1. Viscosity

2. Fluid Resistance
An object moving through or on a fluid meets resistance.
Force causes the fluid to move.
The velocity is proportional to the force. F vx

3. Velocity Gradient The resistance tends to keep the fluid in place.
Law of inertia
The fluid moves most near the object and least farther away.
This is a velocity gradient. F vx y

4. Law of Viscosity Newton combined these two proportionalities.
This is the law of viscosity.
A is the area of the solid sliding on the fluid
The constant h is the dynamic viscosity and depends on the type of fluid. F vx y

5. Poiseuille’s Law
Flow in a tube is affected by sides in all directions.
The relationship between velocity and distance is
The total volume flow rate is r P1 vx P2 L

6. Drag Kinetic friction is a constant force.
If there is a net force an object would accelerate forever
Air resistance causes a friction called drag.
At low velocity drag is proportional to velocity, Fd = bv
At higher velocity drag goes as velocity squared, Fd = cv2
The direction of drag force is opposite to the velocity.

7. Falling Leaves The drag coefficient depends on the surface area.
Large surfaces – high drag
Leaves
Feathers
Papers
Small surfaces – low drag
Stones
Balls
Bullets

8. Drag Force Objects falling through a fluid reach terminal velocity.
For low speeds this is due to viscocity.
Stokes’s Law describes the drag force. Fd Fb Fg

9. Terminal Velocity
An object may fall through the air at constant velocity.
By the law of inertia the net force is zero.
The force of drag must balance the force of gravity.
This velocity is called the terminal velocity.
Fg = -mg