FM 10CV35 Question Papers

Fluid Mechanics

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Third Semester B.E. Degree Examination, June/July 2011 Fluid Mechanics Note: Answer FIVE full questions, selecting at/east TWO questions each front Part - A and Part - B. PART-A 1 a. Define the following fluid properties with mathematical representation along with units. i) Dynamic viscosity ii) Relative density iii) Surface tension iv) Mass density. (08) b What is capillarity? Obtain an expression for capillary rise. (06) c The velocity distribution for flow over a flat plate is given by u ■ 0.75y - y in which u is the velocity in meter per second at a distance y meters above the plate. Determine the shear stress at y = 0.I5m. Take dynamic viscosity of fluid as 8.5 poise (0.85Pa-s). (06) 2 a. Define Absolute pressure. Vacuum pressure and Gauge pressure with a sketch showing the relationship between them. (06) b. Explain Bourdan tube pressure gauge, with a neat sketch. (06) c. The left leg of a U - tube mercury manometer is connected to a pipe line conveying water, the level of mercury in the leg being 0.6m below the center of pipe line and the right leg is open to atmosphere. The level of mercury in the right leg is 0.45m above that in the left leg and the space above mercury in the right leg contains Benzene having a specific gravity of 0.88 to a height of 0.3m. Find the pressure in the pipe. (08) 3 a. Derive the formula for Hydrostatic force and depth of centre of pressure for an inclined plane surface submerged in a liquid. (08) b. A vertical gate closes a horizontal tunnel 5m high and 3m wide running full with water. The pressure at the bottom of the gate is 196.20kN/m. Determine the total pressure on the gate and position of the centre of the pressure. (06) c. Draw the pressure diagram for horizontal, inclined and vertical plane surface and explain briefly. (06) 4 a. List the types of fluid flow. Explain any two of them. (06) b. Obtain an expression for continuity equation in three dimensional form. (08) c. The velocity potential function is given by $ = 5(S: - y2). Calculate the velocity components at the point (4,5). (06) PART -B 5 a. Apply Bernoulli's equation for Venturimeter and derive the discharge equation. (08) b. Which arc the forces causing die motion of a fluid? Explain any two of them. (06) c. A submarine moves horizontally in sea and has its axis 15m below the surface of water. A Pitot tube properly placed just in front of the sub - marine and along its axis is connected to die two limbs of a U - tube containing mercury. The difference of Hg level is found to be 170mm. Find die speed of the sub- marine knowing dial the sp.gr of Hg is 13.6 and that of sea water is 1.026 with respect of fresh water. (06) 6 a. What do you understand by major energy losses and minor energy losses in pipes? Derive an expression for the loss of head due to sudden expansion of (low in a pipe. (08) b. A pipe line of 0.6m diameter is 1.5 km long. To increase the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. Neglecting

minor losses, find the increase in discharge if 4f - 0.04. The head at inlet is 300mm. (12) 7 a.. Obtain an expression for discharge through large rectangular orifice. (05) b. What is a mouth piece? How arc they classified? (04) c. The head of water over an orifice of diameter 100mm is 10m. The water coming out from orifice is collected in a circular lank of diameter 1,5m. The rise of water level in this tank is 1.0m in 25seconds. Also the co-ordinates of a point on the jet measured from vena contracta arc 4.3m horizontal and 0.5m vertical. Find the three hydraulic co-efficients Cd, Cv and Cc. (08) 8 a. What arc the advantages of triangular notch over rectangular notch? (04 ) b. Derive an equation for discharge over rectangular notch. (06) c. A broad crested weir 50m length has 500mm height of water above its crest. Find the maximum discharge. Take Cd = 0.60. neglect velocity of approach. If the velocity of approach is to be taken into consideration, find the maximum discharge when the channel has a cross sectional area of 50m: on the upstream side. (07) d. Write a note on ventilation of weirs. (03)

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Third Semester B.E. Degree Examination, December 2010 06CV35 Fluid Mechanics Note: Answer any FIVE full questions, choosing at least TWO form each part PART-A 1 a. Define the following : i) Specific mass ii) Relative density iii) Surface tension iv) Dynamic viscosity. ( 08 Marks) b. Specific gravity of an oil is 0.85. Find the specific mass and weight density.(04 Marks) c. A shaft of 20 mm dia and mass 15 kg slides vertically in a sleeve with a velocity of 5 m/s. The gap between the shaft and the sleeve is 0.1 mm and is filled with oil. Calculate the viscosity of oil, if the length of the shaft is 500 mm. (08 Marks) 2 a. Distinguish between i) Pressure and pressure head ii) Gauge pressure and absolute pressure iii) Simple manometer and differential manometer. (06 Marks) b. Make a note on Bourdon's tube pressure gauge. (06 Marks) c. A differential manometer connected between two point A and B of a horizontal pipeline carrying an oil of relative density 0.8, shows a difference of mercury level as 0.225 m. Determine the difference in pressure between two points A and B in terms of head of water and N/m2. (08 Marks) 3 a. Derive an expression for the total pressure on one side of an inclined plane and show that the centre of pressure lies below its centriod. (10 Marks) b. A square aperture in a vertical side of a tank has one diagonal vertical and is completely covered by a plane plate hinged along the upper side of the aperture. The diagonals of aperture are 2 m long and the tank contains a liquid of relative density 1.5. The centre of aperture is 1.5 m below the free surface. Calculate the thrust exerted on plate by the liquid and position of it. (10 Marks) 4 a. Distinguish between

Fluid Mechanics

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i) Steady flow and unsteady flow ii) Uniform flow and non uniform flow iii) Laminar flow and turbulent flow, (06 Marks) Define stream function and velocity potential function. Establish the relation between them. (08 Marks) A stream function is given by ψ = 2xy. Show that the flow is irrotational and continuous. (06 Marks) PART-B Make a note on energies of a flowing fluid. (06 Marks) Derive the equation for discharge through a Venturimeter. (08 Marks) An oil of relative density 0.8 is flowing through a pipe of length 400 m. The pipe is laid at a slope of 1 in 100. The rate of flow of oil in the pipe is 300 lps. The diameter at the higher end of pipe is 1.2m and that at lower end is 0.60 m. If the pressure at the higher end is 0.08 N/mm , find the pressure at the lower end.(06 Marks) Define hydraulic gradient and energy gradient. (06 Marks) Distinguish between compound pipe and equivalent pipe. (06 Marks) Determine the difference in elevation between the water surfaces of two tanks which are connected by a horizontal pipe of diameter 300 mm and length 400 m. The rate of flow of water through the pipe is 300 Lps. Consider all losses and assume friction factor = 0.032. (08 Marks) What is the difference between an orifice and mouthpiece? (04 Marks) Derive the discharge equation for an external cylindrical mouthpiece. (08 Marks) A closed cylindrical tank is 3.5 m high and contains an oil of relative density 0.85 to a height of 3 m above the bottom. The space above the oil surface contains air under a pressure of 50 kN/m2. If an orifice of diameter 8 cm is provided on the side of the tank with its centre 25 cm above the bottom, estimate the weight of fluid discharged in one minute. Take Cd = 0.60. (08 Marks) Make a note on Cipolletti Notch (04 Marks) Derive an equation for discharge over triangular weir. (06 Marks) A flow from a channel is controlled by a trapezoidal notch so that the full supply discharge of 2 m /s flows over the notch at a head of 1.2 m measured over the crest. At half this head, a discharge of 0.6 m3/s passes over the notch. Assuming Cd = 0.62, calculate the base width and side slope of notch. (10 Marks)

