The document provides a comprehensive overview of fluid mechanics, covering topics such as the properties of fluids, pressure variations, Archimedes' principle, buoyancy, and the principles governing fluid dynamics. It details various formulas and concepts like Torricelli's law, Bernoulli's principle, and viscosity, alongside practical applications like the use of barometers and hydraulic lifts. Numerous questions and problems related to these topics are included to facilitate understanding and application of the concepts discussed.

1. BATCH
BASIC MATHS
FLUID
MECHANICS

2. 1. Liquids and gases can flow and are therefore, called
fluids.
Introduction
2. An Ideal Fluid is one which is
a) Incompressible
b) Non - Viscous

3. Pressure
Pressure is a scalar quantity

4. Unit Of Pressure
Unit Of Volume

5. Q1)

6. •Pressure in Fluids
When an object is submerged
in a fluid at rest, the fluid
exerts a force on its surface.
This force is always normal to
the object’s surface

7. •Density of Fluids

8. •The relative density of a substance is the ratio of its
density to the density of water at 4oC.
•Relative Density /specific gravity

10. Q2)

11. •Variation of Fluid Pressure with depth

12. a) P=Po +𝝆g(1)
b) P=Po +𝝆g(2)
c) P=Po +𝝆g(
𝟏
𝟐
)
d) P=Po
Q3)

13. •Graph between P and h

14. •Gauge Pressure and Absolute Pressure

15. Q4)

16. Q5)

17. a) 5km
b) 8km
c) 11km
d) 13km
Q6)The density of the atmosphere at sea level is 1.29 kg/m3
. Assume that it does not change with altitude. Then how
high would the atmosphere extend?
h

19. Q7)

20. a) maximum in vessel A
b) maximum in vessel B
c) maximum in vessel C
d) equal in all vessels
Q8)The three vessels shown in the following figure have
same base area. Equal volumes of a liquid are poured in. The
force on the base will be

21. Q9)

23. a) 5x105 N
b) 25x105 N
c) 5x106 N
d) 2.5x106 N
Q10)The force acting on a window of area 50 cm x 50 cm of a
submarine at a depth of 2000 m in an ocean, the interior of
which is maintained at sea level atmospheric pressure is
(Density of sea water= 103kg m-3 , g=10 m/s2)

25. •Variation of Fluid Pressure along the same
Horizontal Level
For a liquid in equilibrium the pressure
is same at all points in a horizontal
plane. Suppose the pressure were not
equal in different parts of the fluid, then
there would be a flow as the fluid will
have some net force acting on it. Hence
in the absence of flow the pressure in
the fluid must be same everywhere in a
horizontal plane.

26. Q11)

27. •U – tube problems

28. Q12)

30. Q13)

31. Q14)

33. Q15)Find x , so
that fluid remains
in equilibrium
a) 1 cm
b) 2cm
c) 3cm
d) 4cm
9
cm
9
cm
 = 1g/cm3
 = 2g/cm3
Sliding boundary

x
x

34. 9
cm
9
cm
 = 1g/cm3
 = 2g/cm3
Sliding boundary

x
x

35. Q16)

36. •Variation of Pressure in vertically
accelerating Fluid –

38. •Variation of Pressure in horizontally
accelerating Fluid –

39. Q17)

40. i. Maximum at (ii) minimum at
(a) (i) B (ii)D
(b) (i)C (ii)D
(c) (i)B (ii)C
(d) (i)B (ii)A
Q18)A closed rectangular tank is completely filled with water
and is accelerated horizontally with an acceleration towards
right. Pressure is

41. Shape of Liquid Surface due to horizontal
acceleration

43. Q19)

44. • Torricelli devised a method for
measuring atmospheric pressure.
• A long glass tube closed at one
end and filled with mercury is
inverted into a trough of mercury
• This device is known as ‘mercury
barometer’.
•Barometer

45. • In the experiment it is found that the mercury column in the
barometer has a height of about 76 cm at sea level
• A pressure equivalent of 1 mm is called a torr
(after Torricelli). 1 torr = 133 Pa.

46. •Manometer

47. •Pascal’s Law
“ Whenever external pressure is applied
on any part of a fluid contained in a
vessel, it is transmitted undiminished
and equally in all directions”

48. •Hydraulic Lift

49. Q20)Two pistons of a hydraulic machine have diameters 20 cm and
2 cm. Find the force exerted on the larger piston when 50 kg wt is
placed on the smaller piston. When the smaller piston moves
through 50 cm, by what distance the other piston moves out?

51. •Upthrust / Buoyancy

52. When a body is immersed wholly or
partially in a fluid, it is lifted up by a
force equal to the weight of fluid
displaced by the body.
•Archimede’s Principle

53. a) 300N
b) 100 N
c) 75N
d) 10N
Q21) A Stone of density 3000 kg/m3 is submerged in
water.If the mass of stone is 30kg , find upthrust.

54. a) 50N
b) 80N
c) 40N
d) 10N
Q22)An iron cube of mass 5kg and side 10 cm is
suspended by a thread in water. Find the tension in
thread.

