Ch+9+-+Solids+and+Fluids

=SOLIDS AND FLUIDS =


 * Topics to be Discussed**: Pressure, Stress/Strain, Buoyancy, Moving Fluids

Pressure
Pressure in fluids vary with depth--**//All points at same depth must be at same pressure!//** The __density__ of a substance of a uniform composition is defined as its mass per unit volume.
 * What is __pressure__?:** When dealing with fluids, the quantity F/A refers to pressure.
 * Pressure (on fluids) units:** (P=F/A) N/m^2, Pa, atm, torr, kPa, psi
 * Examples of pressure:**
 * spike shoes vs. flat shoes
 * snow shoes
 * Bed of nails
 * Density = //p//
 * Density(//p//)=M/V
 * kg/m^3
 * g/cm^3


 * Pressure varies with Depth**
 * P=Po+//p//gh
 * 1 atm= 1.013x10^5 Pa

__**Specific Gravity**-__-Ratio of substance to density of water at 4 degrees Celsius.
 * SG= //p// object///p// water
 * //p// water=1000 kg/m^3 = 1 g/cm

W=mg //p//=m/V W=//p//Ahg m=//p//V Weight is a force =//p//gh V= Ah m=//p//Ah
 * Using weight in Equations**
 * P**

Blaise Pascal was a very influencial French mathematician and philosopher who contributed to many areas of mathematics. He worked on conic sections and projective geometry and in correspondence with Fermat he laid the foundations for the theory of probability.
 * BLAISE PASCAL**

__Pascal's Principle__**- A change in pressure to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container.**
 * **P1=P2**
 * **F1/A1=F2/A2**
 * **small force/small area = large force/large area**

__Measuring pressure__
 * Same depth=same pressure**
 * **Manometer**
 * **Barometer**

__**About the Manometer**__ The manometer is an instrument used in measuring pressure differences, normally atmospheric. The most commonly used type of manometer is the U-tube, not to be confused with YouTube "Broadcast Yourself". This instrument is pictured below

**The Manometer**

In this device, there is a large u-shaped tube that contains water. If air is pumped out of one end, then a vaccum is formed and the water rises on the side that the air is pumped out of and sinks on the opposite side. The difference in height of each side of the U with the other is known as one atmosphere. But when the water levels are equal on each side of the U, it means that there is the same amount of pressure exerted on the water on each side of the tube.

The barometer is also an instrument that measures atmospheric pressure. There are two variations of barometers. The first one is the mercurial barometer, which was invented first. The second type is the aneroid barometer. The mercurial barometer was invented by Evangelista Torricelli. This was also referred to in his time period as "Torricelli's Tube".
 * __About the Barometer__**

__**Evangelista Torricelli**__ Evangelista Torricelli was born October 15, 1608 in the city of Faenza, Italy. He was an avid physicist and mathematician. In 1641, he moved to Florence, Italy to assist Galileo, a brilliant astronomer. In fact Galileo suggested that Torricelli should use the element mercury in his vacuum experiments. Evangelista Torricelli died on October 22, 1647 in Florence, Italy. //Torricelli pictured with his invention, the barometer//

The Earth's surface is under a constant pressure caused by the atomosphere. This pressure can vary with changing elevations or even weather patterns. The standard atmospheric pressure is measured in various units: 1 atmosphere = 760 mmHg = 29.92 inHg = 14.7 lb/in2 = 101.3 KPa The fundamental SI unit of pressure the Pascal (Pa), but it is a small unit so kPa is the most common direct pressure unit for atmospheric pressure. Since the static fluid pressure is dependent only upon density and depth, choosing a liquid of standard density like mercury or water allows you to express the pressure in units of height or depth, e.g., mmHg or inches of water. The mercury barometer is the standard instrument for atmospheric pressure measurement in weather reporting. The decrease in atmospheric pressure with height can be predicted from the baromatic formula. For weather applications, the standard atmospheric pressure is often called 1 bar or 1000 millibars. This has been found to be convenient for recording the relatively small deviations from standard atmospheric pressure with normal weather patterns.
 * __Atmospheric Pressure__**



 STRESS AND STRAIN

Liquid-variable shape & definite volume Gas-variavle shape & volume Plasma-ionized substance** crystalline** Strain-measure of degree of deformation**
 * Types of Matter:
 * Solid-definite shape & volume
 * Solids are Crystalline or Amorphous
 * [[image:http://tbn0.google.com/images?q=tbn:Uw4jioJ9tFFHqM:http://www.molsci.ucla.edu/images/crystalline_solids_small.jpg width="124" height="96" link="http://images.google.com/imgres?imgurl=http://www.molsci.ucla.edu/images/crystalline_solids_small.jpg&imgrefurl=http://www.molsci.ucla.edu/pub/explorations.html&h=311&w=400&sz=39&hl=en&start=1&tbnid=Uw4jioJ9tFFHqM:&tbnh=96&tbnw=124&prev=/images%3Fq%3Dcrystalline%26gbv%3D2%26hl%3Den"]]
 * Deforming Solids
 * All solids deform to some extent (occurs when external force applied); most objects return to shape once force is removed**
 * Elastic Properties:
 * Stress-related to force causing deformation

k = F/x Tesile, Compressive Stress = F/A Unit: N/m or Pa Strain = Change in L/initial L NOTE: NO UNITS B/C DIMENSIONLESS!
 * ELASTIC MODULUS = Stress/Strain*
 * Types of Stress
 * **Strain**

Young's Modulus = F*(initial Length)/Area*(change in length) Measures how difficult it is to deform a solid

Buoyancy   Archimedes Principle= An object submerged in a fluid will displace a volume equal to its own.

Buoyancy= Upward force of a fluid equal to the weight of the fluid displaced. B = //W// fluid

Buoyant Equations

B = //W// fluid B = //M// fluid //g M = pV// B = //p// fluid //Vg W// object //= M// object //g W// object = //p// object //Vg//

Totally submerged object



Moving Fluids
Types of Flow: Streamline, Turbulent  Ideal Fluid:  •  Nonviscous - no friction Incompressible - constant density No turbulance - no spinning motion with fluid

Equation of Continuity - used to solve problems involving water traveling through a nozzle-shaped container A1v1=A2v2 where the areas are the cross-sectional area of each end of the tube and v is the velocity of the fluid as it passes that point.

Bernoulli's equation W = 1/2mv^2 - 1/2mv^2 + mgy - mgy Final Initial Final Initial - is the order of the right side of the formula Bernoulli's Equation is basically Conservation of Energy for Fluids. Also... W = PV can be used

Where can this be used? This property of fluids and the equations can be used in ...
 * Airplane lift
 * Golf ball flights
 * Sailing Upwind
 * Atomizers

Buoyancy Problems: