Liquids & Buoyant Force
Notes (p275 HRW)
Liquids
Study of liquids
Hydrostatics liquids that are stationary Archimedes, Pascal
Hydrodynamics liquids that are moving Bernouilli
Fundamental Characteristic
Density ()
How is density defined? mass/volume
= m/V What are density units in SI
kg/m3 (standard) or gm/cc (common) Example
water = 1000 kg/m3 (or 1 gm/cc) gold = 19.3 x water lead = 11.3 x iron = 7.8 x ice = 0.92 x balsa = 0.12 x air = 1.2 kg/m3
Lower density floats
on higher density
Pressure (p)
Definition:
force perpendicular to plane/area over which force is acting P = Force/Area = F/A
SI Units = pascals (Newtons/meter2) Air Pressure
Standard air pressure @ sea level and 20C, expressed as: 1.01 x 105 Pa 1 atmosphere 760 mm (or 76 cm) of mercury 30 inches of mercury
Measured by a barometer or manometer Average tire pressure ~ 200 kPa or 30 psi (lbs/in2)
Hydrostatic (Gauge) Pressure
Fluid pressure increases with depth because the water at a depth must support the weight of water above it. Ex.
Diving to the bottom of the deep end of a pool what do you feel?
Air pressure P = gh, where
= density of fluid g = 9.8 m/sec2 h = depth of fluid (ex. height of water
column)
This is gauge pressure
Container shape?
NO EFFECT!
Absolute/Total Pressure
Add atmospheric pressure (Pair) which acts on the surface of the fluid and the total pressure becomes Ptotal = Pair + gh
Generically The pressure at the bottom of a
column (Pb) equals the pressure at the top (Pt) PLUS the pressure due to the column, or
Pb = Pt + gh
Practice - submarines
A sub dives to a depth of 200 m. How
much water pressure must the hull be
able to withstand, or what is the (gauge)
water pressure at 200 m?
Solve P = gh P = 1000 x 9.8 x 200 P = 1.96 x 106 Pa Every sq meter of surface must
withstand ~ 2 million newtons
Note: in this example we have NOT included the air pressure pushing on the top of the water!
Submarines
Maximum depth classified, but generally believed to be ~1500 ft for US
and ~2500 ft for Russian
Sub disasters
Thresher (63), sank off Cape Cod in 8400 ft after joint to outer hull failed, flooding sub
Kursk (2000), Barents Sea, 350 ft after torpedo accident
Practice
How deep (h) must a diver go before he experiences another atmosphere (1.01 x 105 Pa) of water pressure?
Solve for h in water ( = 1000 kg/m3) P = gh 1.01 x 105 = 1000 x 9.8 x h h = 10.31 m (~34 feet)
Roughly, every 30 feet of dive adds 1 atmosphere of pressure to a diver
Interesting facts on diving!
Deepest free dive
124 m (~400 ft) feet Deepest assisted dive
214 m (~700 ft) Breath holding record
>19 minutes
Mini-lab
Density determination of 3 samples
Measure Write-up Submit
Pascals Principle
Pressure applied to an enclosed fluid is
transmitted equally and undiminished to
every part of the fluid, as well as the walls
of the container.
P1 = P2, (Pressure a point 1 = pressure at point 2)
2
2
1
1
A
F
A
F
Application of Pascals Principle
Hydraulic lift service stations
Examples of Pascals Principle
Examples
Example
The small piston of a hydraulic lift has an
area of 0.2 m2. If a car weighing 1.2e4 N
sits on the large piston, area 0.9 m2, how
large a force must be applied to the small
piston to support the car?
F1/A1 = F2/A2 F1/0.2 = 1.2e4/0.9 F1 = 0.2*1.2e4/0.9 = 2.7e3 N
What is buoyancy?
In physics, buoyancy is
the upward force acting
on an object in a fluid,
and can be:
Positive Neutral Negative
Alligators & crocodiles?
What causes buoyancy?
Buoyancy is the result of the difference
in pressure exerted on the top and
bottom of an object.
Question
If you place a rock into a
bucket of water, say filled,
what will you observe about
the water line in the bucket?
It will rise to reflect the
volume of the rock if the rock was 0.1 m3, the water
would rise 0.1 m3, b/c the
rock is submerged.
This is an example of Archimedes Principle
Archimedes Principle - example
In air the stone
weighs 44 N
In water the stone
weighs 36 N
Buoyant force is the
difference = 8N
Buoyancy Example
Weight in
air Apparent
weight
Fb = Weight in air weight in water
Buoyancy - Archimedes
Archimedes Principle When a body is partly or wholly submerged in a fluid,
it will experience a buoyant force (Fb)equal to the weight of the fluid displaced.
Buoyant (Upthrust) force (Fb) Fb = Weightfluid displaced = (massfluid)*(g) Fb = (fluid)*(Vfluid displaced)*(g) (Note: =m/V or m= *V)
Fb = (V)*g directed upward! Case 1 object is submerged
Fb = (fluid)*(Vfluid displaced)*(g) Case 2 object is partially submerged (floating)
Fb = (object)*(Vobject)*(g)
Buoyancy Summary Table
IF THEN
object > fluid Wobj > Fb sinking
object = fluid Wobj = Fb neither sink nor float
object < fluid Wobj < Fb float
= density, W = weight Fb = buoyant force
Example of Archimedes
Principle & Buoyant Force
If a house brick of density () 2000 kg/m3 and volume (V) of 0.00123 m3 is placed in
a bucket of water, what is the buoyant force
(Fb) acting on a brick?
Solve: Fb = Vg
Fb = 1000 x 0.00123 x 9.8
Fb = 12.05 N
Buoyant Force Practice
An ice cube is floating in a glass of water
(=1000 kg/m3). The ice, whose density is 917 kg/m3, has dimensions of 0.03 x 0.02 x
0.02 m. What is the buoyant force on the ice?
Solve: Note: the ice is floating thus the
buoyant force = weight of the ice
Fb = (V)*g (use , V for ice, not water) Fb = 917*(0.03*0.02*0.02)*9.8 Fb = 0.11 N
Buoyant Force Practice
A ferry boat is 4 m wide and 6 m long. When a truck pulls onto it, the boat sinks 4 cm in the water. What is the weight of the truck?
Use Archimedes Principle: Weight of truck = weight of water displaced (find
this displacement)
Weight = mass x g Mass of water (m) = density x volume m= 1000 x (4 x 6 x 0.04) = 960 kg
Weight = m x g = 960 x 9.8 = 9,408N
Buoyant Force Practice
Example
A piece of metal weighs 7.84N in air and 6.86N when completely immersed in water.
What is the buoyant force? Fb = 7.84 6.86 = 0.98N
What is the density () of the object? Fb = Vg (, V refer to the fluid when submerged) V = Fb /g = 0.98/(1000*9.8) = 0.0001 m3 Mass = Weight/9.8 = 0.8 kg = m/V = 0.8/0.0001 = 8000 kg/m3
Buoyancy - icebergs
If an object is floating on the
surface, then the volume that
is below the surface can be
determined as follows:
Vf/Vo = o/f, where Vf= volume of object that is below
surface
Vo= volume of the object o = density of the object f = density of the fluid
% Iceberg in salt water that is below surface = .92/1.025 = 89%
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