Basic Concept of Fluid Mechanics
Exam Duration: 45 Mins Total Questions : 30
A differential manometer as shown in figure below is used to measure the difference in pressure at points A and B in terms of specific weight of water w. The specific gravities of the liquids x, y and z are respectively, S1,S2 and S3·
The correct difference \((\frac{P_{A}}{W}-\frac{P_{a}}{W})\) is given by
- (a)
h3S2 - h1S1 + h2S3
- (b)
h1,S1 + h2S3 - h3S2
- (c)
h3S1 - h1S2 + h2S3
- (d)
h1S1 + h2S2 - h3S3
The normal stress is the same in all directions at a point in a fluid only when
- (a)
the fluid is frictional
- (b)
the fluid is frictionless and incompressible
- (c)
the fluid has zero viscosity and is at rest
- (d)
one fluid layer has not motion relative to an adjacent layer
A wooden rectangular block of length L is made to float in water with its axis vertical. The centre of gravity of the floating body is 0.15 L above the centre of buoyancy. What is the specific gravity of the wooden block?
- (a)
0.6
- (b)
0.65
- (c)
0.7
- (d)
0.75
How is the metacentric height, GM expressed?
where, I = moment of inertia of the plane of the floating body at the water surface
V = volume of the body submerged in water
BG = distance between the centre of gravity
(G) and the centre of buoyancy (B)
- (a)
GM = BG - (I/V)
- (b)
GM = (V/I) - BG
- (c)
GM = (I/V) - (BG)
- (d)
GM= BG - (V/I)
Consider the following statements related to the stability of floating bodies:
1. The metacentre should be above the centre of gravity of the floating body for stable equilibrium during small oscillations.
2. For a floating body, stability is not determined simply by the relative positions of centre of gravity and centre of buoyancy.
3. The position of metacentre of a floating body is fixed irrespective of the axis of oscillations.
4. Large value of metacentric height reduces the period of roll of the vessel.
Which of these statements are correct?
- (a)
1 and 3
- (b)
2 and 4
- (c)
1, 2 and 4
- (d)
1, 2, 3 and 4
A tank has in its side a very small horizontal cylinder fitted with a frictionless piston. The head of liquid above the piston is h and the piston area a, the liquid having a specific weight \(\gamma\). What is the force that must be exerted on the piston to hold it in position against the hydrostatic pressure?
- (a)
2\(\gamma\)ha
- (b)
\(\gamma\)ha
- (c)
\(\frac{2\gamma \ ha}{3}\)
- (d)
\(\frac{\gamma \ ha}{3}\)
A circular disc of radius R is kept at small height h over a oil of viscosity μ. Torque required to move the disc with angular velocity ω is
- (a)
\(T=\frac{\pi \mu \omega R^{4}}{2h}\)
- (b)
\(T=\frac{\pi \mu \omega R^{2}}{2h}\)
- (c)
\(T=\frac{\pi \mu \omega^{2} R^{4}}{h^{2}}\)
- (d)
\(T=\frac{\pi \mu \omega R^{4}}{2h}\)
A solid cylinder (d = 2 m, h = 2 m) is floating in water with its axis vertical. If specific gravity of cylinder is 0.65 then,metacentric height is
- (a)
0.110 m
- (b)
0.273 m
- (c)
0.157 m
- (d)
0.191 m
In a two-dimensional flow, the velocity components in X and Y-directions in terms of stream function (\(\Psi \)) are
- (a)
\(u=\frac{\partial \Psi }{\partial y}, v=\frac{\partial \Psi}{\partial y}\)
- (b)
\(u=\frac{\partial \Psi }{\partial y}, v=\frac{\partial \Psi}{\partial x}\)
- (c)
\(u=-\frac{\partial \Psi }{\partial y}, v=\frac{\partial \Psi}{\partial x}\)
- (d)
\(u=\frac{\partial \Psi }{\partial x}, v= -\frac{\partial \Psi}{\partial y}\)
While measuring the velocity of air (p = 1.2 kg/m3 ), the difference in the stagnation and static pressures of a Pitot static tube was found to be 380 Pa. The velocity at that location is
- (a)
24.03 m/s
- (b)
4.02 m/s
- (c)
17.8 m/s
- (d)
25.17 m/s
For irrotational and incompressible flow, the velocity potential and stream functions are given by \(\phi\) and \(\Psi\)respectively. Which one of the following sets is correct?
- (a)
\({ \triangledown }^{ 2 }\phi =0,{ \triangledown }^{ 2 }\Psi =0\)
- (b)
\({ \triangledown }^{ 2 }\phi \ne0,{ \triangledown }^{ 2 }\Psi =0\)
- (c)
\({ \triangledown }^{ 2 }\phi =0,{ \triangledown }^{ 2 }\Psi \ne0\)
- (d)
\({ \triangledown }^{ 2 }\phi \ne0,{ \triangledown }^{ 2 }\Psi \ne0\)
Euler equation for water turbine is derived on the basis of
- (a)
conservation of mass
- (b)
rate of change of linear momentum
- (c)
rate of change of angular momentum
- (d)
rate of change of velocity
Which one of the following statements is true to a two-dimensional flow of ideal fluids?
