A109210105 FLUID MECHANICS papers_2.pdf8.a) How does the velocity of approach affect the expression...

R09Code No:A109210105 SET-1

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 ---

1.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 0.0735 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

water surface. Prove that the depth of pressure is equal to 2

.12dp

p⎛ ⎞

+⎜ ⎟⎝ ⎠ [15]

3.a) Explain Lagrangian and Eulerian methods of describing fluid flow.

b) If the velocity potential function is given by 3 4 .x yψ = − 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 m3 / 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 0

1u u dyU U

δ

θ ⎛ ⎞= −⎜ ⎟⎝ ⎠∫ and

2

2u y yU δ δ

⎛ ⎞ ⎛ ⎞= −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

. [15]

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6.a) Derive Hagen-Poiseuilles 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 196.2 N/m2, 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=0.006. [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]

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1.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/m3 and weight of mansonry is 22kN/m3. 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) A stream function follows the law 2 2x yψ = − . 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 350 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 m3/s if the pipe diameter is 300. Take venturimeter constant is 0.975. [15]

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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 as log xy

φ = . Find the thickness of

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 coefficient of drag also. Take μ for water is 0.001 Ns/m2. [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/m2, determine:

i) Rate of flow of oil ii) Centre-line 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 Cd = 0.6.

c) Why is it necessary to ventilate a nappe? What is the arrangement for ventilating the nappe of a suppressed weir? [15]

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1.a) Determine the mass density, specific volume and specific weight of a liquid whose

specific gravity is 0.85. b) A flat plate weighing 0.45 kN has a surface area of 0.1 m2. It slides down an inclined

plane at 300 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/m2, 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 three-dimensional flow.

b) A stream function follows the law log xay

ψ = . State if the flow is continuous or not.

Also state if the flow is rotational or irrotational. c) In a two-dimensional 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 m3/s. Find the reading of oil–mercury differential manometer. Take venturimeter constant as 0.98. [15]

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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 0.8+0.8 m weighing 3.924 N assumes an angle of 120 to the horizontal. The string attached to the kite makes an angle of 450 to the horizontal. The pull on the string is 24.525 N when the wind is flowing at a speed of 30km/h. Find the corresponding co-efficient of drag and lift, Take ρ for air = 1.25 kg/m3. [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/m2 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 0.400 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]

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1.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 0.125 N.s/m2, 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 1.45. 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 300 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

law log xy

φ = . [15]

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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 co-efficient of discharge, C d = 0.98.

[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 m2. It is maintained in air at an angle of 100 to the horizontal. The string attached to the kite makes an angle of 450 to the horizontal and at this position the values of co-efficient 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/m3 [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 = 0.0075.

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 = 0.01. 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 Cd=0.85 and allow for two end contractions. Neglect velocity of approach. [15]

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R09 Set No. 2Code No: A109210105

1

II B.Tech I Semester Examinations,MAY 2011FLUID MECHANICS

Civil EngineeringTime: 3 hours Max Marks: 75

Answer any FIVE QuestionsAll Questions carry equal marks

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1. (a) Find the loss of head when a pipe of diameter 200 mm is suddenly enlargedto a diameter of 400 mm. The rate of flow of water through the pipe is250 litres/s.

(b) Water is flowing through a horizontal pipe of diameter 200 mm at a velocityof 3 m/s. A circular solid plate of diameter 150 mm is placed in the pipe toobstruct the flow. Find the loss of head due to obstruction in the pipe ifCc = 0.62. [7+8]

2. Find the displacement thickness, momentum thickness and energy thickness forthe Velocity distribution in the boundary layer given by u/U = y/δ where u is thevelocity at a distance y from the plate and u=U at y=δ, where δ= boundary layerthickness. [15]

3. (a) Calculate the velocity at the point (5,5) for the following stream functions:

i. ψ = -x ln xy + x

ii. ψ = 1/2( 3y2-4x2)+xy+6

(b) Write short notes on:

i. Path line, streak line and stream tube

ii. Stream function, velocity potential function and flow nets. [7+8]

