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Viscosity
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
vx  F
Velocity Gradient

The resistance tends to keep
the fluid in place.
F
• Law of inertia
vx


The fluid moves most near
the object and least farther
away.
This is a velocity gradient.
vx  y
y
Law of Viscosity


Newton combined these two
proportionalities.
This is the law of viscosity.
F
vx
• 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.
vx
F  hA
y
y
Poiseuille’s Law

Flow in a tube is affected by
sides in all directions.
r

The relationship between
velocity and distance is
vx 

P 2 2
(R  r )
4hL
The total volume flow rate is
V R 4 P

t
8hL
P1
vx
L
P2
Drag Force
Fb

Objects falling through a fluid
reach terminal velocity.

For low speeds this is due to
viscocity.

Stokes’s Law describes the
drag force.
Fd
Fg
Fd  6hrv
Surface Tension


Liquid molecules attract
each other.
At the surface this force is
the surface tension.
• Force per length parallel to
the surface.
• Constant for different liquids
insect leg on water
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