Summary Fluid mechanics, Short notes with PYQs and most important questions
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Course
Neet
Institution
Neet
Chapter fluid mechanics physics class 11, Neet preparation, Short notes with PYQs and most important questions. Best study material for preparation
All the best for your exam
• Fluids, Surface Tension, Viscosity & Elasticity:
f F A
Hydraulic press. p= = or F= ×f
a A a
Hydrostatic Paradox P= A P=
B PC
(i) Liquid placed in elevator: When elevator accelerates upward with acceleration ao then
pressure in
fluid, at depth 'h' may be given by,
=p h p [g + a 0 ]
B m [g + a 0 ]
and force of buoyancy,=
(ii) Free surface of liquid in horizontal acceleration:
a
tan θ = o
g
λa
p1 − p 2 = ρ a 0 where p1 and p2 are pressures at points 1and 2 Then h1 − h 2 =0
g
(iii) Free surface of liquid in case of rotating cylinder.
v 2 ω2 r 2
h =
=
2g 2g
Equation of Continuity a1v1 = a 2 v 2
221
, Fluid Mechanics & Properties of Matter
ln general av = constant
P 1
i.e., + V 2 + gh = constant
ρ 2
2gh
(vi) Torricelli's theorem - (speed =
of efflux) v = , A2 area
= of hole A1 area of vessel
A 22
1− 2
A1
Elasticity & Viscosity:
restoring force F
=stress =
area of the body A
change in configuration
Strain,∈=
original configuration
∆L
Longitudinalstrain =
L
∆V
=∈v volume
= strain
V
x
Shear strain : tan φ or φ =
F/A FL
1. Young's modulus of elasticity
= Y =
∆L / L A∆L
2. Bulk modulus :
Pressure
K=
Volume strain
The reciprocal of bulk modulus of elasticity is called compressibility. K solids > K liquids > K gases
Isothermal modulus of elasticity of gas K = P (pressure of gas)
C
Adiabatic modulus of elasticity of gas K = γ × P where γ = p
Cv
Tan gentialstress F/A F
Modulus of rigidity is given by
= η or η =
=
Shear strain φ Aφ
222
,Fluid Mechanics & Properties of Matter
1 1
Potential Energy per unit volume = ( stress × strain ) = ( Y × strain 2 )
2 2
Inter-Atomic Force-Constant k = Yr0
Thus, inter-atomic force-constant k is equal to the product of Young's modulus of the material of
the wire and the normal distance r0 between the atoms of the wire.
dv dv
Newton's Law of viscosity, F ∝ A or F = −ηA
dx dx
(10 dyne ) × s × (10 cm )
−2
η is called Coefficient of viscosity. 1 decapoise
= 1N= sm −2 5 2
= 10
1
dynes
= cm −2 10 poise; η ∝
T
2 r (ρ − σ) g
2
Stoke's Law F= 6πηrv Terminal velocity =
9 η
Surface Tension
Total force on eitheir of the imaginary line ( F ) ∆W
Surface tension (T) = ;T= S=
Length of the line ( ) A
Thus, surface tension is numerically equal to surface energy or work done per unit increase
surface area.
4T
Inside a bubble: ( p − p a ) = = p excess
r
2T
Inside a drop: ( p − p a ) = = p excess
r
2T
Inside air bubble in a liquid: ( p − p a ) = = p excess
r
2T cos θ
Capillary Rise: h =
rρg
If two parallel plates with the spacing 'd' are placed in water reservoir, then height of rise
2T
⇒ 2T = ρhdg or h =
ρdg
If two concentric tubes of radius 'r1' and 'r2' (inner one is solid) are placed in water reservoir, then
2T
height of rise ⇒ h =
( r2 − r1 ) ρg
r 2T cos θ
If weight of the liquid in the meniscus is to be consider : h + =
3 tρg
Capillary Rise in a Tube of insufficient Length :
When the capillary tube is cut and its length is less then h (i.e. h'), then the liquid rises upto the
top of the tube and spreads in such a way that the radius (R') of the liquid meniscus increases and
it becomes more flat so that hR = h'R'= Constant. Hence the liquid does not overflow
r r
If h ' < h then R ' > R or > ⇒ cos θ ' < cos θ ⇒ θ ' > θ .
cos θ ' cos θ
223
, Fluid Mechanics & Properties of Matter
Practical Questions
1. A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two
immiscible liquids, whose densities areρ1 and ρ2 (ρ1>ρ2) fill half the circle. The angle θ between the
radius vector passing through the common interface and the vertical is : (2018)
π ρ1 + ρ 2
(a) θ = tan −1
2 ρ1 − ρ 2
ρ1 − ρ 2
(b) θ = tan −1
ρ1 + ρ 2
−1 π ρ 2
(c) θ = tan
2 ρ1
ρ1
(d) θ = tan −1 π
ρ2
2. There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d1 and d2 are
filled in the tube. Each liquid subtends 900angle at centre. Radius joining their interface makes an angle
α with the vertical. Ratio d1/d2 (2014)
1 + sin α
(a)
1 − sin α
1 + cos α
(b)
1 − cos α
1 + tan α
(c)
1 − tan α
1 + sin α
(d)
1 − cos α
3. A wooden block, with a coin placed on its top, floats in water as shown m figure. The distance l and h
are shown there. After sometime the coin falls into the water. Then (2002)
224
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