I Semester M.E. (Civil) (Water Resources Engg.) Degree Examination, July/August 2013 (New Scheme) 2K8 WR 104 : ADVANCED FLUID MECHANICS Time : 3 Hours
Max. Marks : 100
Instructions : 1) Answer any five full questions. 2) Assume any missing data suitably. 3) Use of relevant statistical tables are permitted. 1. a) Write a note on the different types of displacement of fluid particles.
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b) A painter is painting a wall 3m × 4m with a brush 10 cm wide and 1.25 cm thick. The thickness of one coat of paint is 0.5 mm and viscosity of the paint is 3 N-s/m2. Calculate the total energy required for painting one side of the wall if he moves the brush with a velocity of 10 cm/sec. 10 2. a) Define path line, stream line, stream tube and streak line, draw neat sketches.
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b) Determine whether the following specified flows are rotational or otherwise. Determine the expression for the velocity potential in case of irrotational flow. i) u = y & v = –1.5 x ii) u = xy2 & v = x2y
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3. a) Define laminar flow and list its characteristics.
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b) In the injection moulding of a certain plastic the heated compound is forced under a pressure difference of 686 kN/m2 through a tube of 0.5 cm diameter and 25 cm long. If the mean velocity of flow is 40 cm/sec, calculate the viscosity of the compound assuming laminar flow. If the specific gravity of the compound is 1.5, calculate the Reynold’s number of the flow. 10 4. a) From first principles derive Hagen-Poiseuille equation for steady laminar flow in pipes.
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b) Determine the velocity of flow at a distance 50 mm from the axis of a pipe 150 mm in diameter, when Reynold’s number of flow is 1500. Oil of kinematic viscosity 2.4 × 10 –6 m2/s and density 808 kg/m3 flows through the pipe.
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P.T.O.
JE – 946
-2-
*JE946*
5. a) Derive expressions for Energy and Momentem correction factors.
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b) The velocity distribution in an open rectangular channel is given by V = 4 y 0.7. If the width of the channel is 8 m and the depth of flow is 1 m, find the average velocity, energy correction factor and momentum correction factor.
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6. a) With neat sketches, explain the various water surface profiles on critical slope and horizontal slope with examples.
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b) A trapezoidal channel having a bottom width of 6 m, side slope 2H : 1V, Manning’s roughness coefficient of 0.025 and bed slope of 0.0016, carries a discharge of 10 m3/s. Compute the backwater profile created by a dam which backs up the water to a depth of 2 m immediately behind the dam. Use direct step method and take 4 steps. 7. a) Explain the direct step method of computation of gradually varied flow profile.
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b) A rectangular channel 15 m wide carries a discharge with a normal depth of 3 m. The bed slope of the channel is 1 in 3600. If at a certain section, the depth of flow is to be raised to 4 m by constructing a weir across the channel, determine how far upstream of this section, the depth of flow would be within 10% of the normal depth. Use graphical integration method. Assume Manning’s n as 0.015.
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8. a) Derive an expression for the depth of Hydraulic jump. State the assumptions made.
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b) Flood discharge of 14 m3/s/m flows over a spillway and then over a horizontal concrete apron. The total head is 12 m. The flow meets a river flow (4.4 m flow depth) with a hydraulic jump. Taking the loss of head over the spillway as 1.5 m and Manning’s ‘n’ for concrete apron as 0.014, determine the total length of apron such that the jump remains entirely within the apron. Also find the energy lost in the jump.
1. a) Write a note on the different types of displacement of fluid particles. 10. b) A painter is painting a wall 3m à 4m with a brush 10 cm wide and 1.25 cm. thick.
1. a) Derive the three dimensional continuity equation and explain its significance. 10. b) Calculate the velocity gradient at distances of 0, 100 and 160 mm from ...
tool to direct the advanced manufacturing research and development efforts. ... Foundation Engineering Research Center for Compact and Efficient Fluid Power ... Manufacturing Co ... m - AMTech Progress Report #2 (70NANB15H061).pdf.
In laminar entry pipe flow, a boundary layer of thickness δ(z) grows along the sides of the pipe throughout the 'inlet region', until its thickness becomes comparable to the pipe radius. Mohanty & Asthana (1978) calculate the streamwise extent of th
(a) Newton's law of viscosity states that. (i) shear stress is directly proportional to. the velocity. (ii) shear stress is directly proportional to ... energy with the help of a mathematical. expression. 4. (b) Derive Euler's equations of motion. 10
Subject Name: Fluid Mechanics. ... l) In a foot step bearing, if the speed of the shaft is doubled, then the torque required ... Displaying Fluid Mechanics..pdf.
(a) Derive the Darcy - Weisbach equation for. friction head loss in a pipe. . Water is flowing'through a horizantal pipe. line 1500 m long and 200 mm in diameter,.
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upon the notes for a Siggraph course on Fluid Simulation[Bridson. 2007]. I also used .... âAt each time step all the fluid properties are moved by the flow field u.
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