Third Semester B.E. Degree Examination, May/June 2010 Fluid Mechanics Note: Answer any FIVE full questions, selecting at least TWO questions from each part. PART-A 1 a. Define the following fluid properties. Give their dimensions. i) Mass density ii) Specific gravity iii) Dynamic viscosity iv) Vapour pressure v) Capillarity. (10) b. The dynamic viscosity of oil used for lubrication between a shaft and a sleeve is 5 poise (0.5 Ns/m2). The diameter of the shaft is 40 cm and it rotates at 200 rpm. Calculate the power lost in the bearing for a sleeve length of 100 mm. The thickness of oil film is 2 mm. (10) Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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2 a. State and prove hydrostatic pressure law in its differential form. (06) b. Explain the working principle of Bourdon pressure gauge, with a neat sketch. 08 c. An U-tube differential manometer is attached to two points A and B in a horizontal pipeline carrying water, 5 m apart. The pressure at A is 7 N/cm2 and pressure head at B is 150 mm of mercury. Find the mercury level difference in the manometer. (06) 3 a. Define: i) Total pressure ii) Center of pressure. (04) b. Obtain the expressions for horizontal and vertical components of the resultant hydrostatic force on a submerged curved surface. (06) c. An equilateral triangular plate of 6 m side is immersed in water with its base at 5 m below the free surface. The apex of the plate is at 9 m below the free surface. Determine the total pressure on the plate and the location of the center of pressure below the free surface. (10) 4 a. Write the differences between Lagrangian and Eulerian concepts. (04) b. For a given velocity field V = ( y 2 + z 2 )i + (x 2 + z 2 ) j + (x 2 + y 2 )k , find at (1,1,1) : i) the components of acceleration, ii) the components of rotation. (08) c. The velocity components of the two-dimensional plane motion of a fluid are : y2 − x2 2 xy u= and v = 2 2 2 2 2 x +y x + y2 Show that the f1uid is incompressible and flow is irrotational. (08) PART-B 5 a. Explain the working principle of a venturimeter, with a neat sketch. Derive the expression for the measurement of discharge through a horizontal venturimeter. (10) b. A 300 mm diameter pipe carries water under a head of 20 m, with a velocity of 3.5 m/s. If the axis of the pipe turns through 45°, find the magnitude and direction of the resultant force at the bend. (10) 6 a. Derive the Darcy- Weisbach equation for head loss due to friction in a pipe. b. Define Reynold number and obtain the expression for it. What is its use in pipe flow? (05) c. Two pipes A and B are connected between two tanks in parallel. Pipe A is 150 m long and 150 mm in diameter and pipe B is 100 m long and 120 mm in diameter. Both 2 pipes have same value of 'f' used in h = f LV and is equal to 0.018. The total f 2 gD discharge carried by both pipes is 50 Ips. Calculate discharge in each pipe. (08) 7 a. Define orifice and mouthpiece. Give the detailed classification of orifices and mouthpieces with neat sketches. Mention whether orifice or mouthpiece is advantageous and why. (10) b. Derive the expression C = x with usual notations. (06)

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c. A rectangular orifice 1.5 m wide and 1.2 m deep is discharging water from a tank. If the water level in the tank is 3 m above the top edge of the orifice, find the discharge through the orifice. Take C, = 0.6. (04) 8 a. Explain: i) Ventilation of weir, ii) Clinging nappe, iii) Cippoletti notch iv) Submerged weir, with neat sketches. (12) Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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b. A venturimeter is used to calibrate the V -notch in the laboratory. The water discharged from the venturimeter flows over the 90° V-notch with] 85.4 mm head. The inlet and throat diameters of the venturimeter are respectively 250 mm and 125 mm. The pressure head difference between inlet and throat is 20 cm of water. C, for venturimeter is 0.97. Find C, for V-notch. (08) Third Semester B.E. Degree Examination, Dec.09-Jan.l0 Fluid Mechanics Note: Answer any FIVE full questions, selecting at least TWO questions from each part. PART-A 1 a. Define the following fluid properties: Relative density, surface tension and vapour pressure. Give their dimensions.(09) b. State and prove Newton's law of viscosity. (06) c. Determine the minimum size of a glass tube for the capillary rise in it not to exceed 0.2mm of water. The surface tension of water in contact with air is 0.0725 N/m and contact angle 60°. (05) 2 a.List out the characteristics of manometric liquids. Give examples for manometric liquid. (06) b. Sketch and explain the use of V-tube differential manometer. Also write the pressure equation representing the pressure difference between two points in a horizontal pipe. (06) c. Determine the pressure difference between two pipes A and B shown in Fig.2( c), carrying water. The specific gravity of manometric liquid is 0.9 (08) 3 a. Sketch the pressure diagrams for plane surfaces immersed in water: i) horizontally, ii) vertically and iii) inclined. Also write the expression for total pressure and location of centre of pressure for each of them (09) b. A cylindrical gate of 2.5m diameter retains two liquids on either side of it as shown in Fig.3(b). Estimate the resultant pressure force acting on unit length of the gate. (11) 4 a. Distinguish between: i) Laminar flow and turbulent flow ii) Rotational flow and irrotational flow 04 b. Show that stream lines and equipotential lines meet orthogonally. (06) c. The velocity vector in a fluid flow is, v = 4x3i - 10x2yj + 2tk. Find the velocity and acceleration of a fluid particle at (2, 1, 3) and at time t = 1 (10) PART-B

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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5 a. Derive Euler's equation of motion. (06) b. A venturimeter 150mmx75mm is installed in a horizontal pipe line of 150mm diameter carrying oil (S = 0.9). The mercury level difference in the If-tube manometer connected to inlet and throat is 175mm. If Cd = 0.97, find the rate of flow through the pipe. (06) c. Water flows up a tapered pipe as shown in Fig.5(c). Find the mercury deflection 'h' in the manometer corresponding to the discharge of 120 Ips. Neglect all losses. (08) 6 a. Define Reynolds number. Give the expression, defining each term. (04) b. Derive Darcy- Weisbach equation for head loss due to friction in a pipe. 08 c. Two pipes A and B are connected in parallel as shown in Fig.6( c). Pipe A is 150m long and 15cm in diameter. Pipe B is 100m long and 12cm in diameter. Both the 2 pipes have friction factor f = 0.018 used in h = fLV . A partially closed valve in f

