S.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100

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1 Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]-113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B. : Answer three questions from Section I and three questions from Section II. (iii) (iv) (v) Figures to the right indicate full marks. Draw suitable sketches wherever necessary. Assume suitable data, wherever necessary. Answers to the two Sections should be written in separate answer-books. (vi) Use of electronic pocket calculator is allowed. SECTION I Unit I 1. (a) Develop the expression for the relation between gauge pressure P inside a droplet of liquid and the surface tension. [4] P.T.O.

2 Explain : [6] (iii) (iv) Streak line Streamline Stream function Velocity Potential. (c) A vertical gap 2.2 cm wide of infinite extent contains a fluid of viscosity 2 Ns/m 2 and specific gravity 0.9. A metallic plate 1.2 m * 1.2 m * 0.2 cm is to be lifted up with a constant velocity of 0.15 m/s, through the gap. If the plate is in the middle of the gap, find force required. The weight of the plate is 40 N. [8] 2. (a) What is flow net? Explain any one method to draw the flow net. [6] The flow is described by the stream function ψ = 2 3 xy. Locate the point at which the velocity vector has a magnitude of 4 units and makes an angle of 150 with the x-axis. [6] (c) Given the velocity of fluid : V = (6 + 2xy + t 2 ) i (xy t) j + 25k. What is an acceleration of a particle at (3, 0, 2) at time t = 1? [6] [4262]-113 2

3 Unit II 3. (a) Derive an analytical expression for determination of metacentric height of a partially submerged body. [8] A circular opening, 3 m diameter, in a vertical side of a tank is closed by a disc of 3 m diameter which can rotate about a horizontal diameter. Calculate : The force on the disc. The torque required to maintain the disc in equilibrium in the vertical position when the head of water above the horizontal diameter is 4 m. [8] 4. (a) State and explain Pascal s law. [4] Derive an expression for determination of centre of pressure of a vertically immersed plane surface. [6] (c) A weight of 120 kn is moved through a distance of 6 m across the deck of a vessel of total weight 10 MN displacement floating in water. This makes a pendulum of 2.8 m length swing through a distance 12.5 cm horizontal. Calculate metacentric height of the vessel. [6] [4262] P.T.O.

4 Unit III 5. (a) Derive an expression for the error in discharge due to error in measurement of the head over triangular notch. [8] A pipe carrying water has a 30 cm* 15 cm venturimeter which is positioned inclined at 30 to the horizontal. The flow is upwards. The converging cone is 45 cm in length and the coefficient of the discharge of the meter is A differential U tube manometer with mercury as indicating fluid is connected to the inlet and throat and shows a differential column height of 30 cm. Calculate the discharge in the pipe. If the pressure in the inlet section is 50 kpa, determine the pressure at the throat. [8] 6. (a) Derive an expression for Bernoulli s equation along a streamline. State the assumptions made. [8] A Pitot tube is inserted in pipe of 300 mm diameter. The static pressure in pipe is 100 mm of mercury (vacuum). The stagnation pressure at the center of pipe, recorded by the Pitot tube is N/cm 2. Calculate the rate of flow of water through pipe, if the mean velocity of the flow is 0.85 times the central velocity. Take coefficient of velocity as [8] [4262]-113 4

5 SECTION II Unit IV 7. (a) Prove that the velocity distribution for Laminar flow between two parallel plates when both plates are fixed across a section is parabolic in nature. Also prove that maximum velocity is equal to one and half times the average velocity. [10] Derive the expression for the resistance R to the motion of a completely submerged body depends upon the length of the body L velocity of flow V mass density of fluid ρ and kinematic viscosity of fluid υ using Buckingham s Π theorem. [8] 8. (a) Explain the following : [8] (iii) (iv) Reynolds number Euler s number Froude s number Mach s number. [4262] P.T.O.

6 An 8 cm diameter pipe, 300 m long conveys oil of kinematic viscosity 1.5 stokes and mass density 900 kg/m 3. Assuming laminar flow : Find the rate of flow if it takes 5 kw of power input to a pump set of overall efficiency 60% to drive the flow. Verify whether the assumption of Laminar flow is correct. [10] Unit V 9. (a) Water flows through a pipeline whose diameter varies from 20 cm to 10 cm in a length of 10 cm. If the Darcy-Weisbach friction factor is 0.02 for the whole pipe, determine the head loss in friction when the pipe is flowing full with a discharge of 50 lps. [8] Show that the loss of head due to sudden expansion in a pipeline is a function of velocity head. [8] 10. (a) Two pipes each of length L and diameters D 1 and D 2 are arranged in parallel; the loss of head when a total quantity [4262]-113 6

7 of water Q flows through them being h 1. If the pipes are arranged in series and the same quantity of water, Q, flows through them, the loss of head is h 2. If D 1 = 2 * D 2, find the ratio of h 1 to h 2. Neglect minor losses and assume the friction factor to be constant and to have the same value for both the pipes. [8] Derive an expression for determination of maximum power transmission through the pipe. [8] Unit VI 11. (a) Obtain expression for velocity distribution for turbulent flow in pipes. [6] Differentiate between : [6] Streamline body and bluff body Friction drag and pressure drag. (c) Explain in brief Computational Fluid Dynamics. [4] 12. (a) What do you mean by boundary layer separation? What is the effect of pressure gradient on the boundary layer separation? [6] [4262] P.T.O.

8 A truck having a projected area of 6.5 square meter travelling at 70 km/hr has a total resistance of 2000 N. Of this 20 per cent is due to rolling fricition and 10 per cent is due to surface friction. The rest is due to form drag. Calculate the coefficient of form drag. Take density of 1.25 kg/m 3. [6] (c) Define the following : [4] (iii) (iv) Airfoil Chord length Angle of attack Span of an airfoil. [4262]-113 8

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