4. Two parallel plates kept 75 mm apart have laminar flow of glycerine between themwith a maximum velocity of 1 m/s. Calculate the discharge per metre width, theshear stress at the plates, the difference in pressure between two points 25 m apart,the velocity gradients at the plates and velocity at 15 mm from the plate.Take µ of glycerine as 8.35 poise. [15]

5. (a) A fireman holds a water hose ending into a nozzle that issues a 25mm diameterjet of water. If the pressure of water in the 60mm diameter hose is 750kPa,find the force experienced by the fireman.

(b) Derive Euler‘s equation of motion along a stream line. [10+5]

6. (a) The pressure inside a droplet of water is 0.04N/cm2 greater than the atmo-spheric pressure. Calculate the diameter of the droplet. Take surface tension(water with air) = 81N/m.

(b) A velocity profile of a flowing fluid over a flat plate is parabolic and givenby u = ay2+by+c where a, b and c are constants. The velocity of fluid is1.4m/s at 15cm from the plate. The plate is the vertex point of the velocity

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distribution. Find out the velocity gradients and shear stresses at y = 0, 8and 18 cm respectively. [4+11]

7. (a) A suppressed rectangular weir is constructed across a channel of 0.77 m widthwith a head of 0.39 m and the crest 0.6 m above the bed of the channel.Estimate the discharge over it. Consider velocity of approach and assume Cd

= 0.623.

(b) A sharp crested rectangular weir of 1 m height extends across a rectangularchannel of 3 m width. If the head of water over the weir is 0.45 m, calculatethe discharge, Consider velocity of approach and assume Cd = 0.623. [7+8]

8. A rectangular lamina 3m×1m is held in water at a depth of 1.5m below the freewater surface:

(a) If the 3m height is vertical, determine the total pressure force on the laminaand depth of centre of pressure.

(b) If 1m side lies in the vertical plane at the same depth, then find out the changein total pressure force acting and depth of centre of pressure.

(c) Another circular lamina having same area of rectangle is also kept at 1.5mbelow the free water surface. Find the total pressure force acting on thecircular lamina and centre of pressure. [15]

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1. A discharge of 2000 m3/s is to pass over a rectangular weir. The weir is dividedinto a number of openings each of span 10 m. If the velocity of approach is 4 m/s,find the number of openings needed in order that the head of water over the crestis not to exceed 2 m. [15]

2. Find the total pressure and depth of centre of pressure on a triangular plate of base3m and height 3m which is immersed inwater such that plane of the plate makes anangle of 600 with the free surface. The base of the plate is parallel to water surfaceand at a depth of 2m from water surface. [15]

3. A horizontal pipe line 40 m long is connected to a water tank at one end anddischarges freely into the atmosphere at the other end. For the first 25 m of itslength from the tank, the pipe is 150 mm diameter and its diameter is suddenlyenlarged to 300 mm. The height of water level in the tank is 8 m above the centreof the pipe. Considering all losses of head, determine the rate of flow. Take f = 0.1for both sections of the pipe. [15]

4. (a) Explain the terms:

i. path line

ii. streak line

iii. stream line and

iv. stream tube.

(b) A fluid flow field is given by V = x2y3 i+y2zj-(2xyz+yz2)k. Prove that it is acase of possible steady incompressible fluid flow. Calculate the velocity at thepoint (2,3,7). [7+8]

5. Obtain an expression for the boundary shear stress in terms of momentum thickness.[15]

6. (a) State the assumptions involved in Bernoulli’s energy theorem. Write any fourlimitations of the theorem.