55. Q23)

57. •Apparent Weight Of a Body
When a body is wholly immersed in a fluid,
it’s effective weight decreases.

58. •Apparent Weight formulae

59. a) 1200 N
b) 1000 N
c) 850 N
d) 812 N
Q24)A stone of density 3000 kg/m3 is lying submerged in
water of density 1000 kg/m. If the mass of stone in air is 150
kg, calculate the force required to lift the stone.

61. Q25)

63. •Condition for floatation & sinking

64. •Law Of Floatation

65. •For Cylindrical or cubical body

66. Q26)

67. Q27)

69. Q28)

71. Q29)

74. REMEMBER

75. Q30)

77. Q31)

79. Fluid Dynamics

80. Steady Flow / Streamlined Flow / Laminar Flow
At different points,
➢ velocities of fluid particles
can be different.
➢ But velocity at a given
point is constant with time

81. • The flow of the fluid is said to be steady if at any given
point, the velocity of each passing fluid particle remains
constant in time
• This does not mean that the velocity at different points
is same. The velocity of a particular particle may change
as it moves from one point to another.
• That is, at some other point the particle may have a
different velocity, but every other particle which passes
through same point behaves exactly as the previous
particle that has just passed that point.

82. Properties Of Streamline Flow

83. (iv)

84. (i)
(ii)
Turbulent Flow

86. Reynolds Number →dimensionless number

87. Equation Of Continuity

89. Volume Rate of Flow

90. Q32)

91. Q33)

93. Q34)

95. BERNOULLI’S PRINCIPLE
We now suppose that an incompressible ,
Non – Viscous and Irrotational fluid is
flowing through the pipe in a steady flow

97. Different Heads

98. For Fluid at Rest

99. In a Horizontal Pipe

100. Q35)

101. Q36)

103. Q37)

105. MENTOZ METHOD

106. Q38)

108. Q39)

109. (density of air = 1kg/m3)
Q40)

111. Q41)

113. Venturimeter The Venturi-meter is a device to measure the
flow speed of incompressible fluid.

116. Q42) The speed of Water at X is 30cm/s . Find the speed of
water at Y , if difference in heights of two coloumns of
water is 2 cm.
a) 70 cm/s
b) 65 cm/s
c) 80 cm/s
d) 100 cm/s

117. Q43)The Area of cross section of wide and narrow
portions of the tube are 5cm2 and 1cm2 respectively. The
rate of flow of water through the tube is 500 cm3/s. Find
the difference in heights of two coloumn.
a) 0.1 m
b) 0.6m
c) 0.9m
d) 1.2m

119. Speed of Efflux: Torricelli’s Law
OPEN TANK / VESSEL
Very small hole

120. Rate of Flow

121. Q44)

122. Q45)

124. Q46)

125. Q47)

126. Range

127. a) 10 cm
b) 8 cm
c) 9.8 cm
d) 980 cm
Q48)Figure shows two holes in a wide tank containing a liquid in
common. The water streams coming out of these holes strike
the ground at the same point. The height of liquid column in
tank is

129. Maximum Range

130. Time taken to empty the tank

131. a) 9 min
b) 7 min
c) 5 min
d) 3 min
Q49)A rectangular vessel when full of water, takes 10 min to be
emptied through an orifice in its bottom. How much time will
it take to be emptied when half filled with water?

132. Q50)

134. Velocity of Efflux in closed container

136. Viscosity

137. Viscous Force -
1)Viscosity is internal friction in a fluid
motion
2)It occurs due to relative motion
between layers of liquid
3)The internal friction force in fluids is
called Viscous Force.
4)Viscous Force depends on relative
motion between layers (velocity
gradient) , Area of contact between
two layers and type of fluid.

138. Velocity profiles of fluids-
1) A layer of liquid sandwiched
between two parallel glass plates,
in which the lower plate is fixed
and the upper one is moving to
the right with velocity v

139. For any layer of liquid, its upper layer pulls it forward
while lower layer pulls it backward. This results in force
between the layers. This type of flow is known as
laminar.

140. Coeffecient of Viscosity
The viscosity of liquids decreases with temperature, while it
increases in the case of gases.

141. 2) velocity distribution for viscous flow in a pipe

142. Q51)

144. Stoke’s Law
When an object moves
through a fluid , it
experiences a viscous force
It is seen that the viscous force
is proportional to the velocity
of the object and is opposite to
the direction of motion.

145. Terminal velocity

147. Terminal velocity VS radius and time

148. If density of sphere is less than that of fluid

149. We consider a raindrop in air. It
accelerates initially due to gravity. As
the velocity increases, the retarding
force also increases. Finally, when
viscous force plus buoyant force
becomes equal to the force due to
gravity, the net force becomes zero
and so does the acceleration. The
sphere (raindrop) then descends with
a constant velocity
Rain drops

150. Q52)

151. Q53)

153. Q54)

155. Q55)

156. Q56)

158. Q57)