- (a)
Potential function exists if stream function exists
- (b)
Stream function mayor may not exist
- (c)
Both potential function and stream function must exist for every flow
- (d)
Stream function will exist but potential function may or may not exist
For an irrotational flow, the velocity potential lines and the streamlines are always
- (a)
parallel to each other
- (b)
coplanar
- (c)
orthogonal to each other
- (d)
inclined to the horizontal
If velocity potential ф=x (2y -1) then stream function will be
- (a)
\(\Psi=x^{2}+y^{2}-y\)
- (b)
\(\Psi=y^{2}-y-x^{2}\)
- (c)
\(\Psi=y^{2}+y-x^{2}\)
- (d)
\(\Psi=y^{2}-x^{2}\)
If u = ax2 + by and w = 0, then velocity in Y-direction is (v = 0 at y = 0)
- (a)
-2a2xy
- (b)
-2axy
- (c)
-2axy2
- (d)
-2a (xy)2
If velocity potential \(\phi\) = x2 - y2 then,Select the correct option.
- (a)
Flow is possible and rotational
- (b)
Flow is possible and irrotational
- (c)
Flow is not possible
- (d)
Cannot be determined
A closed cylinder of radius R and height H is completely filled with water. It is rotated about its
vertical axis with angular speed co, Now, determine, total pressure force exerted by water on the top
surface.
- (a)
\(\frac{\rho \omega^{2} \pi R^{4}}{4}\)
- (b)
\(\frac{\rho \omega^{2} \pi R^{2}}{4}\)
- (c)
\(\frac{\rho \omega.\pi^{2} R^{4}}{4}\)
- (d)
Zero
The water is flowing through a pipe having 1= 100 m and diameter at lower end = 300 mm and at upper end = 600 mm at the rate of 50 L/s. If pressure at higher level is 19.62 N/cm2 then, pressure at lower level is (slope of pipe is 1 in 30)
- (a)
20.6 N/cm2
- (b)
50 N/cm2
- (c)
22 N/cm2
- (d)
30 N/cm2
All experiments far indicate that there can be a laminar flow in a pipe, if the Reynolds number is
- (a)
2300
- (b)
40002000
- (c)
2000
- (d)
40000
The equivalent length of the stepped pipeline shown in the figure below, can be expressed in terms of the diameter D as
- (a)
5.25 L
- (b)
9.5 L
- (c)
33\(\frac{1}{32}L\)
- (d)
33\(\frac{1}{8}L\)
The head loss in a sudden expansion from 6 cm diameter pipe to 12 cm diameter pipe in terms of velocity v1 in the smaller diameter pipe is
- (a)
\(\frac{3}{16}.\frac{v^{2}_{1}}{2g}\)
- (b)
\(\frac{5}{16}.\frac{v^{2}_{1}}{2g}\)
- (c)
\(\frac{7}{16}.\frac{v^{2}_{1}}{2g}\)
- (d)
\(\frac{9}{16}.\frac{v^{2}_{1}}{2g}\)
Laminar developed flow at an average velocity of 5 m/s occurs in a pipe of 10 em radius. The velocity at 5 cm radius is
- (a)
7.5 m/s
- (b)
10 m/s
- (c)
2.5 m/s
- (d)
5 m/s
If Reynolds number is 1600, then coefficient of friciton is
- (a)
0.01
- (b)
0.001
- (c)
0.10
- (d)
None of these
Syphon tube is shown in figure.
Select the correct option for this figure.
- (a)
Pc > Patm
- (b)
Pc= Patm
- (c)
Pc < Patm
- (d)
Pc = 0
A fluid flowing through pipe has flow rate 3.5 L/s. Fluid has viscosity 0.1 N-s/m2 and relative density 0.9. If diameter of pipe is 50 mm and length 300 m then,pressure drop in length of 300 m is
- (a)
70.4 N/cm2
- (b)
68.4 N/cm2
- (c)
81 N/cm2
- (d)
zero
A fluid flowing through pipe has flow rate 3.5 L/s. Fluid has viscosity 0.1 N-s/m2 and relative density 0.9. If diameter of pipe is 50 mm and length 300 m then,shear stress at pipe wall is
- (a)
30 N/m2
- (b)
20 N/m2
- (c)
28 N/m2
- (d)
zero
A fluid of viscosity 0.72 N-s/m2 and specific gravity 1.34 is flowing through a circular pipe of diameter 100 mm. The maximum shear stress at pipe wall is given as 200 N/m2 then,average velocity in m/s is
- (a)
5.4
- (b)
3.4
- (c)
7.1
- (d)
2.9
In the given figure, arrangements are shown to maintain the flow rate 5 x 10-4 m3/s. Level of water H should be (f = 0.0295)
Consider all losses in above figure, value of (H1-H2) is (if f = 0.008)
- (a)
100 m
- (b)
50 m
- (c)
30 m
- (d)
40 m
The velocity distribution in the boundary layer is given by \(\frac{u}{U}=\frac{y}{\delta}\) where u is velocity at distance y from the plate.\(\delta\) is boundary layer thickness. Then,momentum thickness is
- (a)
\(\theta=\frac{\delta}{2}\)
- (b)
\(\theta=\frac{\delta}{6}\)
- (c)
\(\theta=\frac{\delta}{3}\)
- (d)
\(\theta=\frac{\delta}{4}\)
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