(b) The diameter of a pipe changes from 220mm at a section 6m above datum to95mm at a section 2.5m above datum. The pressure of water at first sectionis 400 kPa. If the velocity of flow at the first section is 2m/s, determine theintensity of pressure at the second section. [7+8]

7. Lubricating oil of specific gravity 0.82 and dynamic viscosity 12.066 × 102 N.s/m2 ispumped at a rate of 0.02 m3/s through a 0.15 m diameter 300m long pipe. Calculate

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the pressure drop, average shear stress at the wall of the pipe and the power requiredto maintain flow, if the pipe is inclined at 15 degree with the horizontal and theflow is in downward direction. [15]

8. A hydraulic lift consists of a 25cm diameter ram which slides in a 25.015cm diametercylinder, the annular space being filled with oil having a kinetic viscosity of 0.025cm2/sec and specific gravity of 0.85. If the rate of travel of the ram is 9.15m/min,find the fractional resistance when 0.3m of the ram is engaged. [15]

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1. State Bernoulli’s theorem for steady flow of an incompressible fluid. Derive anexpression for Bernoulli‘s equation from first principles and state the assumptionsmade for such a derivation. [15]

2. Show that ψ=x2-y2 represents on two dimentional irrotational flow. Find the po-tential function [15]

3. Find the thickness of the boundary layer at the trailing edge of smooth plate oflength 4m and of width 1.5m, when the plate is moving with a velocity of 4m/s instationary air. Take kinematic viscosity of air as 1.5×10−5 m2/s. [15]

4. (a) A piston 886mm diameter and 250mm long works in a cylinder of 900mmdiameter. If the annular space is filled with a lubricating oil of viscosity6 poise, calculate the speed of descent of piston in vertical position. Theweight of piston and axial load are 11.8N.

(b) Explain the phenomenon of vapour pressure. [10+5]

5. The friction factor for turbulent flow through rough pipes can be determined byKarman- Prandtl equation, 1/

√f = 2 log10 (R0/k) + 1.74 where f= friction factor,

R0 = pipe radius, k = average roughness.Two reservoirs with a surface level difference of 20 metres are to be connected by1 metre diameter pipe 6 km long. What will be the discharge when a cast ironpipe of roughness k = 0.3 mm is used ? what will be the percentage increase inthe discharge if the cast iron pipe is replaced by a steel pipe of roughness k = 0.1mm? Neglect all local losses. [15]

6. (a) Derive an expression for the depth of centre of pressure from free surface ofliquid of an inclined plane surface submerged in the liquid.

(b) Find the total pressure and position of centre of pressure on a triangular plateof base 2.4m and height 3.6m which is immersed in water in such a way thatthe plan of the plate makes an angle of 600 with the free surface of the water.The base of the plate is parallel to water surface and is at a depth of 3.0mfrom water surface. [7+8]

7. Lubricating oil of specific gravity 0.82 and dynamic viscosity 12.066 × 102 N.s/m2 ispumped at a rate of 0.02 m3/s through a 0.15 m diameter 300m long pipe. Calculatethe pressure drop, average shear stress at the wall of the pipe and the power requiredto maintain flow, if the pipe is inclined at 15 degree with the horizontal and theflow is in upward direction. [15]

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8. (a) Find the throat diameter of a venturimeter, when fitted to a horizontal main10 cm diameter having a discharges of 20 liters per second. Pressure gaugesinserted at the entrance and throat indicate pressures 158 kPa and 82 kParespectively. Take Cd = 0.95.

(b) If instead of pressure gauges, the entrance and throat of the meter are con-nected to the two limbs of a U-tube mercury manometer, determine its readingin cm of differential mercury column.

(c) In case the venturimeter is located in a vertical pipe, with water flowing up-wards, find the difference in the readings of the mercury manometer. Throatsection is 20 cm above the entrance section of the venturimeter. Further, di-mensions of pipe and venturimeter remain unaltered, as well as the dischargethrough the pipe. [6+5+4]

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1. (a) Compare the advantages of using venturimetrs and orifice meters in fluid flowmeasurements.