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pipe A causes the discharge in two pipes to be same. Estimate the value of the valve coefficient 'k'. Neglect other minor losses. (08) 7 a. Derive a relationship to determine the coefficient of velocity for flow through an orifice. (06) b. Show that the coefficient of velocity for an external cylindrical mouthpiece is 0.855. (08) c. The head of water over an orifice of 100mm diameter is lam. The discharge through the orifice is 70 Ips. If the coordinates of a point on the jet, measured from venacontracta are 4.3m horizontal and 0.5m vertical, determine Cd, Cv, and Cc. (06) 8 a. What are the advantages of Y -notch over a rectangular notch? (05) b. What is ventilation? Why it is necessary? How it is provided? (06) c. A discharge of 100 Lps is to be measured by a triangular notch of crest angle 60°. What would be the head over the crest? If the accuracy of reading the head is 1 mm, what error in discharge can be expected? Take Cd = 0.6. (09) Third Semester B.E. Degree Examination, June-July 2009 Fluid Mechanics Answer any FIVE full questions selecting at least Two form each part. PART - A 1 a. Define the following terms (04) i) Specific weight; ii) Mass density; iii) Specific Volume; iv) Specific gravity. State the Newton's law of viscosity. Sketch the Newton's law relationship for Newtonian and Non-Newtonian fluids. Give one example for each fluid. (08) b. The velocity distribution over a plate is given by V = ⎛⎜ y − y 2 ⎞⎟ in which V is the ⎝3 ⎠ velocity in m/s. at a distance y m above the plate. Determine the shear stress at y=0 Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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and y = 0.1 m. Take u = 0.835 N-s/m (08) 2 a.Derive the variation of pressure in a static mess of fluid in differentiate form 10 b. The left leg of a u-tube mercury manometer is connected to a pipe-line conveying water, the level of mercury in the leg being 0.6m below the center of pipe line, and the right leg is open to atmosphere. The level of mercury in the right leg is 0.45m above than that in the left leg and the space above mercury in the right leg contains Benzene (sp. Gr. 0.88) to a height of 0.3m. Find the pressure in the pipe. (06) c. A hydraulic press has a ram of 300mm diameter and a plunger of 45mm diameter. Find the weight lifted by the hydraulic press when the force applied at the plunger is 500N. (04) 3 a. Derive an expression for the total pressure on a vertical plane. Show that for plane vertical surface, the center of pressure is always below the center of gravity of the surface. (10) b. Find the magnitude and line of a action at the resultant force exerted upon the side of a box tank which is 0.6m square and 1.2m deep when filled half fully with liquid having a specific gravity of 2, while the remainder is filled with liquid having a specific gravity of 1.(10) 4 a. Define the following i) Uniform and Non-uniform flow ii) Steady and Unsteady flow iii) Rotational and Irrotational flow (10) b. Derive the continuity equation in differential form. c. A stream function ψ in a two-dimensional flow is given by ψ = uxy Show that the flow is irrotational, and find the corresponding velocity potential function (10) PART-B 5 a. Derive the Benoulli's energy equation from the Euler's motion equation, mentioning clearly the assumptions made in the derivation. (08) b. A pipe 300m long has a slope of 1 in 100 and tapers from 1.2m diameter at the high end to 0.6m diameter at the low end. Quantity of water flowing is 5,400 lit/minute. If the pressure at the high end is 68.67 kPa, find the pressure at the lower end. Neglect losses. (06) c. A Venturi-meter has its axis vertical, the inlet and throat diameters being 150mm and 75mm respectively. The throat is 223mm 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.(06) 6 a. Derive the equation to find the head loss due to sudden enlargement in a pipe. (06) b. A pipe line consists of 3 pipes in series: (06) i) 300m long, 15 cm diameter ii) 150m long, 10 cm diameter iii) 240m long, 20 cm diameter The pipeline takes off from a reservoir with water at an elevation of 500m. The elevation at the exit is 400m. Find the discharge. Neglect minor losses. Take f = 0.04. c. A pipe line 0.225m in diameter and 1580m long has a slope of 1 in 200 for the first 790mt and 1 in 100 for the next 790mt. The pressure at the upper end of the pipeline is 107.91Kpa and at the lower end is 53.955kPa. Taking f = 0.032 determine the discharge through the pipe. (08)

7 a. Define the following i) Coefficient of velocity ii) Coefficient of contraction iii) Coefficient of discharge iv) Coefficient of resistance. (04) b. The head of water over an orifice of diameter 10cm is 10m. The water coming out from orifice is collected in a circular tank of diameter 1.5m. The rise of water level in this tank is 1.0m in 25 seconds. Also the co-ordinates of a point on the jet, measured from venacontract are 4.3m. horizontal and 0.5m vertical. Find the co-efficients Cd, C, and Ce. (08) c. A reservoir discharge through a sluice 0.913m wide by 1.22m deep. The top of the opening is 0.61 m below the water level in the reservoir and the downstream water level is below the bottom of the opening. Calculate i) The discharge through the opening if Cd = 0.6 and ii) Percentage error if the opening is treated as a small orifice. (08) 8 a. What is the difference between weir and a notch? How are the weirs classified? What is the difference between a sharp crested and a broad crested weir. (08) b. Water flows over a rectangular weir 1m wide at a depth of 15cm and afterwards passes through a triangular right angled weir. Taking Cd for the rectangular and triangular weir as 0.62 and 0.59 respectively, Find the depth over the triangular weir. (06) c. A rectangular notch of crest width 0.4m is used to measure the flow of water in a rectangular channel 0.6m wide and 0.45m deep. If the water level in the channel is 0.225m above the weir crest, find the discharge in the channel. For the notch Cd = 0.63 and take velocity of approach into account. (06) Third Semester B.E. Degree Examination, June/July 08 Fluid Mechanics Note : Answer any FIVE full questions selecting at least TWO from each part. Part - A 1 a. Distinguish between i) Solids and liquids ii) Real and Ideal fluids (04) b Define for a fluid the following terms : i) Specific gravity ii) Kinematic viscosity iii) Surface tension iv) Capillarity (08) c. Calculate the velocity gradient at distances 0, 100, 150 mm from the boundary if the velocity profile is a parabola with vertex 150 mm from the boundary where the velocity is 1 m/s. Also calculate the shear stresses at these points if the fluid has a viscosity of 0.804 N-S/m2. (08) 2 a. With the help of a neat sketch define the terms : Absolute, gauge and vacuum pressure. Bring out the relationship between absolute and gauge pressure. (08) b. What is a manometer? Derive the equation for the pressure difference between the points as referred in inverted U-tube manometer. (06) c. A U-tube differential manometer containing mercury is connected on one side to pipe A containing carbon tetrachloride of specific gravity 1.6 under a pressure of 120 kPa and on the other side of pipe B containing oil of specific gravity 0.8 under a pressure of 200 kPa. The pipe A lies 2.5 m above pipe B and the mercury level in

