Fluid Mechanics
1. Define viscosity
state and explain Newton’s Law of viscosity. [11-sp, 06-sp, 04-sp, 10-Apr, 03-Apr,
00-Oct]
2. Derive an
expression for the depth of centre of pressure from free surface of liquid of
an inclined planed surface submerged in the liquid. [11-Oct, 07-Sep, 94, 95]
3. Find an expression
for the drag force on smooth sphere of diameter D, Moving with uniform velocity
v fluid density ρ and dynamic viscosity μ. [11-Oct, 10-Oct, 04-Sep]
4. State and
prove Bernoulli’s equation. List the assumption, you made during derivation.
[11-Oct, 12-Apr, 11-Apr, 10-Oct, 09-Oct, 08-Oct, 07-May, 05-Sep, 04-Sep, 03-Set,
02-Oct]
5. Derive an
expression for mass flow rate of compressible fluid thorough an orifice or
nozzle to a large tank, what is the condition for maximum rate of flow?
6. Write down
dimension in terms of fundamental quantities of the following both in M-L-T and
F-L-T system: mass, angular velocity, discharge, stream function, force,
density, specific weight, absolute viscosity, shear stress, thermal conductivity,
pressure, energy, surface tension, mass flow-rate, torque and moment. [11-Apr,
08-Oct, 06-May, 83, 96]
7. Using Buckingham’s π-theorem, show that the velocity through a
circular orifice is given by, where H=heat of flow, D=diameter of orifice,
μ=absolute viscosity, ρ=density & g=acceleration due to gravity. [11-Apr,
09-Apr, 04-May]
8. What is the meant
by “Most economical Section” of an open channel? How is it determinal? [11-Apr,
09-Apr, 05-Sep, (p-771)]
9. Differentiate between: (1) frictional force and viscous force; (2)
Dynamic viscosity and kinematic viscosity; (3) Newtonian fluid and
non-Newtonian fluid. [10-Oct]
10. Illustrate briefly the importance of dimension less numbers in
analyzing the characteristics of different fluid flow problems and fluid
machineries. [10-Oct, (p-294)]
11. Deduce the expression for a flew through a v-notch? * Triangular notch. [10-Oct, 04-May (u 11)]
12 Show that for the most economical rectangular channel section (1) The
depth of flow is equal to half the base width; (2) Hydraulic radius is equal to
half the depth. [10-Oct (p: 771-772)]
13 What is centre of pressure? Prove that for an inclined plane surface
submerged in a static fluid, center of pressure in always below center of
gravity. [10-Apr, 02-Apr]
14 Deduce the continuity equation for a control volume in differential
form. [10-Apr]
15 compare between an orifice-meter and a venture-meter? [10-Apr,
(p-232)]
16 Deduce an equation for the actual flow rate of water through a
venture-meter inclined at an angle of 30 degree with the horizontal. [10-Apr]
17 What is Buckingham’s π-theorem? Give its merits and demerits over
Rayleigh’s method. [10-Apr, 02-Apr]
18 What are the conditions for maximum velocity and maximum discharge
through a circular open channel? Prove these conditions. [10-Apr, 09-Apr, 06-May,
(p: 791-93)]
19. Prove that the steady laminar flow through a circle pipe, the
velocity distribution across the section is parabolic and the average velocity
is half the maximum local velocity. [10-Apr]
20. derive an
expression for the hydrostatic force on a submerged plane surface. Also, derive
the expression for the respective centre of pressure. [09-Oct]
21. Derive an
expression for the velocity profile of a fully developed laminar flow in a
pipe. List all the assumptions made derive the expression for: a) the maximum
velocity; b) the average velocity; c) the Pressure drop; d) the head loss.
