Stokes Law

to apply Stokes formula when solving experiment, calculation and qualitative problems

Viscosity
Velocity gradient
Shearing stress
Absolute viscosity
Kinematic viscosity
Resistive force
Cohesion or Intermolecular forces
Molecular collisions

https://www.youtube.com/watch?v=uXTjOpmlyZw

It is the quantity that describes a fluid’s resistance to flow.
A fluid with a higher viscosity flows slowly; while a fluid with low viscosity flows fast.

We can say:
The water is less viscous than oil.
The water is thinner than oil.
Vice versa, we can say:
The oil is more viscous than water.
The oil is thicker than water.

Absolute Viscosity
Kinematic Viscosity

It is sometimes called dynamic viscosity or simple viscosity.
It is the ratio of the shearing stress to the velocity gradient of the fluid.
It uses the symbol “eta” ( η ).

Suppose that we have two plates separated by a layer of liquid (d) with a certain viscosity (η).

A horizontal force is then applied to the moving plate.

The force required to move the upper plate distorts a portion of the liquid from its original shape.

Which layer of liquid has the highest velocity? Lowest velocity?

It is the ratio of the shearing stress to the velocity gradient of the fluid.
It uses the symbol “eta” ( η ).

For a fixed speed v, the force required to move the upper plate is equal to:

An increase in fluid viscosity, increases the force required.

An increase in the contact area of the plate, increases the force required.

An increase in velocity, increases the force required.

An increase in the liquid layer, decreases the force required.

Its SI unit is Pascal second [ Pa·s ]
But its most common unit is dyne second per square centimeter [ dyne·s·cm-2 ] or poise [P].

It is the ratio of the viscosity of a fluid to its density.
It uses the symbol “nu” ( ν ).


Its SI unit is meter square per second [m2/s].
Its most common unit is centimeter square per second [ cm2/s ] or stokes [St].

A falling body accelerates due to the force of gravity.
However, the presence of air yields two opposing forces:
Bouyant force
Resistive force (Air friction)

Since air friction increases as speed increases, the resultant force acting on the body will eventually be equal to zero.
At that instance, the body moves at its maximum constant velocity or terminal velocity.

If we assume that the falling body is a small sphere with radius r falling slowly at a speed of v through a fluid of viscosity η, its resistive force can be determined by:

where:
Fr is the resistive force
η is the viscosity of the fluid
r is the radius of the sphere
v is the velocity of the falling sphere

The block of ice (temperature 0°C) shown below is drawn over a level surface lubricated by a layer of water 0.10 mm thick. Determine the magnitude of the force F needed to pull the block with a constant speed of 0.50 m/s. At 0°C, the viscosity of water has the value of 1.79 x 10-3 N·s/m2.

The viscous force on an oil drop is measured to be equal to 3.0 x 10-15 N when the drop is falling through with a speed of 4.5 x 10-4 m/s. If the diameter of the drop is 5.0 x 10-6 m, what is the viscosity of air?

oil drop

Using the relationship:
𝑣𝑣=𝑘𝑘 𝑑 2 𝑑𝑑 𝑑 2 2 𝑑 2
On our next lesson, we will find out the value of k and its consistency by dropping marbles of different diameters into a container of oil.

THANK YOU!