(b) A venturimeter of throat diameter 6 cm has a discharge coefficient of 0.97, andwith a flow of 0.025 m3/s, the pressure differential is 10 N/m2. Make calcula-tions for the flow rate, when an orifice of 6 cm is installed in the same pipe.The discharge coefficient for the orifice is 0.62 and the pressure differential isthe same. [7+8]

2. Derive the equation to find velocity at a particular point from the centre of aninclined pipe through which a laminar flow is there. [15]

3. An U-tube differntial manometerwas used to connnect two pressure pipes P andQ as shown in figure 3. The pipe ‘P’ contains a liquid having specific gravity of1.8 under a pressure of 95 KN/m2. The pipe ‘Q’ contains another liquid havingspecific gravity 0.9 under a pressure of 180 kN/m2. Find the difference of pressureif mercury is used as a U-tube liquid. [15]

Figure 3

4. (a) A pipe line AB of diameter 300 mm and of length 400 m carries water at therate of 50 litres/s. The flow takes place from A to B where point B is 30metres above A. Find the pressure at A if the pressure at B is 19.62 N/cm2

Take f = 0.008.

(b) Water is flowing through a horizontal pipe of diameter 250 mm at a velocityof 4 m/s. A circular solid plate of diameter 170 mm is placed in the pipe toobstruct the flow. Find the loss of head due to obstruction in the pipe if Cc

= 0.63. [7+8]

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5. (a) The stream function in a two dimensional flow is ψ = 3x-2y+5xy. Verifywhether the flow is irrotational. Determine the direction of stream line at apoint (1,-2). Determine also the expression for the velocity potential.

(b) What do you mean by flow net? Cite any two examples where the flow net isutilized as a tool in analyzing flow problems. Also show that the stream linesand equipotential lines form a net of mutually perpendicular lines. [7+8]

6. A trapezoidal plate of parallel sides ‘l’ and ‘2l’ and height ‘h’ is immersed verticallyin water with its side of length ‘l’ horizontal and topmost. The top edge is at adepth ‘h’ below the water surface. Determine:

(a) Total force on one side of the plate

(b) Location of the centre of pressure. [15]

7. A smooth flat plate of length 5 m and width 2 m is moving with a velocity of 4 m/sin stationary air of density as 1.25 kg/m3 and kinematic viscosity 1.5 × 10−5 m2/s.Determine thickness of the boundary layer at the trailing edge of the smooth plate.Find the total drag on one side of the plate assuming that the boundary layer isturbulent from the very beginning. [15]

8. In a 450 bend a rectangular air duct of 1m2 cross sectional area is gradually reducedto 0.5 m2 area. Find the magnitude and direction of force required to hold theduct in position, if the velocity of flow at 1 m2 section is 10m/sec and pressure is30 kN/m2. Assume specific weight of air as 0.0118 kN/m3. [15]

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SET-1Code.No: A109211901 R09

II B.TECH – I SEM EXAMINATIONS, NOVEMBER - 2010FLUID MECHANICS AND HYDRAULIC MACHINERY(ELECTRICAL AND ELECTRONICS ENGINEERING)

Time: 3hours Max.Marks:75Answer any FIVE questions

All questions carry equal marks- - -

1.a) Distinguish between U-tube differential manometers and inverted U-tubedifferential manometers. Discuss their applications.

b) Two large fixed parallel plates are 12mm apart. The space between the surfaces isfilled with oil of viscosity 0.972 N.s/m2. A flat plate 0.25 m2 area moves throughthe oil at a velocity of 0.3 m/s. Calculate the forcei) When the thin plate is equidistant from both the plates.ii) When the thin plate is at a distant of 4mm from one of the plane surfaces.

