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3/3/13 PHYS 220 General Physics I
A large fish is perfectly motionless about two feet below the
surface of a lake. Which of these best describes the free body
diagram for the fish?
mg A.
Spring Semester 2013
Assigned Reading: Ch 10, sections 4-7
mg mg B.
C.
mg D.
mg E.
Lecture 16
Buoyancy
A short time later, the fish swims away. The space that
used to be occupied by the fish is now filled with water,
which is also at rest. Does this volume of water have the
same free body diagram as the fish?
Are the forces exerted by the water on the fish any
different from the forces exerted on the water that took
the place of the fish?
Would the forces exerted by the water be any different if
the actual fish were replaced by a heavy marble statue
that was exactly the same size and shape as the fish?
Archimedes's Principle: When an object is
immersed in a fluid, the fluid exerts an upward
force on the object that is equal to the weight
of the fluid displaced by the object
Buoyant force arises
because of the differences
in the pressures on the top
and the bottom of the
object (which arise
because of the weight of
the fluid).
1 3/3/13 A heavy mass is slowly lowered into
a beaker of water until it is
completely submerged, but it does
not touch bottom. How does the
weight of the scale under the beaker
change?
Archimedes’ Principle
A. Unchanged, as long as the mass does not touch bottom.
B. Increases by the actual weight of the mass.
C. Something else….
Buoyant Force
A floating object experiences a buoyant force due only
to the submerged portion of the object
If an object with an area A and height h is
submerged in a liquid of density ρliq, the buoyant
force of the liquid, Fliq, on the object is….
Fbuoyant = m f g = Vsubmerged rg
F liq = + P bot A− P top A
The maximum buoyant force is
experienced by a fully
submerged object.
P bot= P top + ρ liq g h
F liq= (P top+ ρ liq gh) A− P top A
mg Fbuoyant = m f g
F liq= ρliq g h A= ρ liq gV = mliq g
…equal to the weight of the fluid displaced by the
object. Vr f g
V:
Total volume of the
object
2 3/3/13 “Light” versus Regular Coke
Why does one sink but the
other one doesn’t?
(Does this have anything to
do with the calorie content
of Diet Coke vs regular
Coke?)
Why do some objects float and others sink?
Fbuoyancy
Fgravity
Fbuoyancy
Fbuoyancy
Fgravity
Fgravity
Fgravity > Fbuoyancy
Bernoulli Cans
Fluid Dynamics
3 3/3/13 Li* on a Plane Wing Assume fluids are “Ideal”
Assump8ons: Density is constant Fluid velocity is independent of 8me (not of posi8on) No fric8on (no viscosity) No complex flow paIerns (no turbulence) Equation of Continuity
Work-­‐Energy and Fluids Principle of con8nuity: The amount of fluid that flows through a pipe must be conserved. The rate at which a volume of fluid flows into a sec8on of pipe must be the same as the rate at which the same volume leaves the pipe Vin = Vout
vL AL = vR AR
4 3/3/13 Bernoulli's Equa8on Venturi Tubes
1 2
1 2
P 1+ ρ v 1+ ρ g h1= P 2+ ρ v 2+ ρ g h2
2
2
Change in energy due to work done at point 1 Kine8c energy at point 1 Kine8c Poten8al energy at energy at point 1 Change in point 2 energy due to work done at point 2 Poten8al energy at point 1 This predicts that pressure is connected to changes in
velocity, and to changes in the height of the fluid.
(Follows from conservation of energy.)
Real Fluids Fric8on between the fluid and the wall of the container or object it is flowing around – viscous forces. Forces depend on the speed of the fluid and the type of fluid. Viscosity of the fluid (air) led to the drag forces (Stokes's Law) discussed in Chapter 3 Surface Tension Arises from interac8ons of fluid molecules with themselves and with a surface. η
5 3/3/13 Capillary Pressure Explains how plants (and paper towels) work. For a pressure difference of 1 atm (the atmospheric pressure), water can be “pumped” a height of 10m. Some trees grow significantly taller than 10m. 6