ViscosityViscosity

Fluid ResistanceFluid Resistance

An object moving through or An object moving through or on a fluid meets resistance.on a fluid meets resistance.

Force causes the fluid to Force causes the fluid to move.move.

The velocity is proportional The velocity is proportional to the force.to the force.

Fvx

F

vx

Velocity GradientVelocity Gradient

The resistance tends to keep The resistance tends to keep the fluid in place.the fluid in place.• Law of inertiaLaw of inertia

The fluid moves most near The fluid moves most near the object and least farther the object and least farther away.away.

This is a velocity This is a velocity gradientgradient..

yvx

yvx

F

Law of ViscosityLaw of Viscosity

Newton combined these two Newton combined these two proportionalities.proportionalities.

This is the law of viscosity.This is the law of viscosity.• AA is the area of the solid is the area of the solid

sliding on the fluidsliding on the fluid

The constant The constant is the is the dynamic viscositydynamic viscosity and and depends on the type of fluid.depends on the type of fluid. y

vAF x

yvx

F

Poiseuille’s LawPoiseuille’s Law

Flow in a tube is affected by Flow in a tube is affected by sides in all directions.sides in all directions.

The relationship between The relationship between velocity and distance isvelocity and distance is

The total volume flow rate is The total volume flow rate is

)(4

22 rRL

Pvx

rvxP1 P2

L

L

PR

t

V

8

4

Drag ForceDrag Force

Objects falling through a fluid Objects falling through a fluid reach terminal velocity.reach terminal velocity.

For low speeds this is due to For low speeds this is due to viscocity.viscocity.

Stokes’s Law describes the Stokes’s Law describes the drag force.drag force.

Fg

FbFd

rvFd 6

Surface TensionSurface Tension

Liquid molecules attract Liquid molecules attract each other.each other.

At the surface this force is At the surface this force is the the surface tensionsurface tension..• Force per length parallel to Force per length parallel to

the surface.the surface.

• Constant for different liquidsConstant for different liquids

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