Mechanical Properties Of Fluids
Lecture - 6
i. The property of the liquid by virtue of which it opposes the relative
motion between its adjacent layers is known as viscosity.
ii. Internal tangential force which try to retard the relative motion
between the layers is called viscous force.
iii. Viscosity comes into play only when there is a relative motion
between the layers of the same material. This is why it does not act
in solids.
Newton’s Law Of Viscosity
I. Suppose a liquid is flowing in stream-lined motion on a horizontal
surface OX. The liquid layer in contact with the surface is at rest
while the velocity of other layers increases with increasing distance
from the surface OX. The highest layer flows with maximum
velocity.
II. Let us consider two parallel layers R S vx + vx
PQ and RS at distances z and z+z z
Q vx
from OX. Thus the change in P
velocity in a perpendicular
distance z is v. The rate of z
change of velocity with distance
perpendicular to the direction of
, is called velocity- O X
∆𝑉
flow is
∆𝑍
gradient.
III. Now let us consider a liquid layer of area A at a height z above OX.
The layer of the liquid immediately above it, tends to accelerate it
with a tangential viscous force F, while the layer immediately below
it tends to retard it backward with the same tangential viscous
force F.
z F
IV. According to Newton,
𝐹 ∝ 𝐴
∆𝑉
𝐹 ∝
∆𝑍
∆𝑉
⇒𝐹 ∝𝐴
∆𝑍
∆𝑉
⇒𝐹=𝜂𝐴
∆𝑍
Here 𝜂 = coefficient of viscosity
V. The coefficient of viscosity of a liquid is defined as the viscous force
per unit area of contact between two layers having a unit velocity
gradient.
VI. The viscosity of liquids decreases with rise in temperature but the
viscosity of gases increase with rise in temperature.
VII. Newtonian fluids are fluids which obey Newton’s law of viscosity.
VIII. ηL > ηG
SI Unit : Kg/m-sec or Poiseuille
CGS Unit : g/cm-sec or Poise
1 Poiseuille = 10 Poise
Non Newtonian Fluid
Q. If boat has contact area with water surface of 10 m² and boat is moving
with a speed of 2 m/s in water depth of 1 m. Find a tangential force
required to move the boat with constant speed. (ηw = 0.01 Poise)
Q. A Square plate of 0.1 m side moves parallel to a second plate with a
relative velocity of 0.1 m/s both plates being immersed in the water. If
the viscous force is 0.002 N and coefficient of viscosity is 0.01 poise,
what is the distance between the plates?
Q. A metal block of area 0.10 m2 is
connected to a 0.010 kg mass via a
string that passes over an ideal
pulley (considered massless and
frictionless). A liquid with a film
thickness of 0.30 mm is placed
between the block and the table.
When released the block moves to
the right with a constant speed of
0.085 m s-1. Find the coefficient of
viscosity of the liquid.
Stoke’s Law
i. When a body falls through a liquid the, forces act upon the body
are:
a) Weight of the body
b) Buoyant force
c) Viscous force
ii. Since viscous force depends on the velocity of the body, the body
attains a constant velocity called terminal velocity.
iii. According to Stoke’s law if a spherical body of radius ‘r’ is moving
with a velocity ‘v’ in a homogeneous medium of viscosity ‘η’ then
viscous force acting on it is:
Calculation Of terminal Velocity :
Consider a small spherical body of radius ‘r’ and density ‘ρ’ falling in a
fluid of density ‘σ’ and coefficient of viscosity ‘η’. When it attains the
terminal velocity (VT), net force on it becomes zero.
Q. Raindrop reaching ground with terminal velocity has momentum P
another group of twice videos which terminal velocity has momentum:
A) 4P
B) 8P
C) 16P
D)
. 32P
Previous Year Question - NEET
Q.14 A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is
produced due to viscous force. The rate of production of heat when the sphere
attains its terminal velocity, is proportional to -
2018
(A) r3 (B) r2 (C) r5 (D) r4
𝒅(𝑯𝒆𝒂𝒕) Ans. [C]
= Power by viscous force
𝒅𝒕
= – 6rv.v
= – 6r[v2] (v r2)
