Download - 2 Archimedes 2 s
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 = P/g = Double diameter, pressure does not change
On Mars pressure would decrease
Mars has smaller value of g
Archimedes’ Principle What happens if you put an object in a fluid?
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?
Density
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
Ideal Fluids
Steady --
Incompressible -- density is constant Nonviscous -- Irrotational -- constant velocity through
a cross section
The ideal fluid approximation is usually not very good
Moving Fluids
What happens if the pipe narrows?
Av = constant If the density is constant then,
Av= constant = R = volume flow rate
Constricting a flow increases its velocity Because the amount of fluid going in must equal the
amount of fluid going out Or, a big slow flow moves as much mass as a small fast flow
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
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
Wg = -mg(y2-y1) = -gV(y2-y1) The work of the system due to pressure is,
Wp=Fd=pAd=pV=-(p2-p1)V
(1/2mv2)=1/2V(v22-v1
2)
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 Blowing between two
pieces of paper
Convertible top bulging out
Airplanes taking off into the wind
Lift
If the velocity of the flow is less on the bottom than on top there is a net pressure on the bottom and thus a net force pushing up
If you can somehow get air to flow
over an object to produce lift, what happens?
Deriving Lift Use Bernoulli’s equation:
pt+1/2vt2=pb+1/2vb
2
The difference in pressure is:pb-pt=1/2vt
2-1/2vb2
(Fb/A)-(Ft/A)=1/2(vt
2-vb2)
L= (½)A(vt
2-vb2)
Next Time
Read: 15.1-15.3 Homework: Ch 14, P: 37, 42, 47,
Ch 15, P: 6, 7
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