Transcript A Brief History of Planetary Science

Archimedes’ Principle
Physics 202
Professor Lee Carkner
Lecture 2
PAL #1 Fluids
Column of water to produce 1 atm of
pressure
P = rgh
P =
r = 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,
riVig=rwVwg
Vw=Vi (ri/rw)
rw = 1024 kg/m3 and ri = 917 kg/m3
Vw=
Continuity
For a moving fluid

Energy must be conserved

Mass must be conserved so,
Avr = 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 = -Dmg(y2-y1) = -rgDV(y2-y1)

Wp=Fd=pAd=DpDV=-(p2-p1)DV

D(1/2mv2)=1/2rDV(v22-v12)
Equating work and DKE yields,
p1+(1/2)rv12+rgy1=p2+(1/2)rv22+rgy2
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)
b)
c)
d)
e)
Doubling your mass
Doubling the mass of the earth
Doubling your height
Doubling the size of your shoes
Doubling air pressure
Which of the following would
increase the pressure of a column
of fluid of fixed mass the most?
a)
b)
c)
d)
Doubling the width of the column
Halving the density of the fluid
Halving the mass of the Earth
Halving the speed of the Earth’s
rotation
e) Doubling the height of the column
Summary: Fluid Basics
Density =r=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+rgh
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
Bernoulli
p1+1/2rv12+rgy1=p2+1/2rv22+rgy2
Slow moving fluids exert more pressure
than fast moving fluids