[09-Oct]
22. Derive an
expression of word done for the force exerted by a jet of water which strikes a
flat plate with a velocity v, when the plate moves with a velocity u and is
inclined at an angle θ. [09-Apr]
23. Deduce the
conditions for the rectangular channel of best section? [09(Apr)]
24. Find an expression of pressure ratio in terms of “mach number” in the
upstream and downstream of a normal shock wave. [09-Apr]
25. What is metacentric
height? Derive an expression to calculate it. [08(Oct), 06(May), 04(Sep)]
26. Show that the
maximum efficiency of the jet striling normally on a series of flat plates mounted
on the periphery of a wheel is 50%. [05-Oct]
27. Show that for a
laminar flow through a pipe of radius, the average velocity of flow occurs at a
distance of from the centre. [08-Oct]
28. What is meant by “critical flow” in a nozzle for air flow through a
convergent divergent nozzle? Find an expression to relate area ratio & Mach
number considering critical flow. [08-Oct]
29. For the flow through a pipe, the pressure drop per unit length AP/L,
depends on the pipe diameter D, the pipe roughness k, the average velocity v,
the fluid density ρ, the fluid viscosity μ find the group of dimensionless
numbers. [08-Apr]
30. Show that the Reynolds number VD/μ is the ratio of inertia force and
viscous force. [08-Apr]
31. Fond the condition for the most economical trapezoidal channel
section. [08-Apr]
32. Explain briefly the following types of equilibrium of floating
bodies a) stable equilibrium b) unstable equilibrium c) Neutral equilibrium d)
Meta centre. [07-Sep, 06-May, 03Sep]
33. A care of specific gravity so is floating in water with its apex
downwards. It has a radius R, and vertical height H, show that for stable
equilibrium of cone. and , where h is the
depth of immersion & 2α is the apex angle. [07-Sep]
34. Define the following dimensionless number and state their
significance for fluid flow problems: a) Reynolds number b) Fraud’s number c)
Mach’s number. [07-Sep, 05-Sep]
35. The velocity distribution in a pipe is given by where the symbols have their usual meaning.
Obtain an expression for average velocity in terms of. [07-Sep, 04-Sep]
36. The frictional torque T of a disc of diameter D, rotating at a speed
of N in a fluid of viscosity μ & density ρ in a turbulent flow is given
by , Prove this by the method of
dimensional analysis. [07-May]
37. Derive Hagen Poiseulle equation and state the assumptions. [12-Apr,
07-May]
38. Prove that in case of forced vortex, the nise of liquid level at the
ends y equal to the fall of liquid level at the axis of rotation. [12-Apr,
06-Sep, 04-Sep]
39. Describe an orifice-meter and find an expression for measuring
discharge through a pipe with this device. [06-Sep]
40. What is a pitot tube? How is it used to measure velocity of flow at
any point in a pipe? [06-Sep]
41. Show that co-efficient friction for laminar flow through a circular
pipe is given by where Re is the
Reginald’s number. [06-Sep]
42. For a trapezoidal channel of most economic section prove: a) Half of
top width to length of one of the sloping sides. b) Hydraulic mean depth is
equal to half the depth of flow. [06-Sep, 03-Sep]
43. The discharge Q of a centrifugal pump depends on the mass density of
fluid ρ, speed of the pump N, the diameter of impeller D, the menometric H and
the viscosity of the fluid μ, show that . [06-May, 03-Apr]
44. Derive an expression for discharge through a stepped rectangular
notch having width of with depth of the
flow respectively. [06-May]
45. What is Chezy’s formula is an open channel flow? Derive it. [06-May]
46. What Newtonian, Non-Newtonian & plastic fluids. Show them on a
shear stress vs velocity gradient point. [05-Sep]
47. Define the terms: Vortex flow, forced vortex, free vortex. [05-Sep]
48. Write short note: a) Moody diagram b) Orifice-meter c) pitot static
tube d) Meta Centric Height e) Total head. [05-Sep. 05-May, 02-Apr]
49. What is the difference between centre of pressure & centre of
gravity? [05-May]
50. What are minor losses? Find an expression to determine the loss of
head due to friction a uniform pipe for turbulent flow. [05-May (p-503,504)]
