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Reg. No. : ..................................... Name : ........................................
Third Semester B.Tech. Degree Examination, November 2009 (2008 Scheme) Branch : Civil 08.303 : FLUID MECHANICS – I Time : 3 Hours
Max. Marks : 100
Instruction: Answer all questions from Part – A and one full question from each Module of Part – B. PART – A I. a) Differentiate between i) absolute pressure and gauge pressure. ii) Simple manometer and differential manometer. b) Show that centre of pressure of any lamina immersed under a liquid is always below the centre of pressure. c) Explain the terms metacenter and metacentric height. d) What do you understand by convective acceleration, local acceleraion and total acceleration ? e) Describe the uses and limitations of flownets. f) What is a compound pipe ? How would you determine the equivalent size of a compound pipe ? g) Define the various coefficients for an orifice. h) Explain the characteristics of laminar and turbulent boundary layers. (8×5 = 40 Marks) P.T.O.
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PART – B Module – I II. a) An inverted u-tube manometer using oil of 0.8 specific gravity as manometric fluid is connected to the pipes A and B carrying the liquids of specific gravities of 1.2 and 1 respectively. The pipes A and B are at same level. The height of the liquid of specific gravity 1.2 in the limb connected to pipe A from the centre of the pipe is 40 cm. Find out the differential reading of the manometer. Assume all liquids are immiscible and the pressure in pipe B is 2000 Pa above the pressure in pipe A. 10 b) A circular plate of diameter 0.75 m is immersed in a liquid of relative density 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 the location of the centre of pressure. 10 III. a) A wooden block in the form of a rectangular prism floats in water with its shortest axis vertical. The block is 40 cm long, 20 cm wide and 15 cm deep with a depth of immersion of 12 cm. Calculate the position of the metacentre and comment on the stability of the block. 10 b) A pipe 25 cm in diameter carrying water branches into two pipes of 10 cm and 20 cm in diameters. The water velocity in 25 cm pipe is 2 m/s, find the quantity of water flowing through this pipe. Also find the velocity of water in 10 cm pipe if the velocity in 20 cm pipe is 1.5 m/s. 10 Module – II IV. a) A flow field is represented by a velocity potential function given by φ = 4 (x2 – y2). Determine the stream function for the same flow field. 10 b) A venturimeter 30 cm ×10 cm is used for measuring the discharge of oil (specific gravity = 0.85) passing through a vertical pipe in upward direction. The difference between the entrance and throat section of the venturimeter is 40 cm. The reading recorded by mercury manometer is 20 cm. Find the discharge and pressure 10 difference between the entrance and throat section . Take Cd = 0.97.
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V. a) Derive Darcy-Weisbach equation to compute the head loss in pipes due to friction.
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b) A pipe carrying water suddenly increases from 10 cm in diameter to 20 cm. Find out the loss of head due to sudden increase in diameter, if the discharge of water through the pipe is 150 liter/s. Also find out the pressure difference between the two sections. The pipe is horizontal. 10 Module – III VI. a) An external cylindrical mouthpiece 15 cm diameter is fitted to a tank. The head over the mouth piece is 5m maintained constant. Find the discharge through the mouthpiece and pressure head at vena-contracta.
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b) How are weirs classified ? c) A rectangular weir 0.75 m high and 1.5 m long is to be used for discharging water from a tank under a head of 0.5 m. Estimate the discharge when it is used as a i) weir without end contractions ii) weir with end contractions. Take Cd as 0.661 for both cases and neglect velocity of approach. VII. a) Derive Hagen-Poisueille equation.
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b) The velocity distribution in a boundary layer is given by u y = U δ
Where u is the local velocity at distance y from the boundary, U is the main stream velocity, δ is the nominal boundary layer thickness. Find out the displacement, momentum and energy thickness. 10 ______________