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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the limb connecting with pipe A lies 4 m below the pipe A. Determine the difference in levels of mercury in the two limbs of manometer. (06) 3 a.Derive an expression for the total pressure on one side of an inclined plane and show that the centre of pressure lies lower than its centroid. (10) b. Gate PQ shown in Fig.3(b) is 1.25 m wide and 2 m height is hinged at P. Pressure gauge reads — 14.175 kN/m2. The left hand tank contains water and the right hand tank contains oil of specific gravity 0.75 up to the height shown. What is the horizontal force to be applied at Q to keep the gate closed? (10) 4 a Define : i) Path line ii) Stream line iii) Streak line (06) b. Define stream function and velocity potential function. Establish the condition that the stream lines and potential lines are orthogonal to each others. (06) c. In a two dimensional incompressible flow the fluid velocity components are given by u = x - 4y and v = -y - 4x. Show that velocity potential exists and determine it and also the corresponding stream function. (08)

Fluid Mechanics

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(Figure not to scale) Fig.3(b) Part - B State the Bernoulli's theorem. Starting from Euler's equation of motion of a stream line, derive the Bernoulli's equation. List the assumptions and limitations. (08) 250 It/s water is flowing in a pipe having diameter 300 mm. If the pipe is bent by 135° to the direction of flow at inlet, find the magnitude and direction of resultant force on the bend. Take the pressure of water flowing as 392.4 kPa. (06) In a 100 mm diameter horizontal pipe, a venturimeter 100 mm x 50 mm has been fitted. The head of water on the meter when there is no flow is 3 m (gauge). Find the rate of flow for which the throat pressure will be 2 m of water absolute. Discharge coefficient for the meter is 0.97 (06) Derive expressions for head loss due to sudden enlargement and also due to friction. A pipe line ABC 180 m long is laid on an upward slope of 1 in 60. The length of the portion AB is 90 m and its diameter is 0.15 m. At B the pipe section suddenly enlarges to 0.30 m and remains for the remainder of its length BC, 90 m. A flow of 50 lt/s is pumped into the pipe at its lower end A and is discharged at upper end C into a closed tank. The pressure at the supply end A is 137.34 kN/m2. Sketch (i) the

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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total energy line (ii) Hydraulic gradient line. Also find the pressure at the discharge 2 end C. Take f - 0.02 in the equation h f = f lV (10) 2 gd Explain the terms : i) Vena contracta ii) Coefficient of contraction (04) Determine the value of coefficient of contraction in case of Bordas Mouth piece running free. (06) A tank has two identical orifices 50 mm in diameter in one of its vertical sides and are situated one above the other. The upper orifice is 4 m below the water surface and the lower one is 6 m below the water surface. The coefficient of contraction and velocity are 0.64 and 0.98 for both the orifices. Find : i) The combined rate of discharge from two orifices ii) The distances of point of inter section of the two jets from vertical side. (10) Distinguish between : i) Notch and weir ii) Broad crested weir and submerged weir iii) Free nappe and clinging nappe. (06) Derive an expression for discharge over a triangular notch. (06) A rectangular notch of crest width 0.4 m is used to measure the flow of water in a rectangular channel 0.6 m wide and 0.45 m deep. If the water level in the channel is 0.225m above the crest, find the discharge in the channel. For the notch assume Cd = 0.63. Take velocity approach into account. (08)

Third Semester B.E. Degree Examination, Dec. 07 / Jan. 08 Fluid Mechanics Note : Answer FIVE full questions. 1 a. Distinguish between : i) Ideal and real fluids ii) Newtonian and non-Newtonian fluids. (08) b. A tank 5 m long and 3m wide contains water to a depth of 2 m. Determine, what is the total hydro-static pressure acting an the bottom of the tank. Also, determine the intensity of pressure, assuming density of water = 1000 kg /m3. c. At the ocean surface, the specific weight is 10,000 kN /m3. Calculate the specific weight and specific volume at a depth of 12 km, if the pressure here is 120,600 kN/m2 and the average bulk-modulus of sea water is 2.345 x 106 kN /m2 .(06) 2 a. Derive the formulae for hydrostatic force on one side of a thin vertical plate submerged in a liquid and depth of centre of pressure. (10) b. A trapezoidal plate of top width 5 m, bottom width 4 m and height 3 m is immersed vertically with its sides parallel to the water level and its top edge at a depth of 2 m below the water level. Find the water thrust on one side of the plate and the depth of centre of pressure. (10) 3 a. Explain with sketches, the working principle of the following i) Inverted differential manometer ii) micromanometer. (10) b. A closed tank of height 8 m is filled with bromine of specific gravity 3.1 to a depth of 2m and turpentine of specific gravity. 0.87 to a depth of 5 m. The upper part of Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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the tank contains air under a pressure of 25 kPa (Vac). Find the absolute pressure at the bottom of the tank in kPa and in cm of mercury. Atmospheric pressure = 101.3 kPa. Neglect density of air. (10) a. Define stream line, path line and streak line. Derive mathematical expressions for each of these lines. (12) b. The velocity distribution in a three-dimensional flow is given by u = - x, v = 2y and w = (3- z). Find the equation of the stream line that passes through point (1, 1, 1). (08) a. Derive Bernoulli's equation from Euler's equation for a steady flow of fluid. (10) b. 5000 Ips of petrol of density 0.8 kg /liter flows through a 18 cms diameter by 9 cms vertical venturimeter. The flow is in the upward direction and the Cd of the meter is 0.9. The length of converging cone of the meter is 30 cms. Compute the pressure difference between the inlet and threat sections and the deflection that would be recorded by a mercury differential U-gauge connected between these sections. (10) a. Define the hydraulic coefficients of an orifice and derive relationship between Cd, Cv, Cc. (10) b. Differentiate between orifice and mouth piece. Classify mouth pieces with neat sketches. (10) a. Differentiate between broad crested and sharp crested weir. Derive the discharge equation for a broad crested weir considering the velocity of approach. (12) b. A sharp - crested rectangular notch of 0.8 m width and a 90° V-notch are to be used alternatively for measuring an expected flow of 45 liters /sec of the liquid. Find the percentage error in discharge that would result in the two cases if an error 1 mm is made in the head measurement. Assume Cd = 0.6 for both the notches. Assume Cd = 0.6 for both notches. (08) a. Derive the Darcy-Weisbach equation for friction head loss in a pipe. (10) b. Two reservoirs whose water surface elevations differ by 60 m are connected by a 0.3 m diameter pipe 4000 m long. In order to increase the rate of flow by 25 percent, another pipe is laid to the original pipe over the first half of its length. Compute the diameter of the additional pipe. Neglect losses and f = 0.030 for all pipes. (10)