[7+8]

2.a) How is the continuity equation based on the principle of conservation of massstated? Derive the continuity equation in Cartesian coordinates for one-dimensional flow.

b) Derive the expression for Bernulli’s theorem for steady incompressible fluid fromfirst principle. What are the limitations of the Bernoulli’s equation? [7+8]

3.a) Explain what do you understand by Hydraulic Grade Line and Total Energy Line.Discuss its practical significance in analysis of fluid flow problems.

b) Two pipes each 300 m long are available for connecting to a reservoir from whicha flow of 0.085 m3/s is required. If the diameters of the two pipes are 300mm and150mm respectively. Determine the ratio of head lost when the pipes areconnected in series to the head lost when they are connected in parallel. Neglectminor losses. [7+8]

4. A jet of water having a velocity of 35m/s impinges on a series of vanes movingwith a velocity of 20 m/s. The jet makes an angle of 300 to the direction of motionof vanes when entering and leaves at an angle of 1200. Draw the velocity trianglesat inlet and outlet and findi) The angles of vanes tip so that water enters and leaves without shock.ii) The work done for N of water entering the vanes andiii) The efficiency. [15]

5.a) What are the different types of hydropower plants? Describe each one briefly?b) What is a mass curve? Explain the procedure for preparing a mass curve and also

its uses. [7+8]

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6. Design a Francis turbine for the given data; Gross head available is 100m; Lossesin the penstocks is 14% of gross head; Speed of the turbine is 750 rpm; Outputpower developed is 450kw; hydraulic efficiency is 96% and overall efficiency is85%. Assume 5% of the circumferential area of the runner is occupied by thethickness of vanes. The velocity of flow remains constant throughout. Assumeany missing data suitably. [15]

7.a) What do you meant by Unit quantities and specific quantities? Explain the‘Specific Speed’ of a turbine and deduce the expression for the same.

b) What are the characteristic curves of a hydraulic turbine? How are they useful toPractical Engineer? [8+7]

8.a) What is the role of volute and vortex chamber in a centrifugal pump.b) What are the operating characteristic curves of a centrifugal pump? Explain them.c) When are centrifugal pumps coupled in parallel? Sketch and explain. [5+5+5]

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SET-2Code.No: A109211901 R09




1.a) Classify the fluids, giving examples, according to the nature of variation ofviscosity.

b) Differentiate between Absolute pressure, gauge pressure and atmosphericpressure. Explain the relationship between them with neat sketch.

c) The dynamic viscosity of oil, used for lubrication between a shaft and sleeve is0.6 N-s/m2. The shaft is of diameter 400 mm and rotates at 190 r p m. Calculatethe power lost in the bearing for a sleeve length of 90 mm. The thickness of theoil film is 1.5 mm. [5+5+5]

2.a) Explain the termsi) Path line ii) Streak lineiii) Stream line and iv) Stream tube.

b) Distinguish betweeni) Steady and unsteady flow ii) Uniform and Non-uniform flowiii) Rotational and Irrotational flow.

c) What are the various forces that may influence the motion of fluid? [5+6+4]

3.a) What is “turbulence”? Derive an expression for loss of head due to friction in apipe flow.

b) A venturimeter of 300 mm inlet diameter and 150 mm throat diameter is providedin a vertical pipeline carrying oil of specific gravity 0.9, flow being upward. Thedifference in elevation of a throat section and entrance section of the venturimeteris 300 mm. The differential mercury manometer shows a gauge deflection of 250mm. Calculatei) The discharge of oilii) The pressure difference between the entrance section and throat section.

The coefficient of the meter is 0.98. [8+7]

4.a) Derive an expression for work done per second in the case of a radial curvedvane.

b) A jet of water of diameter 50 mm moving with a velocity of 20 m/s strikes a fixedplate in such a way that the angle between the jet and the plate is 60o. Find theforce exerted by the jet on the platei) in the direction normal to the plateii) in the direction of the plate. [8+7]

5.a) What are the different types of hydropower plants? Describe each one briefly?b) Explain various components of hydro power plants. [8+7]

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6.a) What is a draft tube? What are the functions of a draft tube?b) Calculate the diameter and speed of the runner of a Kaplan turbine developing

