Download Fluid mechanics-I - GH Raisoni College Of Engineering Nagpur

G.H.RAISONI COLLEGE OF ENGINEERING
Digdoh hills, Nagpur.
Fluid Mechanics - I----- Question Bank
UNIT - I
Q. No 1) Explain Newton ‘ s law of viscosity . What is the effect of temperature
on viscosity of water and that of air ?
2)
State and explain different types of fluid .
3) Explain the phenomenon of capillarity.
2) A body weighing 440 N with a flat surface area of 0.0095 m2 slides down a
lubricated inclined plate making a 30 0 angle with the horizontal . For viscosity
of 0.1 Ns/ m2 and body speed of 3m/s. Determine the lubricant film thickness.
3) If the velocity profile of a fluid over a plate is a parabolic described by equation
V = ay2 +by +c, where a , b, care constants, and y is the vertex of the parabola
which is equal to 250mm from the plate. The velocity at the vertex is given as
1.3m/s. Calculate the velocity
0,15,25cm from
4
gradients and shear stress at a distance of
the plate , if the kinematics viscosity of the fluid is 6.63×10-
m2/s. Take relative density of fluid = 126.
4) Calculate capillary rise in a glass tube of 3mm diameter when immersed in water.
Take surface tension for water as 0.07358 N/m . Find the percentage increase in
capillary rise if the diameter of glass tube is 2mm.
5) Two large plane surfaces are 20mm apart and the gap contains oil of dynamic
viscosity
0.60 Pa – s. A thin plate of cross sectional area 0.50m2 is to be pulled
through the gap at a constant velocity of 0.60m/s. The location of the plate will
have to be such that it is 8mm from one of the surfaces. Neglecting edge effects,
estimate the force required for pulling the plate as above.
6) The velocity profile of viscous fluid over a plate is parabolic with vertex 20cm
from the
plate, where the velocity is 120cm/sec. Calculate the velocity gradient
and shear stress at distance 0,5 and 15cm from the plate, given the velocity of the
fluid is 0.84 N – s/m2.
7) A body weighing 441.45 N with flat surface area of 0.095 m2 slides down an
inclined lubricated plan making an angle 30 0 with horizontal. For viscosity
0.1N-s/m2 and body speed of 3m/sec, determine the lubricant film thickness. Also
determine the viscosity when the angle is 40
0 with horizontal with same
thickness of oil film.
8) State and prove “ Pascals’s Law”.
9) What are the different ways in which pressure can be expressed ?
10) How is the pressure of a fluid measured ?& Explain each.
11) Explain the working of single column manometer with neat sketch.
12) Explain the use of “Inverted U-tube differential manometer” with a neat sketch.
Write the necessary gage equation .
13) The pressure between two points M&N in a pipe conveying oil of specific gravity
0.9 is measured by a U-tube manometer and the column connected to point M.A
pressure gauge attached at M reads 19.62 N/cm2, determine its reading when
attached o point N.Manometer liquid is mercury .
14) Two pressure points in a water pipe are connected to a manometer which has the
form of an inverted U-tube. The space above the water in the two limbs of the
manometer is filled with liquid of specific gravity 0.875. If the difference of level
of water columns in the two limbs is equal to 0.12m, what is the corresponding
difference of pressure?
15) Find the force required to lift a weight 20 kN by means of a hydraulic
press which has ram of 20cm diameter and plunger of 3cm diameter. If the
plunger has a stroke of 40cm and if it make 100 strokes per minute. Find the
power required at the plunger.
16) Pipe A carries a liquid of specific gravity 1.1 and is situated 10cm above another
pipe B which carries water. An inverted U- tube manometer containing a liquid of
specific gravity 0.7 on its upper portion is connected across these two pipes. If the
liquid in pipe A and rise 20 and 35 cm above the center line of their respective
pipes. Find the pressure difference between center line of the pipe.
UNIT - II
17) What will be the total pressure force on the surface of plan
for the
following
cases.
(i) Vertical plane surface submerged in liquid.
(ii) Horizontal plane surface submerged in liquid.
(iii) Inclined plane surface submerged in liquid.
18) An annular circular plate of 20m external diameter and 1m internal diameter is
immersed vertically in water so that its lowest edge is 5m below the water
surface. Determine the total force and position of center of pressure.
19) Show that for a plane submerged in a liquid, center of pressure always lies
below the centroid of the plane.