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Take surface tension of water as 0.075 N/m and contact angle as 60°. What will be the percentage change in capillarity, if the tube diameter is reduced to half? 10 a. Define the term gauge pressure, vacuum pressure and absolute pressure. Indicate the relative positions on a chart. 10 b. A U-tube differential mercury manometer is connected between two pipes X and Y Pipe X contains carbon tetra chloride Sp.gr = 1.6 under a pressure of 103 k| (gauge). Pipe Y contains oil Sp.gr 0.8 under a pressure of 172 kpa (gauge). Pipe X 2.5 m above the centre line of pipe Y. Find the manometer reading as shown by centimeter scale attached to it. Assume that the level of mercury in the limb connecting pipe X is level with the centre of pipe Y. Sketch the arrangement. 10 a. Define the term centre of pressure. Show that for an inclined plane lamina submerge in a liquid of specific gravity S, and at an angle 0 to the liquid surface, that the depth of centre of pressure is more than the centroidal depth. 10 b. A trapezoidal channel is 3 m wide at the bottom and 1.5 m deep. It has side slopes 40° with the horizontal. Determine: i) total pressure and ii) depth of centre 1 pressure on the vertical gate closing the channel, when it is full of water. 10 a. Derive the equation of continuity for a steady incompressible fluid flow in the dimensional Cartesian coordinates. 10 b. A stream function in a 2-D flow is defined by l0xy. Show that the flow is irrotational and hence determine the corresponding velocity potential function. a. Derive the equation for discharge through an inclined venturimeter with flow upwards. Sketch the arrangements showing clearly the details of the manometer. 10 b. In fig below compute the manometer reading in cms if elevation of A is 20 m; elevation of B is 15 m. Diameters at A and B are 250 mm and 15 cm respectively. Discharge through the pipe is 6150 1pm. Neglect losses. 10

Third Semester B.E. Degree Examination, Dec.06 / Jan.07 Fluid Mechanics Note: Answer any FIVE full questions. 1 a. Define a fluid. Bring out clearly the differences between a solid and a fluid. 06 b. What do you understand by the term fluid continuum, explain. 04 c. If 10 m3 of mercury weighs 1329 KN. Calculate its specific weight, mass density specific volume and specific gravity. 10 2 a. Through a very narrow gap of height h, a thin plate of large extent is pulled at velocity V, on one side of the plate is oil of viscosity μ1 and on the other side oil of viscosity μ2. Calculate the position of the plate so that, i) the shear force on the two sides of the plate is equal. ii) the pull required to drag the plate is minimum. 10 b. A capillary tube having an inside diameter of 4 mm is dipped in water at atmosphere temperature of 20°C. Determine the height of water which will rise in the tube. Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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Fluid Mechanics

Fig. Q6 (b) 7. a. Derive an expression for the loss of head due to sudden enlargement of a pipe. 10 b. A 45º reducing bend is connected to a pipe line. The diameter at the inlet and outlet of the bend are 60 cm and 30 cm respectively. Find the force exerted by water on the bend if the intensity of pressure at the inlet of the bend is 9.5 N/cm2 and rate of flow of water is 620 lps. 10 8. a. In performing an experiment to determine different coefficients of a sharp edged orifice a jet of water issuing horizontally from the orifice 25 mm diameter under a constant head of 150 cm fell through 0.9 m vertically and struck the ground at 2.3 m horizontally from vena-contracta. The time required to discharge 91 litres of water was found to be 53 seconds. Calculate all the hydraulic coefficients for the orifice. 10 b. During a test in a laboratory the water passing through a venturimeter was made to How over a 90° V-notch. The throat and inlet diameter of the venturimeter was measured as 120 mm and 250 mm respectively. The pressure head difference between inlet and throat is 20 cm of water when the head over the V-notch is 185.4 mm. If Cd for venturimeter is 0.97, what is the coefficient of discharge for the Vnotch? 10 Third Semester B.E. Degree Examination, July 2006 Fluid Mechanics Note: Answer any FIVE full questions. 1. a. Explain the concept of fluid continuum. b. The specific gravity of mercury at 20 C is 13.6. Calculate its specific weight, specific volume and density. c. A rectangular solid block weighing 90 N slides down a 30° inclined plane. The plane is lubricated by a 3 mm thick film of oil of relative density 0.9 and viscosity 8.0 poise. If the contact area is 0.3 m2, estimate the terminal velocity of the block. 10 2 a. Determine the capillarity between two thin vertical plates 2 mm apart in water having a surface tension of 0.07 N / m and contact angle 10°. 04 b. Derive an equation for the variation of pressure with a depth in a liquid at rest. 06 c. A circular plate of diameter 0.75 m is immersed in a liquid of a relative density of 0.8 with its plane making an angle of 30° with the horizontal. The centre of the plate is at a depth of 1.5 m below the free surface. Calculate the total force on one side of the plate and location of the centre of pressure. 3 a. Show that stream function satisfies the continuity equation in 2 dimensions. 04 b. Derive three dimensional continuity equation for steady incompressible flow. 06 c. For the velocity components in a fluid flow given by u = 2 xy and v = x2 - y2, show that flow is possible. Obtain the relevant stream functions. 10 4 a. Derive the condition for the irrotational flow to exist in 2 - Dimensional plane perpendicular to z - axis in rectangular co-ordinate system. 04 b. Calculate the velocity component v given u = - ²/3 xy3 - x2y so that the equation of continuity is satisfied. 06

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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c. An U - tube differential gauge is attached to two sections A and B in a horizontal pipe carrying water. Calculate the mercury differences in the manometer when the pressure at A is 10 N/cm2 and pressure at B is 100 mm of mercury. 10 5. a. Derive an equation for the discharge through a horizontal venturimeter. 04 b. Derive Bernolli's equation by integrating Euler's equation of motion for steady and incompressible flow along a curved stream line. 06 c. In a 45° bend, a rectangular air duct of 1.0 m2 cross - sectional area is gradually reduced to 0.5 m". Find the magnitude of the force required to hold the duct in position, if the velocity of flow is 20.0 m/s at 1 m2 cross - section and the pressure at both sections is 40 KN/m2. Specific weight of air is 11.0 N/m3 10 6. a. Derive an equation for the head loss due to sudden expansion of a pipe. 04 b. A tapering pipe has a diameter of 250 mm at point 1 (Elevation 25.0 m) and a diameter of 350 mm at the point 2 (Elevation 20.0 m). If the pressure at point 1 is 120 KPa, calculate the pressure at point 2 for a discharge of 0.2 m3/s. of water. The 2 loss of head through a pipe can be assumed to be 1.2, (V1 − V2 ) . The flow is from