6000 kW under an effective head of 50 m. Overall efficiency of the turbine is90%. The diameter of the boss is 0.4 times the external diameter of the runner.The speed ratio is 2 and flow ratio is 0.6. What is the specific speed of theturbine? [5+10]

7.a) Define unit speed, unit power and specific speed as used in connection with theoperation of a hydraulic machine.

b) A hydraulic turbine is to develop 845.6 kW power when running at 100 r p munder a head of 10 m. Work out the maximum flow rate and specific speed for theturbine if the overall efficiency at the best operating point is 92%. In order topredict its performance, a 1:10 scale model is tested under a head of 6 m. whatwould be the speed, power, output and water consumption of the model if it runsunder the similar conditions to the prototype? [5+10]

8.a) What do you mean by ‘priming’? Derive an expression for the specific speed of acentrifugal pump.

b) Find the number of pumps required to lift water from a deep well under a totalhead of 89 m. All the pumps are identical and are running at 800 r p m. Thespecific speed of each pump is given as 25 while the rated capacity of each pumpis 0.16 m3/s. [8+7]

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SET-3Code.No: A109211901 R09




1.a) Define compressible and incompressible fluid. What is specific gravity? How it isrelated to density?

b) Express the Pascal law and give a real-world example of it. A vacuum gaugeconnected to a chamber reads 24 kPa at a location where the atmospheric pressureis 92 kPa. Determine the absolute pressure in the chamber.

c) The hydraulic lift in a car repair shop has an output diameter of 300 mm and is tolift cars up to 20kN. Determine the fluid gauge pressure that must be maintainedin the reservoir. [5+5+5]

2.a) Define streamline, path line and streak line. And what does these lines indicate?How the streak lines differ from stream lines?

b) A pipeline, 600 mm diameter, carrying oil (specific gravity 0-85) at the flow rateof 1.8 m3/s has a 900 bend in horizontal plane. The pressure at the entrance to thebend is15 N/m2 and the loss of head in the bend is 2 m of oil. Find the magnitudeand direction of the force exerted by the oil on the pipe bend and show thedirection of the force on the bend. [8+7]

3.a) What are the different types of head losses in a pipeline. Derive Darcy-WeisbachFormula for calculating loss of head due to friction in a pipe.

b) Two sharp ended pipes of diameter 50 mm and 100 mm respectively each oflength 100 m respectively, are connected in parallel between two reservoirs whichhave a difference of level of 10 m. if the friction factor for each pipe is 0.128,Calculatei) Rate of flow for each pipe and,ii) The diameter of a single pipe 100m long which would give the same

discharge, if it were substituted for the original two pipes. [8+7]

4.a) Series of curved vanes mounted equidistantly fixed on the periphery of a wheel.For maximum efficiency of the wheel, show that the peripheral speed is one-halfof the velocity of the jet.

b) A jet of water having a velocity of 36 m/s strikes a series of radial vanes Mountedon a wheel which is rotating at 240 r p m. The jet makes an angle of 200 with thetangent to the wheel at inlet and leaves the wheel with a velocity of 6 m/s at anangle of 1300 to the tangent to the wheel at outlet. Water is flowing from outwardin a radial direction. Determinei) Vane angle at inlet and outletii) Work done per second per N of water, andiii) Efficiency of Wheel. [7+8]

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5.a) What are the different types of hydropower plants? Describe each one briefly?b) A run-off-river hydel power plant with an installed capacity of 15000 kW

operates at 20% load factor when it serves as a peak load station. What should bethe minimum discharge in the stream so that it may serve as the base load station?The plant efficiency may be taken as 80% when working under a head of 15 m.Also calculate the maximum load factor of the plant when the discharge in thestream is 30 m3/s. [8+7]

6.a) How do the losses in the draft tube effect the pressure at the runner exit. What isthe efficiency of the draft tube?

