Archimedes’ Principle

Physics 202Professor Lee

CarknerLecture 2

PAL #1 Fluids Column of water to produce 1 atm of

pressure P = gh

P = = 1000 kg/m3

g = 9.8 m/s2

h = Double diameter, pressure does not change

On Mars pressure would decrease

Mars has smaller value of g

Archimedes’ Principle The fluid exerts a force on the object

Called the buoyant force If you measure the buoyant force and the

weight of the displaced fluid, you find: An object in a fluid is supported by a buoyant

force equal to the weight of fluid it displaces Applies to objects both floating and

submerged

Will it Float?

What determines if a object will sink or float?

An object less dense than the fluid will float A floating object displaces

fluid equal to its weight

A sinking object displaces fluid equal to its volume

Floating How will an object float?

The volume of fluid displaced is proportional to the ratio of the densities

Example: ice floating in water,

iVig=wVwg

Vw=Vi (i/w)

w = 1024 kg/m3 and i = 917 kg/m3

Vw=

Continuity For a moving fluid

Energy must be conserved

Mass must be conserved so,Av = constant

Av= constant = R = volume flow rate

called the equation of continuity Flow rates in and out must always balance out

Moving Fluids

Constricting a flow increases its velocity

Because the amount of fluid going in must equal the amount of fluid going out

Fluids also must obey energy conservation

Pressure work Kinetic energy

Bernoulli’s Equation Consider a pipe that bends up and gets wider at

the far end with fluid being forced through it

Wg = -mg(y2-y1) = -gV(y2-y1)

Wp=Fd=pAd=pV=-(p2-p1)V

(1/2mv2)=1/2V(v22-v1

2) Equating work and KE yields,

p1+(1/2)v12+gy1=p2+(1/2)v2

2+gy2

Consequences of Bernoulli’s

Fast moving fluids exert less pressure than slow moving fluids

This is known as Bernoulli’s principle

Energy that goes into velocity cannot go into pressure

Note that Bernoulli only holds for moving fluids

Bernoulli in Action

Getting sucked under a train

Airplanes taking off into the wind

Next Time

Read: 15.1-15.3 Homework: Ch 14, P: 37, 42, 47,

Ch 15, P: 6, 7 (This is just for reference, homework is only

done on Webassign)

Which of the following would decrease the pressure you exert on the floor the most?a) Doubling your massb) Doubling the mass of the earthc) Doubling your heightd) Doubling the size of your

shoese) Doubling air pressure

Which of the following would increase the pressure of a column of fluid of fixed mass the most?a) Doubling the width of the columnb) Halving the density of the fluidc) Halving the mass of the Earthd) Halving the speed of the Earth’s

rotatione) Doubling the height of the

column

Summary: Fluid Basics Density ==m/V Pressure=p=F/A On Earth the atmosphere exerts a

pressure and gravity causes columns of fluid to exert pressure

Pressure of column of fluid:p=p0+gh

For fluid of uniform density, pressure only depends on height

Summary: Pascal and Archimedes

Pascal -- pressure on one part of fluid is transmitted to every other part

Hydraulic lever -- A small force applied for a large distance can be transformed into a large force over a short distance

Fo=Fi(Ao/Ai) and do=di(Ai/Ao) Archimedes -- An object is buoyed up by

a force equal to the weight of the fluid it displaces Must be less dense than fluid to float

Summary: Moving Fluids

Continuity -- the volume flow rate (R=Av) is a constant fluid moving into a narrower pipe

speeds up Bernoullip1+1/2v1

2+gy1=p2+1/2v22+gy2

Slow moving fluids exert more pressure than fast moving fluids