orthogonally. (b) Given that u = x2 -y 2 and v = - 2xy. Check whether stream function exists. If so determine the stream function and potential function for the flow. [8+8] 3. (a) Derive Bernoulli’s equation for flow along a stream line. (b) A pipe 200 m long slopes down at 1 in 100 and tapers from 800 mm diameter at the higher end to 400 mm diameter at the lower end and carries 100 lps of oil (S = 0.85). If the pressure gauge reading at the higher end reads 50 kN / m2 , determine, (i) Velocities at the two ends and (ii) pressure at the lower end. Neglect losses [8+8]. 4. (a) What is meant by smooth boundary and a rough boundary? (b) Describe briefly the phenomenon of boundary layer separation. (c) At what wind speed must a 127 mm diameter sphere travel through water to have a drag of 5 N. [4+6+6] 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] 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] 1 of 2

Set No. 4

Code No: RR220301

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) The rate of flow of water in a 150mm diameter pipe is measured with a venturimeter with a 50mm dia. throat. When a mercury manometer is connected across the converging section reads 8mm, the flow rate is 2.7 kg/s. What is the coefficient of discharge at that flow rate and what is permanent loss of head? Specific gravity of mercury = 13.6 (b) What is the device used for measuring fluid pressure? Explain briefly the principle of an inclined Manometer. [8+8] ⋆⋆⋆⋆⋆

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