b) A turbine is to operate under a head of 30 m and a speed of 300 r p m. Thedischarge is 10 m3/s. If the efficiency of the turbine is 90% determinei) The specific speed of the turbineii) Power generated andiii) Type of turbine. [7+8]

7.a) What are the requirements of a governor in hydropower Installation?b) Tests were conducted on a Francis turbine of 0.8 m diameter under a head of 10

m. The turbine developed 115 kW running at 240 r p m and consuming 1.2 m3/s.If the same turbine is operated under a head of 16 m predict its new speed,discharge and power. [7+8]

8.a) Discuss in general the important operating characteristic curves of an axial flowpump. Compare the performance characteristics of a centrifugal pup and axialflow pump.

b) Define and derive an expression for the specific speed of pump. How doesspecific speed help in pump selection? [8+7]

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SET-4Code.No: A109211901 R09




1.a) Differentiate betweeni) Real fluid and ideal fluidii) Newtonian fluid and non- Newtonian fluidiii) Dynamic viscosity and kinematic viscosity and its units

b) Define and classify the manometers. What are the advantages and limitations ofmanometers? [8+7]

2.a) Differentiate between rotational and irrotational flow. Derive the continuityequation for steady incompressible one-dimensional flow in Cartesiancoordinates.

b) A discharge of 0.03 m3/s of oil (specific gravity is 0.81) occurs downwardthrough a converging pipe line held inclined at 600 to the horizontal. The inletdiameter is 200mm and the out let diameter is 150 mm and length of the pipe is 2m. If the pressure at the top of the inlet is 0.8 kgf/cm2, find the pressure at the outlet. Neglect the energy loss. [8+7]

3.a) What is Darcy’s friction factor in pipe flow? On what factors does the coefficientof friction depends?

b) What are the minor losses in pipes? Give the appropriate formulae to calculate thelosses?

c) A Pitot tube is used to measure the velocity of an airplane. A U-tube manometerconnected to the Pitot tube registers a head of 90 mm of mercury. Find the speedof the plane. Assume C = 0.98 and γ air = 12.2 N/m3. [4+4+7]

4.a) A series of flat plates mounted on a wheel intercepts a jet of diameter 60 mm andvelocity 25 m/s normal to the plates successively. If the plates move at a velocityof 10 m/s what is the power developed.

b) A plate of length 600 mm and weighing 100N is hung from the hinge at the top. Itis hit by a jet of water diameter 12 mm having a velocity of 20 m/s, the jet axisbeing 350 mm, below the hinge. Find the angle that the plate will make with thevertical when the jet (at the same level) plays on the plate? [7+8]

5.a) What are the different types of hydropower plants? Explain about pumped storageplants and run-off-river plants.

b) How do you assess the water potential of hydroelectric scheme?c) Write a short note on selection of suitable type of turbine for a hydroelectric

scheme. [8+4+3]

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6.a) What is a draft tube? Why it is used in a reaction turbine? Explain with neatSketch two different types of draft tubes.

b) Discuss the working proportions of a Pelton wheel turbine. [8+7]

7.a) What is significance of Unit and Specific quantities related to turbines?b) A Kaplan turbine is used to develop 2400 kW when running at 240 r p m under a

head of 50 m. In order to predict its performance a model of scale 1:5 is testedunder a net head of 25 m. At what speed should the model run and what powerwould it develop. Determine the discharge in the in the model and in full scale ifthe overall efficiency of the model is 85%. [7+8]

8.a) What do you understand byi) NPSH ii) Priming of pumpiii) Minimum starting speed of pump iv) Multistage pumps

b) A centrifugal pump has an impeller of 350 mm diameter. The discharge at theoutlet is radial. The diameter ratio is 2. Calculate the manometric efficiency of thepump if the total lift is 25 m. Also calculate the blade angle and relative velocityat the inlet. [8+7]

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A109210105 FLUID MECHANICS papers_2.pdf8.a) How does the velocity of approach affect the expression...

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