PAGE EDITOR(S): Hillary Schein, Olivia Bercow, Andy Duemichen, Nathan Serota Natland Note (3/9/10): Still needs to be edited by Andy and Nathan. Mass Density (P)
P= m/v
unit: Kg/m^3

Specific Gravity: ratio of density of subject to water
density of subject/density of water at 4 degrees Celsius
Specific Gravity has no units.

the density of water at 4 degrees Celsius= 1000 kg/m^3.

Common Densities

Material

Density (kg/m3)

Air (1 atm, 20 degrees C)

1.20

Aluminum

2,700

Benzene

900

Blood

1,600

Brass

8,600

Concrete

2,000

Copper

8,900

Ethanol

810

Gold

19,300

Ice

920

Iron

7,800

Lead

11,300

Mercury

13,600

Platinum

21,400

Silver

10,500

Steel

7,800

Water (Freshwater)

1,000

Pressure (P)- scalar
pressure exerted by a fluid is defined as a magnitude of force, F, acting perpendicular to a surface divided by the area, A, over which the force acts/is applied.
K= 1.5(Kb)(T)
Equation: F/A= P
Unit: N/m^2= Pa or lbs/(in^2) or psi
Other units/ conversions for pressure: 10^5 Pa= 1 bar of pressure

Atmospheric Pressure at Sea Level
there is enough air above the surface of the earth to create the following pressure at sea level:
P(initial)= 1.013E5= 1 atm

Incompressible Fluid: a liquid in which equal volumes have equal weights regardless of depth (density does not vary) Pressure at a depth in a Static Fluid
P2= P1 + þgh
P2= pressure at depth in teh fluid
p1= initial pressure at top of fluis
þ= denisty of fluid
h= at what depth you are measuring the pressure

EXAMPLE: PRESSURE AT BOTTOM OF POOL
Pressure= 1.013E5 + (þ of pool water)(gravity)(height of pool)

EXAMPLE: TUBE FILLED WITH OIL, ENCLOSED, WITH A WEIGHT A TOP IT
Pressure= Mg of weight/Area of weight + þgh+ 1.013E5

Pascals Principle
Any change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosed walls.

In accordance with Pascals Principle:
P1= P2
F1/A1= F2/A2

Absolute Pressure= sum of atmospheric pressure and gauge pressure(pressure above atmospheric)
Pgauge= Pabs- Patm

The reason the buoyant force exists is because there is a diff in pressure between the top and bottom of an object. The bouyant force is the same for a given object
Fb= þgV(fluid diplaced by object)
Fb= gm(fluid displaced)

Archimedes Principle
Any fluid applies a buoyant force to an object that is partially or completely immersed in it. The magnitude of the buoyant force equals the weight of the fluid that the object displaces.

Will it float?
þ of object > þ of fluid --> SINK
þ of object< þ of fluid --> FLOAT
þ of object= þ of fluid--> Neutrally Buoyant

EXAMPLES:
Ice floating in water. As it melts, will water level rise, fall or stay the same?
It will stay the same because in the equation þVg=mg as the volume of water displaced by ice cube decreases, the mass of the ice also decreases. So less the space teh ice was taking up is being filled up with the water that the cube is meting.

Helium baloon on the moon will rise, fall, or float?
The baloon will fall because there is no atmosphere on the moon so helium is more dense and would sink.

The weight you see on a scale is actually less than it it is because
Fn + Fb = Mg
Fn= Mg -Fb

Fluid Dynamics
Continuity equation: The mass flow rate has the sam evalue at every position along a tube that has a single netry and a sigle exit point for fluid flow.
þAv=þAv
or
Volume/ change in time =Volume/ change in time

Fluids in Motion An incompressible fluid is one that has a constant density as pressure changes.
For steady flow, speed, pressure and elevation of an incompressible fluid are all related by Bernoullis equation.
Whenever a fluid is flowing in a horizontal pipe and encounters a region of reduced X-area, the pressure drops. This is based on Newtons Law. There must be a greater pressure at P to accelerate fluid in smaller area.
If a fluid goes to a higher elevation pressure at the lower point will be greater than the pressure at the higher point

Bernoullis equation:

One application of Bernoulli's equation is a curveball. When a baseball is thrown normally without any spin, air flows with the same speed and pressure relative to atmospheric pressure on both sides of the ball. However, when an initial spin is put on the baseball, the speed of the air on one half of the ball is increased and the pressure there is decreased. On the other half of the baseball, the speed is decreased, which leads to a smaller reduction in pressure (than when there is no spin). Therefore, the baseball has a net force and curves.

Still needs to be edited by Andy and Nathan.Natland Note (3/9/10):Mass Density (P)P= m/v

unit: Kg/m^3

Specific Gravity: ratio of density of subject to water

density of subject/density of water at 4 degrees Celsius

Specific Gravity has no units.

the density of water at 4 degrees Celsius= 1000 kg/m^3.