2g

04 06

10

section 1 to section 2 08 c. A 100 mm diameter pipe suddenly enlarges into 150 mm diameter pipe. The hydraulic grade line rises by 10 mm of water. Estimate the quantity of water flowing in the pipe. 08 7. a. Derive an equation for maximum discharge over a Broad crested weir 04 b. A rectangular Notch 400 mm long is used for measuring discharge of 0.03m3/s. An error of 1 mm was made while measuring head over the notch. Calculate the percentage error in discharge, given the co - efficient of discharge as 0.6 08 c. An open tank has a sharp edged orifice of 40 mm diameter in one of its side walls. The tank is filled with water to a depth of 2 m, above the centre of the orifice. The orifice discharges water into atmosphere. A micrometer contraction gauge gives a jet diameter of 32.0 mm at vena contracta. The co - ordinates of a point on the jet with respect to vena contracta are x = 12.0 cm and y = 20.0 cm. Determine the discharge in liter per second. 08 8. a. Derive the Darcy-Weisbach equation for head loss due to friction in a pipe. 04 b. A horizontal pipe line 100 m long is connected to a tank at one end discharges freely in to the atmosphere at the other end. For the first 30 m of its length from the tank the pipe is 200 mm diameter and is suddenly enlarged into 400 mm diameter for the remaining length. The height of water level in the tank is 20.00 m above the centre line of the pipe. Considering all minor losses, calculate the rate of flow when the friction factor f = 0.018 for both pipes. Use hf = for head loss. 08 c. Two pipes A and B are connected in parallel between two points. Pipe A is 150 m long and has a diameter of 150.0 mm Pipe B is 100 m long and has a diameter of 120.0 mm. Both the pipes have the same friction factor of 0.018. The total discharge carried by both pipes is 50 Ips. Calculate discharge in each pipe. 08

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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Third Semester B.E. Degree Examination, January/February 2006 Fluid Mechanics Note: 1. Answer any FIVE full questions. 2. Assume any missing data suitably and mention the same. 1. (a) Define the following fluid properties along with its significance i) Vapour pressure ii) Surface tension iii) Cohesion and adhesion iv) Capillarity v) Compressibility 10 (b) The dynamic viscosity of oil used for lubrication between a shaft and sleeve is 6 poise. The shaft is of 0.4 m diameter and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the film is 1.5m (10 poise = lN-s/m2). 10 2. (a) State and prove hydrostatic pressure law in its differential form. 06 (b) Explain the working principle with neat sketch of Bourdon pressure gauge. 06 (c) In the figure given, the air pressure in the left tank is 230 mm of Mercury (Vacuum). Determine the elevation of gauge liquid in the right limb at A. if the liquid In the right tank is water 08

3. (a)

Show that for an inclined plate immersed in a fluid, the centre of pressure always lies lower than its centroid. 08 (b) Fig. shows the cross-section of a tank full of water under pressure. The length of the tank is 2m. An empty cylinder lies along the length of the tank on one of its corner as shown. Find the horizontal and vertical components of the force acting on the curved surface ABC of the cylinder. 12

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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4. (a) Distinguish between : i) Path line, ii) Stream line and iii) Streak line. 06 (b) Derive the discharge continuity equation in two dimensional form. 06 (c) Find the corresponding stream function of a flow with velocity potential defined as φ = x(2y-1). 08 5. (a) Apply Bernoulli's equation for Venturimeter and derive the discharge equation. 08 (b) Derive Bernoulli's energy equation from Euier's equation of motion and explain the terms involved in the equation. 06 (c) A horizontal venturimeter with inlet diameter 200mm diameter and throat diameter 100mm is used to measure the flow of oil of specific gravity 0.8. The discharge of oil through venturimeter is 60 lps. Find the reading of the oil-mercury differential manometer. Take Cd = 0.98. 06 6. (a) What is momentum equation? State and explain. 04 (b) A.45° degree bend is connected in a pipe line, the diameters at the inlet and outlet of the bend being 600 mm and 300 mm respectively. Find the force exerted by water on the bend if intensity of pressure at inlet to bend is 88.29 kPa and rate of flow of water is 600 lps. 08 (c) Derive Darcy's formula for head loss due to friction in for flow through a pipe line. 08 7. (a) Derive the equation for flow through pipes for sudden expansion. 06 (b) Distinguish between hydraulic gradient line and energy gradient line with an example and neat sketch. 06 (c) An old water supply distribution pipe of 250 mm diameter of a city is to be replaced by two parallel equal diameter pipes having equal lengths and friction factor values. Find the new diameter required. 08 8. (a) What are hydraulic coefficients? Explain. 06 (b) Derive a relationship to determine the coefficient of velocity for flow through an orifice. 06 (c) What are the advantages of triangular weir over rectangular weir?Water flows through a triangular right-angled weir first and then over a rectangular weir of 1 m crest width. The discharge coefficients of the triangular and rectangular weirs are 0.6 and 0.7 respectively. If the depth of water over the triangular weir is 360mm, find the depth of water over the rectangular weir. (3+5) Third Semester B.E. Degree Examination, July/August 2005 Fluid Mechanics Note: Answer any FIVE full questions. 1. (a) Define the following interms of expressions and derive their units in SI : i) Density ii) Specific weight iii) Coefficient of viscosity iv) Specific gravity. 04 (b) A body of mass 100 kg slides down at a uniform speed of 1 m/s along lubricated inclined plane making 30° with the horizontal. The viscosity of the lubricant is 0.1 kg/m.s and the contant area is 0.25m2. Determine the thickness of the lubricant assuming a linear velocity distribution. 08 2. (a)State and prove Pascal's law. 08 Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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(b) The vacuum gauge attached to the compartment A in Figure 1 reads 17200 Pa (negative). Determine the piezometer readings attached to the compartments B,C and D and the deflection of mercury manometer shown in the Fig. 12 3. (a) Derive expression for the resultant force and centre of pressure on an inclined plane immersed in a fluid. 10 (b) A cylinder holds water in a channel as shown in Figure 2. Determine the weight of lm length of the cylinder. 10 4. (a) The velocity potential for a flow is given by the function φ = x2 - y2. Verify that the flow is incompressible and determine the stream function. 10 (b) Derive from first principles the Euler's equation of motion along a streamline. State the assumptions made. 10

Fluid Mechanics

Neglecting minor losses, find the increase in discharge, if f = 0.01 and the head at the inlet = 30m. 10 8. (a) An orifice (Cv = 1) present on the inclined face of the tank shown in Fig. 3 discharges water. Determine x and y, corresponding to the maximum height the jet reaches. 12 (b) Discharge over a 90° triangular notch is 200 lps with a Cd = 0.6, find the percentage error in discharge for an error of 1.5mm in the measurement of head 08

