Fluid Mechanics - Basic Concept of Fluid Mechanics
Exam Duration: 45 Mins Total Questions : 30
The expression \((p+\rho gz+\frac{\rho V^{2}}{2})\) commonly used to express Bernoulli's equation, has units of total energy
per unit
- (a)
mass
- (b)
weight
- (c)
volume
- (d)
cross-sectional area of flow
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
Resultant pressure of the liquid in case of an immersed body acts through which one of the following?
- (a)
Centre of gravity
- (b)
Centre of pressure
- (c)
Metacentre
- (d)
Centre of buoyancy
What is buoyant force?
- (a)
Lateral force acting on a submerged body
- (b)
Resultant force acting on a submerged body
- (c)
Resultant force due to water on a body
- (d)
Resultant hydrostatic force on a body due to fluid surrounding it
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)
\(T=\frac{\pi \mu \omega R^{4}}{2h}\)
In given figure determine the pressure of air inside the tank on the basis of given data. Given, h1 = 10 cm, h2 = 150 ern, h3 = 60 cm and specific gravities of fluids are SHg = 13.6, Sw = 1, Soil = 0.75.
- (a)
3.58 kPa
- (b)
-3.58 kPa
- (c)
2.67 kPa
- (d)
-2.67 kPa
Given,l1 = 0.2 m,l3 = 0.3 m, h1 = 0.675 m h2 = 0.45 m, h3 = 0.225 rn, PA = 15.3 kN/m2 then, Pa is
- (a)
115.3 kN/m2
- (b)
96 kN/m2
- (c)
108 kN/m2
- (d)
100 kN/m2
If the given body floats then, percentage volume of body above the water surface is
- (a)
7.2%
- (b)
9.3%
- (c)
8.9%
- (d)
6.2%
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,equilibrium is
- (a)
stable
- (b)
unstable
- (c)
neutral
- (d)
Cannot be determined
Of the possible irrotational flow functions given below, the incorrect relation is (where \(\Psi\) = stream function and \(\phi\) = velocity potential)
- (a)
\(\Psi=xy\)
- (b)
\(\Psi=A(x^{2}-y^{2})\)
- (c)
\(\phi=ur cos\theta+\frac{u}{r}cos\theta\)
- (d)
\(\phi=(r-\frac{2}{r})sin \theta\)
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)
\({ \triangledown }^{ 2 }\phi \ne0,{ \triangledown }^{ 2 }\Psi \ne0\)
How is the difference of pressure head h measured by a mercury-oil differential manometer expressed?
- (a)
\(h=x(1-\frac{S_{g}}{S_{0}})\)
- (b)
h=x(Sg-S0)
- (c)
h=x(S0-Sg)
- (d)
\(h=x(\frac{S_{g}}{S_{0}}-1)\)
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
A glass tube with a 900 bend is open at both the ends. It is inserted into a flowing stream of oil, S = 0.90, so that one opening is directed upstream and the other is directed upward. Oil inside the tube is 50 mm higher than the surface of flowing oil. The velocity measured by the tube is, nearly
- (a)
0.89 m/s
- (b)
0.99 m/s
- (c)
1.40 m/s
- (d)
1.90 m/s
The components of rotation for a three-dimensional flow field \(V_{R}=(y^{2}+z^{2})\overset{\wedge }{i}+(x^{2}+z^{2})\overset{\wedge }{j}+(x^{2}+y^{2})\overset{\wedge }{k}\)
at (1, 2, 3) are
- (a)
ωx= -1 rad/s, ωy= 2 rad/s, ωz= -1 rad/s
- (b)
ωx= -1 rad/s, ωy= -1 rad/s, ωz= 2 rad/s
- (c)
ωx = -2 rad/s, ωy = -1 rad/s, ωz = -2 rad/s
- (d)
ωx = 2 rad/s, ωy = -2 rad/s, ωz = -1 rad/s
If velocity potential \(\phi\) = x2 - y2 then, stream function \(\Psi\) is
- (a)
\(\Psi=2xy^{2}\)
- (b)
\(\Psi=2x^{2}y\)
- (c)
\(\Psi=2xy\)
- (d)
\(\Psi=2x/y\)
In a Pitot tube, stagnation pressure head is 6 m and static pressure head is 5 m. Then, velocity of flow in tube is
- (a)
4.34 m/s
- (b)
4.87 m/s
- (c)
4.21 m/s
- (d)
4.42 m/s
In the given figure,
V1 = 21 mis, d1 = d2, Z1 = 1 m, Z2 = 2 m, P1 = 30 N/cm2, P2 = 10 N/cm2. Take p = 1000 kg/m3, 9 = 10 m/s2. Then, head loss between 1 and 2 is
- (a)
12 m
- (b)
No loss
- (c)
17 m
- (d)
19 m
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 turbulent boundary layer thickness varies as
- (a)
x4/5
- (b)
x1/5
- (c)
x1/2
- (d)
x1/7
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\(\frac{1}{8}L\)
Boundary layer is defined as
- (a)
a thin layer at the surface where gradients of both velocity and temperature are small
- (b)
a thin layer at the surface where velocity and velocity gradients are large
- (c)
a thick layer at the surface where velocity and
temperature gradients are large - (d)
a thin layer at the surface where gradients of both velocity and temperature are large
The velocity profile in a laminar boundary layer is given by \(\frac{u}{U}=\frac{y}{\delta }\).The ratio of momentum thickness to displacement thickness for the boundary is given by which one of the following?
- (a)
2:3
- (b)
1:2
- (c)
1:6
- (d)
1:3
If Reynolds number is 1600, then coefficient of friciton is
- (a)
0.01
- (b)
0.001
- (c)
0.10
- (d)
None of these
The laminar boundary Iayer thickness \(\delta\) at any point x for flow over a flat plate \((\frac{\delta}{x})\) is given by
- (a)
\(\frac{0.664}{\sqrt{Re_{x}}}\)
- (b)
\(\frac{1.328}{\sqrt{Re_{x}}}\)
- (c)
\(\frac{1.75}{\sqrt{Re_{x}}}\)
- (d)
\(\frac{5.0}{\sqrt{Re_{x}}}\)
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,pressure gradient is
- (a)
7000
- (b)
5000
- (c)
6000
- (d)
8000
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,displacement thickness is
- (a)
\(\delta^{x}=s\)
- (b)
\(\delta^{x}=2\delta\)
- (c)
\(\delta^{x}=\delta/2\)
- (d)
\(\delta^{x}=\delta^2\)
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,energy thickness is
- (a)
\(\delta^{xx}={\delta}/{4}\)
- (b)
\(\delta^{xx}={\delta}/{7}\)
- (c)
\(\delta^{xx}={\delta}/{3}\)
- (d)
\(\delta^{xx}={\delta}/{8}\)