51. What do you understand by optimum shape of cross section for an open
channel? Find the conditions of optimum cross section for a trapezoidal
channel. [05-May]
52. What are the different type of similarities which may exist between
a model and a prototype? Explain the different similarities. [05-May]
53. Explain the
different type of energies of a fluid in motion. Derive the Fuller’s equation
for steady flow along a streamline. [05-may]
54. What do you
understand by the terms “viscosity & viscosity index”? [04, 03-Sep]
55. Using Bernoulli’s
equation show how velocity of fluid is measured by pitot tube. [04-Sep]
56. What is meant by
the best hydraulic cross-section for an open channel? [04-Sep]
57. Obtain an
expression of velocity profile for laminar flow through a circular pipe and
show that the centre line velocity is double the average velocity. [04-May]
Another
Question
58. What is an
impulse momentum equation? What are its applications? [12-Apr]
59. Show that the
hydraulic mean depth of trapezoidal channel having the best propotion is half
of the minimum depth. [12-Apr]
60. How do you
differentiate between a laminar flow and turbulent flow? Derive the most
commonly used equation for velocity distribution for laminar flow through
pipes. Hence show that averaged velocity through the pipe is half the central
line velocity. [11-Apr]
61. When liquid in a
cylindrical container is subjected to constant angular rotation, the liquid
surface at the periphery of the cylinder rises to the same amount as the centre
dips in the middle “show this analytically. [11-Apr]
62. Explain why liquid
column mano-meters of different kinds are for the measurement of small
pressures. [08-Apr]
63. Derive an
expression of the depth of paraboloid formed by the surface of a liquid
contained in a cylindrical tank which is rotated at a constant angular speed ω
about its vertical axis. [07-Sep]
64. Define kinematic
viscosity, dynamic viscosity, capillarity and monometry. [06-May]
65. Define Buckingham
π-theorem. Using Buckingham π-theorem prove that power supplied by a pump is
given by where γ is specific weight. Q
is volume flow rate & H is total head. [04-May]
66. Deduce an equation
for the actual flow through a triangular notch? [04-May]
67. Using the method
of dimensional analysis obtain an expression for discharge Q over a rectangular
weir, the discharge depends on head, H over the weir, acceleration due to
gravity g, length of weir erest L, height of weir oner (70) the channel bottom Z and kinematic
viscosity v of the liquid. [03-Sep]
68. Derive an
expression for the universal velocity distribution for a flow through a
circular pipe.[03-Sep]
69. Derive an
expression for the reaction between the gets as
where P is the resultant force due to water acting at night angels to
the gate and α is the angel of inclination of gate to normal side of lock.
[03-Apr]
70. Prove that the when
liquid contained in cylindrical tank at a constant angular velocity ω the rise
of the liquid level at the end is equal to the fall of liquid at the axis of
rotation. [03-Apr]
71. Prove that the
enor in discharge due to enor in the measurement of head over a triangular
notch given by . [03-Apr]
72. Derive an
expression for mass flow rate of compressible fluid through a nozzle to a large
tank. What is the condition for the maximum flow rate? [03-Apr]
73. Explain Bulk
modulus of elasticity with reference of fluid. [02-Oct, 02-Apr]
74. Difference between
pressure head and velocity head. [02-Oct]
75. Prove that the
centre of pressure of a fully submerged uniformly thick plane lamina is always
below the centre of gravity of the lamina. [02-Oct]
76. For laminar flow derive an expression for the friction
co-efficient in terms of the Reynold’s
number. [02-Apr]
77. Draw schematic
diagram of an orifice-meter, find an expression for the actual flow rate
through a venture-meter inclined at an angel of 30 degree with the horizontal.
[02-Apr]
78. What is minor loss? Derive an expression for the loss of head due to
sudden contraction of pipe. [02-Apr]
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