Note: 1. (a) (b) (c) 2. (a)

Figure 2

Figure 1 5. (a) Define the following terms using expressions : i) Pressure ii) Momentum iii) Energy iv) Energy head v) Power. State the units for these quantities, in SI. 10 (b)Water flows upward through a vertical 300mm x 500 mm venturimeter, with a Cd = 0.98. The deflection of a manometer, filled with a liquid of S=1.25 is 1.18m. Determine the discharge if the distance between the two pressure tapings is 457 mm. Work the problem from first principles. 10 6. (a) Explain the principle of Pitot static tube. (b)Water flows up a reducing bend of weight 80 kN placed in a vertical plane. For the bend, the inlet diameter is 2m, outlet diameter 1.3m, angle of deflection 120° and vertical height (distance between the inlet and the outlet) is 3m If the discharge is 8.5m3/s, pressure at the inlet is 280 kPa and the head loss in half the kinetic head at the exit, determine the force on the bend. 12 7. (a) Derive expressions for losses due to sudden contraction and sudden enlargement in pipe flow. 10 (b) A pipeline of 0.6m in diameter is 1.5km long. In order to increase the discharge another parallel line of the same size is introduced in the second half of the length. Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

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(b) (c)

3. (a) (b) (c)

4. (a) (b) (c)

Third Semester B.E. Degree Examination, January/February 2005 Fluid Mechanics 1. Answer any FIVE full questions. 2. Draw neat sketches where required Distinguish between : i) Solid and liquid ii) Real and ideal fluid iii) Compressible and incompressible fluid. 06 At a certain point in a fluid the shear stress in 0.216kN/m2 and the velocity gradient is 0.216/sec. If the mass density of the fluid is 9kN/m3 find the kinematic viscosity. 06 Calculate the specific weight, specific volume, density and specific gravity of one litre of liquid weighing 9.0N. 08 Distinguish between : i) Pressure and pressure head ii)Absolute pressure and gauge pressure iii)Simple and differential manometer State and prove hydrostatic pressure law. 06 The tank in Fig.2(c) contains oil and specific gravity 0.75. Determine the absolute pressure gauge reading at A in mm of mercury if the manometric deflection is 25 cms of mercury. Define : i) Total pressure ii) Centre of pressure iii) Hydrostatic Pressure Determine the total force and location of centre of pressure for a circular plate of 2m diameter immersed vertically in water with its top edge 1.0m below the water surface. 06 Find the horizontal and vertical component of force and its point of application, due to water per metre length of the gate AB having a quadrant shape of radius 2 m as shown in Fig.3(c). Find also the resultant force in magnitude and direction. 08 Distinguish between : i) Convective and local acceleration ii) Steady and uniform flow iii) Stream line and path line. 06 A 25 cms diameter pipe carries oil oi specific gravity 0.9 at a velocity of 3m/sec. At .mother section the diameter is 20cms. Find the velocity at this section and also the mass rate of flow of oil. 06 A stream function in a two dimensional flow is ψ = 2xy. Show that the flow is irrotational and determine the corresponding velocity potential φ. 08

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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5. a) i) State the assumptions made in the derivation of Bernoiillis equation 06 ii) What is a pitot tube? iii) State the governing forces causing pipe flows and river flows. b) A pipe of 40 cms diameter carries water at a velocity of 2.5m/s. The pressure head at points A and B are given as 30m and 23m respectively, while the datum head at A and B are 28m and 30m respectively. Find the loss of head between A and B.06 c) A horizontal venturimeter with inlet diameter 20 cms and throat diameter 10 cms is used to measure the flow of oil of specific gravity 0.8. The discharge of oil through venturimeter is 60 lps. find the reading of the oil-mercury differential manometer. Take Cd =0.98. 08 6. (a) Distinguish between : i) Hydraulic gradient and energy gradient ii) Laminar and turbulent flows iii) Major and minor losses. 06 (b) Find the loss of head when a pipe of 20 cms diameter is suddenly enlarged to a diameter of 40 cms. The rate of flow of water through the pipe is 250 litres/sec. 06 (c) Two reservoirs with difference in water levels of 180m are connected by a 64 km long pipe of 500 mm diameter and friction factor of 0.004. Determine the discharge through the pipe. In order to increase this discharge by 50% another pipe of the same diameter is to be laid from the lower reservoir for part of the length, and connected to the first pipe. Determine the length of additional pipe required. Neglect minor losses. 08 7. (a) Distinguish between : i) Orifice and mouthpiece ii)Coefficient of velocity ,and coefficient of contra iii) Coefficient of discharge and velocity of approach 06 (b) An orifice is fitted at the bottom of one side of a tank having water to a depth of H metres. Derive an expression to estimate the coefficient of velocity experimentally. 06 (c) A rectangular orifice of 0.9m wide and 1.2m deep is discharging water from a vessel. The top edge of the orifice is 0.6m below the water surface in the vessel. Calculate the discharge through the orifice is Cd = 0.6 and percentage error if the orifice is treated as a small orifice. 08 8. (a) Distinguish between : i) Notch and weir ii) Broad crested weir and submerged weir iii) free nappe and clinging nappe. 06 (b) Derive an expression for the discharge over a triangular notch. 06 (c) A sharp crested Cipollitti weir of crest length 60 cms in fitted in a rectangular channel lm wide and 0.5m deep water. If the water level in the channel is 22.5 cms above the weir crest, calculate the discharge over the weir. Take Cd = 0.62 and make correction for velocity of approach 08

Fluid Mechanics

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Third Semester B.E. Degree Examination, July/August 2004 Fluid Mechanics Note: Answer any FIVE full questions 1.(a) Explain Newton's law of viscosity. Differentiate between Newtonian and non Newtonian fluids. How does viscosity vary with temperature in gas and liquids. 10