20) A vertical gate of width 2.0m and height 2.5m controls a sluice opening in a
dam. The top of the gate is 10m below the water surface.
If the gate width 80kN , find the vertical force required to lift the
gate. The coefficient of friction between the gate and the guides can be assumed
to be 0.25
( Neglect buoyancy effect on the gate).
21)Each gate of lock is 7mts high and 5mts wide and is supported by two hinges
which are situated at 0.25m and 6.75m above the bottom of the lock. When the
gates are closed they subtend an angle of 120O . The depths of water on the two
sides of the gate are 6m and 1.5 m respectively. Determine the magnitude,
position and the direction of the resultant water pressure on each gate. Find
also the reactions at the hinges and their directions.
Assume that the common reaction between the gates lies in the same
horizontal plane as that of the resultant water pressure.
22) A 60 O sector gate of 3.6 m redius is mounted on the spillway of dam as shown
in fig. Its hings and one of its end radial arm are at same horizontal level as
the water surface. What is the magnitude and direction of the resultant
pressure on the gate, if the length of the gate is 3 meters?
23) A triangular gate which has a base 1.5 m and an altitude of 2m lies in a
vertical plane with base horizontal . The vertex of gate is 1m below the surface
in a tank which contains oil of specific gravity 0.8. Find the force exerted by
oil on the gate and the position of center of pressure.
24) A 3.8m height by 1.6m wide rectriangular gate AB is vertical and is hinged at
a point 150mm below the center of gravity of the gate. The total depth of
water on the upstream side is 0.7m.What horizontal force must be applied at
the bottom of the gate for equilibrium.
25)Find the horizontal and vertical components of the water pressure exerted on
tainter gate of radius 4m as shown in figure. Consider width of gate unity.
26) Explain the term ‘ metacentric ‘ height.
27) Obtain the expression for determination of metacentric height for a floating
body.( Use analytical method )
28) Obtain the expression for determination of height for a floating body.( Use
experimental method)
29) Under what condition the following bodies will be stable.
i) Fully immersed body, ii) Partially immersed body.
30) Show that a cylindrical buoy of 1.5 m diameter and 3.0 m long weighing 24.5
KN will not float vertically in sea water of sp. Weight 10.10 KN .Find force
necessary in vertical chain attach at the center of base of the buoy that will
kept it vertical.
31) A wooden block of rectangular section 1.25m wide 2m deep , 4m long floats
horizontally in sea water. If the specific gravity of wood is 0.64 and water
1025 kg/ m ³ .Find the volume of liquid displaced and the position of center
of buoyancy.
UNIT - III
32) Show that the stream lines and equipotential lines intersect at right angles in
a flow net.
33) What is flow net ? Explain its importance.
34) Drive an expression for continuity equation for a three – dimensional flow.
35) (a) Define – Circulation and Vorticity.
(b) Explain – Source and Sink .
36) If the expression for the stream function is described by ψ = x³ 3xy².Determine whether the flow is rotational or irrotational .
37) The velocity vector in an incompressible flow is given by
V = ( 6xt + yz²) î + (3t + xy²)j + ( xy – 2xyz – 6tz ) ќ
i) Verify whether the continuity equation is satisfied.
ii) Determine the magnitudes of resultant velocity and acceleration at point A
( 2,1,2 ) at t = 2 sec.
38)Define potent6ial function Ø. If a given incompressible fluid flow,
Ø = 4 (x²-y²), find corresponding stream function ψ .
UNIT - IV
39) What are the different types of forces acting on fluid in motion ?
40) State Bernoulli’s theorem and derive Bernoulli’s equation from Euler’s
equation of motion.
41) What is momentum equation ?
42) What is the force excreted by a flowing fluid on pipe bend ?
43) Water flows through a 0.4 diameter pipe at the rate of 400 lit /s. If the pipe is
bent by 450 .Find the magnitude and direction of the resultant force at the
bent.
44) A pipe line 600 mm in diameter, conveying oil ( sp.gr.= 0.85 ) at a flow rate of
1800 lit/sec has a 900 bend in the horizontal plane . The pressure at the entrance
of the bend is 0.15N/mm² and the loss of head in the bend is 2.0m of oil. Find
the magnitude and direction of the force exerted by the oil on the bend .
45) Explain the working of pitot tube.
46) Derive the expression of pitot tube .
