Transcript A Brief History of Planetary Science

Archimedes’ Principle
Physics 202
Professor Lee Carkner
Lecture 2
“Got to write a book, see,
to prove you’re a
philosopher. Then you
get your … free official
philosopher’s loofah.”
--Terry Pratchett, Small
Gods
PAL #1 Fluids
Column of water to produce 1 atm of
pressure


r = 1000 kg/m3

h = P/rg = 10.3 m
Double diameter, pressure does not change

On Mars pressure would decrease

Archimedes’ Principle

The fluid exerts a force on the object


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
Buoyancy
Will it Float?
What determines if a object will sink or 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 denser the object, the lower it will float, or:

Example: ice floating in water,
W=rVg
Vi/Vw=rw/ri
rw = 1024 kg/m3 and ri = 917 kg/m3
Iceberg
Ideal Fluids
Steady -Incompressible -Nonviscous -Irrotational --
Real fluids are much more complicated
The ideal fluid approximation is usually not very
good
Moving Fluids
Consider a pipe of cross sectional area A with
a fluid moving through it with velocity v

Mass must be conserved so,
If the density is constant then,
Av= constant = R = volume flow rate


Because the amount of fluid going in must
equal the amount of fluid going out

Continuity
R=Av=constant is called the equation
of continuity

You can use it to determine the flow
rates of a system of pipes

Can’t lose or gain any material
Continuity
The Prancing Fluids

How can we keep track of it all?
The laws of physics must be obeyed

Neither energy nor matter can be
created or destroyed
Bernoulli’s Equation
Consider a pipe that bends up and gets wider at
the far end with fluid being forced through it
The work of the system due to lifting the fluid is,
The work of the system due to pressure is,
Wp=Fd=pAd=DpDV=-(p2-p1)DV
The change in kinetic energy is,
Equating work and DKE yields,
p1+(1/2)rv12+rgy1=p2+(1/2)rv22+rgy2
Fluid Flow
Consequences of Bernoulli’s
Equation

Fast moving fluids exert less pressure than
slow moving fluids
This is known as Bernoulli’s principle
Based on conservation of energy

Note that Bernoulli only holds for moving fluids
Constricted Flow
Bernoulli in Action
Blowing between two pieces of paper

Convertible top bulging out

Shower curtains getting sucked into the
shower
Shower Physics
Lift
Consider a thin surface with air flowing
above and below it

This force is called lift
If you can somehow get air to flow over an
object to produce lift, what happens?
December 17, 1903
Deriving Lift
Consider a wing of area A, in air of density r
Use Bernoulli’s equation:
The difference in pressure is:
pb-pt=1/2rvt2-1/2rvb2
Pressure is F/A so:
L=Fb-Ft and so:
If the lift is greater than the weight of the
plane, you fly
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