(b) A cube of 0.3m sides and mass of 30kg slides down a plane inclined at 30° to the horizontal covered by a thin film of viscosity 2.3 x 10-3 Pa-sec. If the thickness of the film is 0.03mm determine the steady state velocity of the block. 10 2. (a) Differentiate between hydrostatic pressure and centre of pressure. 04 (b) Obtain the expressions for horizontal and vertical components of the resultant hydrostatic force on a submerged curved plane surface. 08 (c) A square tank with 2m sides and 1.5m high contains water to a depth of lm and a liquid of sp.gr 0.8 on the water to a depth of 0.5m. Find the magnitude and location of resultant hydrostatic force on one face of the tank. 08 3.(a) With the help of a neat diagram define the terms : Absolute, gauge and vacuum pressures. Bring out the relation between absolute and gauge pressures. (6+2) (b) Explain the construction and use of micromanometer. 06 (c) A differential manometer containing mercury was used to measure the difference in pressure of two pipes A and B containing different liquids of sp.gr 0.9 and 0.8 respectively. Pipe A is 40cm (centre to centre) above pipe B. The mercury level in the limb of manometer connected to B is 0.5 m below its centre and that in limb connected to pipe A is 0.2m below its centre. Express the difference of pressure of two pipes in terms of column of water. 06 4. (a) Differentiate between stream function and potential function. Establish the condition that the stream lines and potential lines are orthogonal to each other. 3+3+2 (b) Prove that potential flow is an irrotational flow. 02 (c) In a 2-D flow, the velocity components are u = 4y and v = -4x. i) is flow possible? ii) if so, determine the stream function. iii) What is the pattern of stream lines? 10 5.(a) Derive Euler's equation of motion along a streamline, from the first principle. 10 (b) The inlet and throat diameters of a vertically mounted venturimeter are 30cm and 10cm respectively. The throat section is below the inlet section at a distance of 10cm. The specify mass of liquid is 900 kg/m3. The intensity of pressure at inlet is 140 kPa and that at the throat is 8 kPa. Calculate the rate of flow in lps. Assume 2% of the differential head is lost between inlet and throat. Take Cd = 0.97. 10 6.(a) Show that for an inclined venturimeter provided with differential manometer, the discharge equation is same as that of a horizontal ventrimeter. 10 (b) Water discharges at the rate of 98 LPS through 12cm diameter vertical sharp edged orifice under a constant head of 10m. At a point on the Jet measured from vena contracta of the jet has coordinates 4.5m horizontal and 0.5m vertical. Find the coefficients Cv,Cc,Cd & Cr. 10 7.(a) Differentiate between : i) Hydraulic gradient and total energy ii) Laminar and turbulent flows iii) Minor and major losses in pipe lines. 2+4+4 (b) For the distribution main of a city water supply a 30cm main is required. As pipes above 25cm diameter are not available, it is decided to lay two parallel mains of the same diameter. Find out the diameter of the parallel main. 10 8.(a) What are the advantages of triangular notch over rectangular notch? 04

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

Fluid Mechanics

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(b) Show that the flow over a cippoletti notch is same as that of a suppressed rectangular notch. 05 (c) Show that for a Bordas mouth piece running full the coefficient of discharge is 0.707. 05 (d) Explain the terms : Vena-contracta, end contractions and velocity of approach. 06

Fluid Mechanics (c) 6.(a)

Third Semester B.E. Degree Examination, January/February 2004 Civil Fluid Mechanics Note:1. Answer any FIVE full questions. 2. Any data missing may be suitably assumed. 1 .(a) Define surface tension. Derive an equation for the capillary rise of water in a cylindrical tube of radius r. 2+4 (b) What is fluid continuum? Under what conditions this property is invalid? 04 (c) The velocity distribution between two parallel plates separated by a distance h is given by u = ⎧⎪5 y − 2 y 2 ⎫⎪ ⎨ ⎪⎩ h

⎬ h ⎪⎭ 2

Where, u is velocity in m/s at a distance y metres above the lower plate. Determine assuming h = 6mm,μ = 0.25 pascal-sec and laminar flow i) The average velocity ii) The shear stress at the plates 10 2.(a) Define pressure. Derive an equation for the variation of pressure with depth in a liquid of specific weight γ. 2+4 (b) With a neat sketch explain the working of a Bourdon's pressure gauge. 06 (c) A U-tube differential manometer connects two pressure pipes A and B. Pipe A contains carbon tetrachloride having a specific gravity 1.594 under a pressure of 130 kN/m2 (gauge) and pipe B contains oil of specific gravity 0.82 under a pressure of 200 kN/m2 (gauge). Pipe A is 2.65m above pipe B. Find the difference of pressure measured by mercury as fluid filling the U-tube. Assume that the level of mercury connecting pipe A is in level with the centre of pipe B. Draw a neat sketch of the arrangement. 08 3. (a) Differentiate between total pressure and hydrostatic pressure. 04 (b) Show that for an inclined submerged plane surface, centre of pressure is always below the centroid. 08 (c) A rectangular tank 10m x 5m and 3.25m. deep is divided by a partition wall parallel to the shorter wall of the tank. One of the compartment contains water to a depth of 3.25m and the other oil of specific gravity 0.85 to a depth of 2m. Find the resultant pressure on the partition. 08 4. (a) Differentiate between uniform flow and unsteady flow. 04 (b) Derive the three dimensional continuity equation for a steady incompressible fluid flow. 08 (c) The stream function and velocity potential for a flow are given by ψ = 2xy, φ = x2-y2. Show that the conditions for continuity and irrotational flow are satisfied 08 5. (a) Derive the Euler's equation of motion along a stream line. 06 (b) Water flows up a conical vertical pipe 450mm diameter at the lower end and 250mm diameter at 2.3m above the lower end. If the pressure and velocity at the lower end are 63 kN/m2 (gauge) and 4.1m/s, assuming the head loss in the pipe to Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore

(b) (c)

7. (a) (b)

(c) (d)

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be 10% of the pressure head at the lower end, calculate the discharge through the pipe. Also calculate the pressure and velocity at the upper end. 08 300 lps of water is flowing in a pipe having a diameter of 300mm is bent by 130°, find the magnitude and direction of the force on the bend. The pressure of water flowing is 425kN/m2 (gauge). 06 With a neat sketch, derive an equation for the discharge through an inclined Venturimeter, with, flow downwards. 06 A 100 mm diameter pipe suddenly enlarges into 150 mm diameter.pipe. Find the loss of head in metres when the flow is 25 lps. Find also the loss of head in meters when the flow is in the opposite direction. 06 Consider two pipes of same length and having the same roughness coefficient, with the diameter of one pipe being 60% of the other. Determine i) the ratio of discharges through the pipes if the friction loss for both of them is to be the same ii) the ratio of friction losses if the pipes carry the same discharge. 08 Derive an equation for the head loss due to sudden expansion of a pipe. 06 A closed tank has a sharp edged orifice of 40mm diameter in one of its side walls. The tank is filled with an oil of weight density 83.6 kN/m3 to a depth of 2m above the centre of the orifice. The air above the oil is under a pressure of 5000 pascals. The orifice discharges the liquid into the atmosphere.A micro manometer contraction gauge gives a jet diameter of 31.5mm at vena contracta. The coordinates of a point on the jet with respect to vena contracta are x = 122cm.& y = 19.3cm. Determine the discharge in lps. To what value should the tank be raised in order to double the discharge through the orifice. 08 Derive the discharge formula for an external cylindrical mouth piece. 06 8. (a) Derive an equation for the maximum discharge over a broad crested weir 06 With neat sketches explain the different types of nappe. 06

Dr. M.N. Shesha Prakash, Vice Principal, Vidya Vikas Institute of Engineering & Technology, Mosore