Common Densities

Pressure (P)- scalarpressure exerted by a fluid is defined as a magnitude of force, F, acting perpendicular to a surface divided by the area, A, over which the force acts/is applied.

K= 1.5(Kb)(T)

Equation: F/A= P

Unit: N/m^2= Pa or lbs/(in^2) or psi

Other units/ conversions for pressure: 10^5 Pa= 1 bar of pressure

Atmospheric Pressure at Sea Levelthere is enough air above the surface of the earth to create the following pressure at sea level:

P(initial)= 1.013E5= 1 atm

Incompressible Fluid: a liquid in which equal volumes have equal weights regardless of depth (density does not vary)Pressure at a depth in a Static FluidP2= P1 + þgh

P2= pressure at depth in teh fluid

p1= initial pressure at top of fluis

þ= denisty of fluid

h= at what depth you are measuring the pressure

EXAMPLE: PRESSURE AT BOTTOM OF POOL

Pressure= 1.013E5 + (þ of pool water)(gravity)(height of pool)

EXAMPLE: TUBE FILLED WITH OIL, ENCLOSED, WITH A WEIGHT A TOP IT

Pressure= Mg of weight/Area of weight + þgh+ 1.013E5

Pascals PrincipleAny change in pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosed walls.

In accordance with Pascals Principle:

P1= P2

F1/A1= F2/A2

Absolute Pressure= sum of atmospheric pressure and gauge pressure(pressure above atmospheric)P

gauge= Pabs- PatmThe reason the buoyant force exists is because there is a diff in pressure between the top and bottom of an object. The bouyant force is the same for a given object

Fb= þgV(fluid diplaced by object)

Fb= gm(fluid displaced)

Archimedes PrincipleAny fluid applies a buoyant force to an object that is partially or completely immersed in it. The magnitude of the buoyant force equals the weight of the fluid that the object displaces.

Will it float?þ of object > þ of fluid --> SINK

þ of object< þ of fluid --> FLOAT

þ of object= þ of fluid--> Neutrally Buoyant

EXAMPLES:

Ice floating in water. As it melts, will water level rise, fall or stay the same?

It will stay the same because in the equation þVg=mg as the volume of water displaced by ice cube decreases, the mass of the ice also decreases. So less the space teh ice was taking up is being filled up with the water that the cube is meting.

Helium baloon on the moon will rise, fall, or float?

The baloon will fall because there is no atmosphere on the moon so helium is more dense and would sink.

The weight you see on a scale is actually less than it it is because

Fn + Fb = Mg

Fn= Mg -Fb

Fluid DynamicsContinuity equation: The mass flow rate has the sam evalue at every position along a tube that has a single netry and a sigle exit point for fluid flow.

þAv=þAv

or

Volume/ change in time =Volume/ change in time

Fluids in MotionAn incompressible fluid is one that has a constant density as pressure changes.

For steady flow, speed, pressure and elevation of an incompressible fluid are all related by Bernoullis equation.

Whenever a fluid is flowing in a horizontal pipe and encounters a region of reduced X-area, the pressure drops. This is based on Newtons Law. There must be a greater pressure at P to accelerate fluid in smaller area.

If a fluid goes to a higher elevation pressure at the lower point will be greater than the pressure at the higher point

Bernoullis equation:

One application of Bernoulli's equation is a curveball. When a baseball is thrown normally without any spin, air flows with the same speed and pressure relative to atmospheric pressure on both sides of the ball. However, when an initial spin is put on the baseball, the speed of the air on one half of the ball is increased and the pressure there is decreased. On the other half of the baseball, the speed is decreased, which leads to a smaller reduction in pressure (than when there is no spin). Therefore, the baseball has a net force and curves.

http://home.earthlink.net/~mmc1919/venturi.html

(if you scroll down, there is an animation that demonstrates how radius, pressure, flow rate, and velocity are related within a pipe)

http://solomon.physics.sc.edu/~tedeschi/demo/movies/pressure2.mov

Interesting Links, Pictures and Videos

http://virtualskies.arc.nasa.gov/aeronautics/tutorial/wings.html

(NASA tutorial on aeronautics and the origin of "lift")

http://www.youtube.com/watch?v=nah0xPnbscY

(youtube.com video of a neat video showing a drop in pressure leading to a rise in fluid when a fire goes out)

http://www.youtube.com/watch?v=a-V9uJgKIrM - A simple demonstration of Bernoulli's principle with a ping pong ball.

http://apphysicsresources.blogspot.com/2009/07/ap-physics-b-multiple-choice-questions.html - Sample fluid mechanics multiple choice questions.

.

SOURCEShttp://physics.about.com/od/fluidmechanics/a/commondens.htm