GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV EXAMINATION — SUMMER 2020
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Subject Code: 2141906 Date:29/10/2020Subject Name: FLUID MECHANICS
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) Define the term continuum as applied to the mechanism of flow. Is the 03
continuum model valid in upper atmosphere?
(b) State and prove the Pascal’s law and give some examples where this 04
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principle is applied.(c) Explain the term total pressure action on a plane surface in a fluid at any 07
angle. Obtain an expression for this, and also for the corresponding depth
of the centre of pressure.
Q.2 (a) Derive Bernoulli’s equation from momentum equation. 03
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(b) Calculate the capillary effect in mm in a glass tube of 4 mm diameter, 04
when immersed in (1) water and (2) mercury. The temperature of the
liquid is 20 °C and the value of the surface tension of water and mercury
at 20 °C in contact with air are 0.073575 N/m and 0.51 N/m respectively.
The angle of contact for water is zero and for mercury is 130 degree.
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Take density of water 998 kg/m³.(c) State and explain stability criteria of submerged and floating bodies. 07
OR
(c) A cylinder 2 m in diameter x 3 m in length and supported as shown in 07
figure-1 retains water on one side. If the cylinder weighs 150 kN, make
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calculations for the vertical reactions at A and the horizontal reactions atB. Ignore the frictional effects.
Q.3 (a) Explain absolute, gauge and vacuum pressure. 03
(b) Sketch and describe a pitot-static probe and explain how it is used to 04
measure the fluid flow through a pipeline.
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(c) Give brief description of classification of fluid flows. 07
OR
Q.3 (a) Explain the difference between a simple and differential manometer. 03
(b) Explain the principle of dimensional homogeneity. Is dimensionally 04
homogeneous equation applicable in all systems of units?
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(c) Prove that for a steady laminar flow between two fixed parallel plates, 07
the velocity distribution across a section is parabolic and that the average
velocity is 2/3™ of the maximum velocity.
Q.4 (a) Explain surface tension with some examples. 03
(b) Obtain Darcy-Weisbach formula for head loss due to friction 04
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(c) The velocity components in a two-dimensional incompressible flow 07
field are expressed as u = y²+2x—x²y and v = xy’ —2y—x² .
Determine the velocity and acceleration at point P(x=1m , y=3m)
OR
Q.4 (a) What is meant by turbulence? How does it affect the flow properties? 03
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(b) Derive Euler’s equation of motion along a stream line. 04
(c) A multifluid manometer as shown in Figure-2. The tank is located on a
mountain at an altitude of 1400 m where the atmospheric pressure is 85.6
kPa. Determine the air pressure in the tank if h1 =0.1 m, h2 =0.2 m, and
h3=0.35 m. Take the densities of water, oil, and mercury to be 1000
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kg/m³, 850 kg/m³, and 13,600 kg/m³, respectively.Q.5 (a) Explain why air flowing at low velocities can be considered 03
incompressible?
(b) The efficiency n of a fan depends on the density p, the dynamic viscosity 04
µ of the fluid, the angular velocity ®, diameter D of the rotor and
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discharge Q. Express 1 in terms of dimensionless parameters.(c) Explain the terms: Mach number, Mach cone, Mach line and Mach angle 07
in the context of compressible flow.
OR
Q.5 (a) Explain the term Vorticity. 03
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(b) Derive the equation for momentum thickness 04
?=?d0(u/U0)(1-u/U0)dy
(c) A pipe carrying oil (Sp. Gr. 0.8) changes in diameter from 300 mm at 07
position 1 to 600 mm diameter at point 2 which is 5 metres at a higher
level. If the pressure at positions 1 and 2 are 100 kN/m² and 60 kN/m²
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respectively and discharge is 300 litres/sec. Determine : (i) loss of head(i1) direction of flow.
Figure 1
Water surface
Mercury
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