47) Explain the working of venturimeter with neat diagram.
48) Obtain an expression for discharge through horizontal venturimeter .
49) “ Coefficient of discharge of venturimeter is more than that of orifice meter .” Is
the statement correct ? If so justify your answer in brief .
50) Explain with reasons :51) A venturimeter is installed in a pipe line of 300mm diameter . The throat pipe
diameter ratio is 1/3. Water flows through the intallation. The pressure in the
pipe line is 137.7 Pa and vacuum in throat is 375mm of mercury. If 4% of the
differential head is lost between the gauges, find the rate of flow through the
pipe .
52) A 20x10 cm venturimeter is provided in a vertical pipe line carrying oil of
specific gravity 0.8 , the flow being upward. The difference in elevation of the
throat section and entrance section of the venturimeter is 50cm. The differential
U-tube mercury manometer shows a guage deflection of 40cm.
Calculate : (i) The discharge of oil. (ii) The pressure difference between the
entrance section and the throat section take. Take Cd = 0.98.
53)
An orifice meter with orifice diameter 10cm is inserted in pipe of 20cm
diameter. The pressure gauge s fitted upstream and downstream of the orifice
meter given readings of 19.62 N/cm2 and 9.81 N/m2 respectively. The coefficient of discharge for the meter is given as 0.6.Find the discharge of water
through pipe .
54) An orifice meter with orifice diameter15cm is inserted in pipe of 30cm diameter
. The pressure difference measured by a mercury oil differential manometer on
the two sides of the orifice meter gives a reading of 50 cm of mercury . Find the
rate of flow of oil of specific gravity 0.9 . When the efficient of discharge of the
meter = 0.64
UNIT - V
55) Give the classification of orifices.
56) Explain how will you determine the values of the different coefficients of a given
orifice.
57) Prove that discharge through mouthpiece is more than discharge through
orifice.
58) A venturimeter is installed in a pipe line of 300mm diameter. The throat pipe
diameter ratio is 1/3. Water flows through the intallation . The pressure in the
pipe line is 137.7Pa and vacuum in throat is 375 mm of mercury. . If 4% of the
differential head is lost between the gauges, find the rate of flow through the
pipe.
59) Show that pressure at vena contracta in an external mouth-piece is negative.
60) A tank 2.5m high standing on the ground is kept full of water . There is an
orifice in its vertical side at a depth “h” meter below the surface of water.
Find the value of ‘h’ in order that the jet may strike the ground of maximum
distance from the tank. Find also its value, if value of coefficient of velocity is
0.98. If coefficient of discharge is 0.68/,will be the rate of flow w.r.t.above
condition?
61) Explain , why Cd for a venturimeter is more than Cd for orifice meter.
62) A venturimeter is installed in a pipe line of 300mm diameter. The throat pipe
diameter ratio is 1/3. Water flows through the intallation . The pressure in the
pipe line is 137.7Pa and vacuum in throat is 375 mm of mercury. . If 4% of the
differential head is lost between the gauges, find the rate of flow through the
pipe line
Also determine the value of coefficient of discharge..
63) A cylindrical tank is having a hemispherical base. The height of cylindrical
portion is 4 m and diameter is 3 m. At the base of this tank, an orifice of
diameter 5 cm is fitted. Find the time required for completely empting the tank.
Take Cd =0.6 .
64) A rectangular vessel contains water to a depth of 1m. Determine the location of a
small orifice in the vertical side of the vessel , so that the jet issuing from the
orifice intersects the horizontal plane passing the base of the vessel at the
maximum distance from the vertical side.
65) A tank has two identical orifices each 5 cm in diameter in one of its vertical side
and are situated one above another. The upper orifice is 4m below water
surface and lower is 6m below water surface. The coefficients of contraction and
velocity are 0.64 and 0.98for both the orifices. Find
i) The combined rate of discharge from the two orifices
ii) The distance of the point of intersection of the two jets from the vertical
side.
66) A 60cm diameter cylindrical tank contains three liquids.
i) 0.3 m3 of liquid ‘ A ‘ with specific gravity 0.8
ii) 0.4 m3 of liquid ‘ B ‘ with specific gravity 1.2
iii) 0.5 m3 of liquid ‘ C ‘ with specific gravity 0.9
The liquids do not inter mix have clear interfaces. The cylindrical tank has a
10cm diameter orifice in its base. The orifice is covered with a lid. After
removing the lid, find the time that will elapse
i)
Before the central liquid flowing out the orifice
ii)
The central liquid stops flowing out the orifice. Take coefficient of
discharge equal to 0.59 .
