Transcript Principle of Flotation

Pressure in Open Systems
• Pressure increases with
depth
• Type of fluid also plays a
role in pressure (more
dense fluids will exert
greater pressures)
• Gravity also plays a role
(larger gravity results in
larger pressure)
P  hg
Pressure due to a liquid depends on DEPTH and
density, not volume!
Why is the water level the same in each vase?
Which teapot can hold more tea?
Problem…
• A reservoir behind a dam is 15 m deep.
What is the pressure of the water in the
following situations?
– At the base of the dam?
– 5.0 m from the top of the dam?
• If the water were saltwater, would the
pressures be greater or less?
Public Water System
Buoyancy
• What happens to water level when something is
placed in it?
– It rises
• How much does it rise?
– The amount of displaced water is equal to the volume of the
submerged part of the object
• A completely submerged object always
displaces a volume of liquid equal to its own
volume.
• This is a good way to find the volume of irregular
shapes
Mr. Archimede’s Bath
King
Hiero’s
Crown
Archimede’s Principle
• Greek scientist Archimede’s (212 B.C.)
discovered that the “Buoyant force acting
on an object placed in a fluid is equivalent
to the weight of the displaced fluid”
• The force does not depend on the weight
of the object, only the weight of the
displaced fluid.
Buoyancy
• A buoyant force is an
upward force exerted on
objects when placed in a
fluid, due to the difference
in pressure between the
bottom and top of an
object
Fb  Vg
– Magnitude of the force
depends on
• Volume of displaced fluid
• Density of displaced fluid
• Magnitude of gravity
1 liter of water = 1000 cm3 = 1 kg = 9.8 N
Flotation
• What is the buoyant force on a 10 ton ship
floating in fresh water?
• In salt water?
• In a lake of mercury?
• 10 tons in each case; the weight of the ship is
constant, so the weight of the water displaced
must also be constant. The volume of the liquid
displaced will differ based on the density of the
liquid.
Flotation
• How can a ship be made of iron if a solid block
of iron sinks?
– It has to do with the shape of the ship
• Principle of Flotation—a floating object
displaces a weight of fluid equal to its own
weight
– The ship must be shaped to displace enough water
to equal its own weight
– The deeper the ship is immersed, the more water it
displaces—a loaded ship will ride lower in the water
than an unloaded ship
Problem…
• A 10 lb box falls overboard a boat, and is
now floating in the water. The box has the
shape of a cube, 1 ft on a side. What is the
buoyancy force on the box?
• How much of the box is under water?
(assume it is floating level)
Problem…
• The float in a toilet tank is a sphere of diameter
10 cm.
• 1) What is the buoyancy force on the float when
it is completely submerged? You might need a
reminder that the volume of a sphere is V =
4/3π(r)3
• 2) Here's a slightly tougher one. If the float must
have an upward buoyancy force of 3.0 N to shut
off the ballcock valve, what percentage of the
float will be submerged?
Buoyancy
• When the weight of the submerged object…
– is greater than the buoyant force, the object will sink
to the bottom
– is equal to the buoyant force, the object will remain at
any level (like a fish)
– is less than the buoyant force, the object will rise to
the surface and float
• In terms of density, if the object is
– denser than the fluid, it will sink
– the same density as the fluid, it will neither sink or
float
– less dense than the fluid, it will float
Can a ship made of concrete float?
• Concrete is usually more dense than
water, and will therefore normally sink
when placed in water.
SS Selma, scuttled in Galveston
Harbor, concrete tanker ship used
during World War I
Apparent Weight = Fg-Fb
Apparent Weight
• Apparent weight depends on the density
• Apparent weight = Fg – Fb = ρoVog – ρfVfg
• For a submerged object:
Fg (object)
FB
 oVg  o


 f Vg  f
• A piece of metal weighs 50.0 N in air, 36.0 N in
water, and 41.0 N in an unknown liquid. Find
the densities of the following:
• The metal
• The unknown liquid
Problem…
• A cubic decimeter, 1.00 X 10-3 m3, of
aluminum is submerged in water. The
density of aluminum is 2.70 X 103kg/m3
– What is the magnitude of the buoyant force
acting on the metal?
– What is the apparent weight of the metal?
Archimedes’ Principle
• Palmer drops an ice cube into his glass of water. The ice,
whose density is 917 kg/m3, has dimensions 0.030 m x
0.020 m x 0.020 m. What is the buoyant force acting on
the ice?
• William’s wedding ring, presumed to be pure gold, has a
mass of 0.1 kg. When submerged in water its apparent
mass is 0.080 kg. The density of water is 1000 kg/m3
which is equivalent to 1 kg/L.
• What is the buoyant force in Newtons?
• What volume of water (in liters) is displaced?
• Is the ring made of pure gold (ρ = 19.3 kg/L)?
• Pine is 0.50 as dense as water and therefore floats in
water. Weight density of water is 9800 N/m3 or 9.80 N/L.
• What weight of water will be displaced by 25 kg of floating pine?
• What additional force would be required to poke the pine beneath the
surface so it is completely submerged?
Hydrometers
• Simple devices used to determine the
density (specific gravity) of a fluid.
What do you think????
• You are floating in a
small raft in your pool.
There's a brick in the
raft. You toss the brick
out of the raft and into
the pool. The brick
sinks to the bottom of
the pool. Does the
water level at the side
of the pool rise, stay
the same, or
decrease?
Germany “Water Bridge”
Did this bridge have to be designed to withstand the
additional weight of ship and barge traffic, or just the
weight of the water?
Streamlines
• Lines drawn to represent the flow of a fluid
• Velocity of fluid is tangent to the streamline
Streamlines
• Can be used to represent either Laminar
or Turbulent flow.
Laminar and turbulent flow over a submarine
Transition from laminar to turbulent flow can be
seen occurring down the length of this missilebody model captured by shadowgraph in highspeed flow.
Notice how the
angle of attack
of the wing can
change the flow
of air over the
wing.
As flow
becomes
turbulent, drag
increases and
lift is lost.
This condition is
known as “stall”
Turbulence in Mt. Spurr eruption, Alaska, 1992