The document discusses fluid pressure and Stokes' law, highlighting its application in determining the speed of bodies falling through fluids and its relevance in experiments like Millikan's oil-drop experiment. It outlines the conditions for Stokes' law to be valid and its limitations, particularly in cases of high solid content and Brownian motion. Additionally, the document includes examples to illustrate the calculation of viscous forces on falling objects and the dynamics of terminal velocity.

1. FLUID PRESSURE

2. FLUID PRESSURE
EFFECTIVE FORCE ON A BODY FALLING IN ALIQUID :STOKES LAW
Viscous force limit the speed of body falling in a liquid
F = 6πηrv

3. FLUID PRESSURE
Importance of Stoke’s Law
Millikan employs this rule in his oil-drop experiment to
determine the electric charge
.
Working of a parachute is based on the principle of Stoke’s
Law.
Cloud formation and floating are explained using Stoke’s Law.

4. FLUID PRESSURE
v = 2r2 × (ρ−σ)g / 9η
where
ρ is the mass density of the sphere
σ is the mass densities of the fluid
r is the radius of the raindrop
Terminal velocity
The maximum constant velocity acquired by a
body while falling through a viscous medium is
called its Terminal Velocity.

5. FLUID PRESSURE
Conditions for Stoke’s Law
Conditions under which Stoke’s Law is valid are,
The fluid through which the body moves must have an infinite extension.
The body is perfectly rigid and smooth.
There is no slip between the body and the fluid. The motion of the body does not give rise to turbulent motion.
Hence, the motion is streamlined.
The size of the body is small, but it is larger than the distance between the molecules of the liquid. Thus, the
medium is homogeneous and continuous for such a body.

6. FLUID PRESSURE
Applications of Stoke’s Law
Velocity of Raindrops
Parachute
When we jump out of an aeroplane, a
parachute assists us in landing safely on the
ground
Terminal Velocity
When a body falls through a viscous fluid, it produces
relative motion between its different layers.

7. Limitations of the Stoke’s Law
FLUID PRESSURE
Stokes’ equation is invalid if the density difference in the equation is negative
When the solid content of a suspension is high, Stokes’ equation may not
show the real sedimentation rate. High solid content imparts additional
viscosity to the system, The equation contains only the viscosity of the medium
Dielectric Constant
Brownian Movement
Another aspect that can affect the precision of Stokes’ equation results is Brownian movement,
which is a spontaneous (zigzag) movement of particles floating in a fluid caused by collisions
with fast-moving atoms or molecules in the gas or liquid. Sedimentation is mitigated to some
degree by Brownian migration.

8. FLUID PRESSURE
1: A raindrop of radius 0.3 mm falls through the air with a terminal velocity of
1 m/s. The viscosity of air is 18 × 10-5 Poise. Find the viscous force on the
raindrop.

9. FLUID PRESSURE
2: A solid metal ball falling in a liquid column attains a terminal velocity of 3 m/s. Find
the viscosity of the liquid if the radius of the ball is r = 7 cm and its density is dl =
1000kg/m3 and the density of the metal ball is ds = 7050 kg/m3 (Take g = 10 m/s2)

10. Viscosity and Laminar Flow; Poiseuille’s Law
FLUID PRESSURE
Layers flow without mixing when flow is laminar