YS IC S
PH RY
IG A TO
E ST
INV EC T
PR O J
L A W
O K E S
S T
o p r a
t y a Ch
A g a s
XI I - A
4
ACKNOWLEDGEMENT
I would like to sincerely thank
Ma’am Bhavana Kapoor for giving me the
opportunity to work on this physics project. It has
strengthened my understanding of scientific
concepts, research, teamwork, and critical thinking.
I am also grateful to Naveen Sir for his support
during the practical work, .
My sincere thanks go to my parents for their
unwavering encouragement and support during this
journey. Lastly, I would like to thank my school for
providing all the necessary resources and a
nurturing environment that made this project
possible.
CERTIFICATE
This is to certify that
Agastya Chopra, a student of
Standard 12th -A of
Montfort School, has successfully
completed the project titled
Stokes Law under the valuable
guidance of
Ma’am Bhavana Kapoor.
Teacher’s Signature Student’s Signature
INDEX
1. Apparatus
2. Theory
3. Procedure
4. Observations
5. Calculations for Glycerine
6. Calculations for Water
7. Graphs -r² versus V
8. Result
9. Precaution
10. Discussion
APPARATUS
A wide and tall cylinder about 4
cm dia. and 1.2 m long, tight fitting
rubber cork with a centrally
fitted glass tube about 1 cm long
and 1 cm diameter, stop watch of
least count 0.1 s , two rubber
bands, half metre scale, (0° to 50°C
range) thermometer , glycerine
,water , forcep and China dish, 10
steel balls of known diameters
varying between 2 mm to 4 mm.
Stokes' Law
THEORY
Statement of Stokes' Law:
Stokes' Law describes the drag force exerted by a viscous fluid
on a small spherical object moving through it. It states that the
force is directly proportional to the velocity of the object, the
radius of the sphere, and the viscosity of the fluid.
The equation for Stokes' law is:
F=6πηrv
Where:
F = Drag force (resistance force) exerted by the fluid
η = Viscosity of the fluid
r = Radius of the spherical object
v = Velocity of the object
π = Mathematical constant Pi
Archimedes' Principle
Archimedes' Principle states that the upward buoyant force
acting on an object submerged in a fluid is equal to the weight
of the displaced fluid.
The net upward buoyant force is:
F_b = (ρ_f - σ) (4/3) π r³ g
Where:
F_b = Buoyant force
ρ_f = Density of the fluid
σ = Density of the spherical object
r = Radius of the spherical object
g = Acceleration due to gravity
Derivation of Viscosity
At terminal velocity, the downward gravitational
force is balanced by the upward buoyant force and
the drag force. Using the net buoyant force from
Archimedes' principle and the drag force from Stokes'
law:
(ρ_f - σ) (4/3) π r³ g = 6 π η r v
Simplifying and solving for viscosity η:
η = ( ρ_f - σ ) r² g / 9 v
Viscosity Definition:
Viscosity is a measure of a fluid's resistance to flow,
quantifying the internal friction that resists
deformation when a shear force is applied. It is
measured in units of Pa·s (Pascal-seconds).
PROCEDURE
1. Fit the rubber cork in the mouth of the wide
bore glass tube after filling it with glycerine and
pass the small tube through it . Fix the tube
vertically in a stand.
2. Fix tWO rubber bands at points A & B, such that
A is 50 cm from B.
3. Now take five balls of different size such that
each can easily pass through the glass tube N.
4. Arrange them in order of increasing radius r and
measure their diameters with a screw gauge in two
mutually perpendicular directions and take the
mean for each ball. Dip the balls in a small quantity
of glycerine. Rinse the balls thoroughly into the
liquid otherwise balls are likely to develop air
bubbles on their surfaces as they enter the liquid
column.
5. Take tHE stop watch . Start with the ball of
smallest diameter. Using forceps, drop the ball
through the narrow glass tube N so that it falls
centrally through the glass cylinder. After moving
through a few centimeters, the ball will attain a
uniform velocity. As soon as the ball passes down the
rubber band A, start the stop watch one & As soon as
the ball reaches rubber band B, stop the stopwatch
6.From this find the velocity of the ball. As v = 1/t.
7. Repeat the experiment by dropping five more balls
of gradually increasing diameters.
8. Calculate the terminal velocity of each ball
9. Repeat the experiment with water at room
temperature.
OBSERVATIONS
Least count of screw gauge = .......... cm
Least count of stopwatch = .......... s
Room temperature (θ) = .......... °C
Density of material of steel ball (ρ) = .......... g/cm³
Density of glycerine (σ) = .......... g/cm³
Density of water (α) = .......... g/cm³
Zero error of screw gauge = ..........cm
Diameter of steel ball(d)- Radius of steel ball(r)- Velocity(v)
Length(l) = 50 cm - Time taken to travel length AB(t)
For Glycerine
For Water
CALCULATIONS
GLYCERINE
CALCULATIONS
WATER
GRAPHS : r² vs V
For Glycerine
For Water
RESULT
The coefficient of viscosity (η) of water at room temperature (θ) = .......... poise.
The coefficient of viscosity (η) of glycerine at room temperature (θ) = .......... poise.
The actual coefficient of viscosity for water (from standard tables) = .......... poise.
The actual coefficient of viscosity for glycerine (from standard tables) = .......... poise.
|Observed value − Actual value|
%age error = ————————————————---------------- x100
Actual value
Percentage error for water = .......... %
Percentage error for glycerine = .......... %
PRECAUTIONS
1. The spherical balls should be small. Their diameters
should be measured by a screw gauge.
2. The radius of wide bore tube through which balls
fall should be very large compared to radii of the
balls.
3. The balls should fall centrally and not touch the
walls of the glass tube.
4. The liquid used should be highly viscous.
5. The temperature of the liquid should be noted as
the viscosity of liquids changes appreciably with the
change of temperature.
DISCUSSION
1. Ensure that radius of wide bore tube
R is much larger than r, the radius of
the ball dropped.
2. The ball must be made fully wet in
viscous liquid otherwise air bubbles will
get attached to the ball as it falls in
viscous liquid. This will affect the actual
value of terminal velocity.
3. The balls selected for the experiment
should be spherical otherwise Stoke's
law (F₁= 6πρην) would not be valid.xt
