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ME406 USN M S 0 M S RAMAIAH INSTITUTE OF TECHNOLOGY (AUTONOMOUS INSTITUTE, AFFILIATED TO VTU) BANGALORE - 560 054 SEMESTER END EXAMINATIONS - JUNE 2010 Course & Branch BE (MECHANICAL ENGINE ERING ) Se me ster Subject : FLUID MECHANICS Ma x. Mar ks : 10 0 Subject Code : ME406 Du rati on : 3 hr IV Instructions to the Candidates: Answer One Full Question From Each Unit. UNIT-I 1. a) Explain the terms dynamic viscosity and kinematic viscosity with their units. (04) b) Explain vapour pressure and cavitation. (04) c) Derive an expression for capillary rise /fall. (04) d) A vertical gap 2.2cm wide of infinite extent contains a fluid of viscosity 2.0 (08) N-s/m2 and specific gravity 0.9. a metallic plate 1.2 m x 1.2m x 0.2 cm is to be lifted up with a continuous velocity of 0.15m/s through the gap. If the plate is in the middle of the gap, find the force required, considering the weight of the plate equal to 40N. 2. a) Explain an inverted differential manometer to measure pressure in pipes (06) which are at different levels, with different fluids in pipes. b) Derive an expression for the depth of canto of pressure from free surface of (06) liquid of an inclined plane surface submerged in liquid. c) A circular plate 3.0 meter diameter immersed in water in such way that its (08) greatest and least depth below the the free surface are 4.Om and 1.5m respectively. Determine the total pressure on one face of the plate and position of centre of pressure. UNIT-II 3. a) Show that the distance between the meta centre and centre of buoyancy (06) and is given by BM=I/V where, I in the moment of inertia of the floating body and V is the submerged volume of the body. b) Explain the conditions of equilibrium of a floating body. (06) c) A solid cylinder of diameter 4.Om has a height of 4m. find the meta centric (08) height of the cylinder if the specific gravity of the material of cylinder = 0.6 and it is floating in water with it axis vertical. State the condition of equilibrium. 4. a) Obtain an expression for continuity equation for 3 dimensional flow in (06) Cartesian co-ordinates. b) State and prove Bernoull's theorem from energy consideration. State the (06) assumptions made. c) The water is flowing through a taper pipe of length 100m having diameter of (08) 60 cms at upper end and 30 cm at the lower end, at the rate of 50 literes/sec. The pipe has a slope of 1 in 30. Find the pressure at the lower end, if the pressure at the higher end is 19.62 N/cm2. Consider the datum line passing through the centre of the lower end of pipe. Page 1 of 2 M E406 UNIT-III 5. a) Derive an expression for the rate of flow through venturimeter in horizontal (06) position. b) Obtain an expression for the discharge over a triangular notch. (06) c) A horizontal venture meter with inlet dia 20 cm and throat dia 10cm is used (08) to measure the flow of oil of specific gravity 0.8. The discharge of oil through venturi meter is 60 Its/sec. Find the reading of the oil mercury differential manometer. Take Cd=0.98. 6. a) Explain with a neat sketch Hydraulic gradient line and total energy line. (06) b) Derive Darcy's formula for the loss of head due to friction in pipes. (06) c) An oil of specific gravity 0.9 and viscosity 0.06 poise is flowing through a (08) pipe of diameter 20cm at the rate of 60 Its/sec. Find the head lost due to friction for a 500m length of pipe. Find the power required to maintain the 0.79 flow when Re >4000 , and f = Re 0.25 ' UNIT-IV 7. a) What is Reynold's number and obtain.the expression for the same. (06) b) Derive an expression for the velocity of flow of viscous fluid through a (06) circular pipe, hence show by sketch the velocity distribution. c) Water is flowing through a pipe of dia 30cm at a vel of 4m/s. Find the (08) velocity of the oil flowing in another pipe of dia 10cm, if the condition of dynamic similarity in satisfied between the two pipes. The viscosity of water and oil is given as 0.01poise and 0.025 poise. The specific gravity of oil is 0.08. 8. a) State and prove Buckingham ' s Pi- theorem and obtain the expression for the (06) same. b) Explain the different types of similarities. (06) c) The frictional torque T of a disc of dia D rotating at a speed N in a fluid of (08) viscosity ,u and density p in a turbulent flow in given by T=D5N2 pO D2Np J Prove this by the method of dimensional analysis. ) UNIT-V Derive an ex pressio n for velocity of sound wave in a fluid. Consider one b) . dimensional case. Explain propagation of pressure wave in a compressible fluid when M is <1, =1 & >1, hence draw a Mach cone. 10 a) b) Explain boundary layer with different zone when fluid flows over a thin flat plate placed parallel to the direction of flow. Derive an equation for the energy thickness, in the case of fluid flowing over a flat plate. **************** Page 2 of 2

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