67) Give the classification of Notch and Wier discharges.
68) Derive an expression for the discharge through a triangular notch .
69) Derive an expression for the discharge through a rectriangular notch
70) Derive the relation for error in measurements of discharge over a notch due to
error in measurement of head .
71) Explain with the help of sketch or write short note on
i) Broad crested weir.
ii) Ogee weir.
iii) Submerged weir or drowned weir.
iv) Cipolletti weir.
72) A 600 triangular weir has a coefficient of discharge of 0.59 . If accuracy of
measuring the angle is 10 , estimate the likely error in the estimated discharge if
head over the crest is 40cm.
73) A rectangular notch has a crest length 1m; the head over the notch is 0.2m and
height of the sill above the bed level is 0.15m . If the width of the channel is 1.2m,
calculate the discharge in cumec, taking into account the velocity of approach.
Take the coefficient of discharge 0.623.
74) A discharge of 100 lit/sec is to be measured by a triangular notch of vertex angle 600
. What would be the head is 1 mm, what error in discharge can be expected at this
level ?
75) A right angled V – notch is used for measuring a discharge of 30lit / sec. An error
of 2mm was made in measuring the head over the notch. Calculate percentage
error in the discharge. Take Cd = 0.62.
UNIT - VI
76) What is mean by ‘ Dimensional analysis , ? Explain its importance in practice.
77) Explain the methods of Dimensional analysis .
78) What do you mean by repeating variable in dimensional analysis? How are they
selected ?
79) What are the advantages of dimensional and model analysis ?
80) Using Buckingham ‘s π theorem , Show that velocity through a circular orifice is
given by –
V = √2gH Ø [ D/H, - µ / pVH]
Where H is the head causing f w, D is the diameter of the orifice, µ is the dynamic
viscosity, p is the mass density and g is the acceleration due to gravity.
81) By dimensional analysis show that Torque T on a shaft of diameter d, revolving at a
speed N in a fluid of viscosity v and mass density p is given by
T = pd 5 N2 Ø [ v/d2N ]
82) What are dimensionless numbers? Define them.
83) Derive from first principle the expression of :
i) Mach number ii) Weber number iii) Froude number.
84) What are the different laws based on which physical models can be constructed in the
laboratories ?
85) The height of a sand column is H and the effective pore size of the column is D. If
average discharge per unit area through the sand column of liquid of density p and
kinematic viscosity is ‘v’ prove that the loss of pressure p in the sand column can be
expressed as P = pv² / d² Ø vD/v, H/D
86) The drag F on a high velocity projectile depends upon the speed V of the projectile
density of fluid p, acoustic velocity C, diameter of projectile D and the viscosity of the
fluid H. Develop an expression for the drag.
87) The discharge Q through a small orifice depends upon the diameter d, head H, mass
density and dynamic viscosity of the fluid flowing through the orifice and the
gravitational acceleration g. Derive an expression for the coefficient of discharge Cd
as a function of dimensional parameters.
88) Using Buckingham’s π theorem, show that velocity through a circular orifice is given
by - V=√2gH Ø [D/H ,µ / pVH ]
Where H is the head causing f1 w, D is the diameter of the orifice, µ is the dynamic
viscosity, p is the mass density and g is the acceleration due to gravity.
89) By dimensional analysis show that Torque T on a shaft of diameter d , revolving at a
speed N in a fluid of viscosity v and mass density p is given by :
T = pd5 N2 Ø [v/d2 N]
90) What do you understand by turbulent flow ? What factor decides the type of flow in
pipe?
91) Oil of viscosity 0.1 Poise and specific gravity 0.9, flows through a horizontal pipe of
25mm diameter . If the pressure drop per meter length of the pipe is 12kpa ,
determine (a) the rate of flow in N/min. (b) the shear stress at the pipe wall (c)the
Reynolds number of the flow and (d) the power required per 50 m length of pipe to
maintain the flow.
92) What type of flow can be expected through a pipe of 200 mm diameter, carrying an
oil of kinematic viscosity 2.25 stokes at a mass rate of flow of 100N/s. Assume mass
density of oil as 800 kN/m3 ?
93) Write the characteristics of laminar flow.