Subject Code: 2141906
GUJARAT TECHNOLOGICAL UNIVERSITY
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BE - SEMESTER-IV (NEW) EXAMINATION - WINTER 2018
Subject Name: Fluid Mechanics
Time: 02:30 PM TO 05:00 PM
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) Define: Specific gravity, Density, Cavitation [03]
(b) Explain surface tension and derive its equation for liquid droplet. [04]
(c) State and derive Pascal’s law with usual notations. States its applications. [07]
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Q.2 (a) What are the advantages and disadvantages of manometers as pressure measuring instrument? [03]
(b) A body of dimensions 2m x 2m x 1m, weights 1970 N in water. Find its weight in air. Find its mass. [04]
(c) Derive an equation of continuity for three dimensional Cartesian coordinate system. [07]
OR
(c) Derive equation of total pressure and center of pressure for vertical submerged body. [07]
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Q.3 (a) Classify fluid flows. [03]
(b) A stream function is given by ? = 5x - 6y. Calculate magnitude and direction of resultant velocity. [04]
(c) Derive the expressions for discharge over a Triangular notch. [07]
OR
(a) Define path line, stream line and streak line. [03]
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(b) Derive Euler’s equation of motion along a stream line. [04]
(c) A horizontal Venturimeter 20 cm x 10 cm is used to measure the flow rate of oil having specific gravity 0.9. The discharge through the venturi meter is 3600 liters / minute. Find the reading of oil — mercury differential manometer. Take Cd=0.98. [07]
Q.4 (a) Define following non dimensional numbers: Reynold’s Number, Weber’s Number, Froude’s Number [03]
(b) List out minor losses for flow through pipe and explain any one in detail. [04]
(c) For viscous flow through pipe, derive equation of velocity distribution and prove that ratio of maximum velocity to average velocity for this flow is 2. [07]
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OR
(a) Explain the phenomenon of water hammer. [03]
(b) An aeroplane is flying at an height of 15 km where the temperature is — 50 °C. Speed of the plane is corresponding to M = 2. Assuming k = 1.4 and R = 287 j/kg K, find the speed of the plane. [04]
Date: 01/12/2018
Total Marks: 70
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Q.5 (c) Show that pressure drop ?P for laminar flow depends upon the velocity, density and roughness. Using Buckingham’s theorem obtain expression of ?P. [07]
Q.5 (a) Determine the head lost due to friction in a pipe using Chezy’s formula. Diameter and length of pipe = 300 mm and 50 m Velocity of water flowing in pipe = 2.5 m/s Chezy’s constant = 60 [03]
(b) What are repeating variables? How are they selected for dimensional analysis? [04]
(c) Prove the velocity of a sound wave in a compressible fluid is given by C = v(?RT) [07]
OR
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Q.5 (a) Distinguish between free vortex flow and forced vortex flow. [03]
(b) A crude oil of viscosity 0.1Ns/m² and relative density 0.9 is flowing through a horizontal circular pipe of diameter 60 mm and length 200 m. calculate the difference of pressure at the two ends of the pipe if flow rate through the pipe is 4 liters/s. [04]
(c) Derive Darcy-Weisbach equation for head loss due to friction in pipe flow. [07]
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