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Physics Module: Fluids, Bernoulli's Equation and Gases
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Gravity
Lessons 6, 7 and 8
Terms in this set (27)
Density of Fluid and solids --- units
Rho = mass/ volume
-density is a scalar quantity
-units for density (kg/m^3)
-also (g/mL) = (g/cm^3)
Density of water is what?
1 g/cm^3
or
1000 kg/m^3
F(g) can be calculated with fluids how?
density of substance x Volume x Acceleration due to gravity (Rho x V x g) --- typically used find Buoyancy Force
What is SG and its use?
it is specific gravity ---- used to compare to Density of water and determine whether the object will float and sink
Equation: SG = density of the Object (rho) / density of water
-can use 1 g/cm^3 or 1000 kg/ m^3
-The units must match with that of the object because SG is UNITLESS number
What is Pressure and corresponding units
Pressure: ratio of Force per Unit Area
P = F / A
Units: N/ m^2
1 Pa = 1 N/m^2
1 atm = 760 torr, 760mm Hg, 101325 Pa
-Pressure is scalar means it only has magnitude and NO direction
HOWEVER----
When there is a differential of pressures they as vectors possibly causing acceleration
ex. pressure outside during hurricane less than pressure indoors causing the windows to shatter to the outside as the pressure inside remains unchanged
Absolute Hydrostatic Pressure
-total pressure that is exerted on an object that is submerged in a fluid
P = P0 + ρgz
P0: incident or ambient pressure (pressure at the surface)
z: depth of the object into the fluid
g: acceleration due to gravity
NOTE: P(o) within a fluid the pressure can be higher or lower than the atmospheric pressure
Gauge Pressure
the difference between the actual pressure and the atmospheric pressure
Equation: P(gauge) = P(in) - P(out- atm)
P(in) = P(o) + rho(g)(z)
-when P(o) = P(amt)
then----- P(gauge) = rho(g)(z)
Pascal's Principle
When force is applied to a confined fluid, the change in pressure, is transmitted equally to all parts of the fluid
Hydraulics mechanics uses pascal's principle---
a small Applied force over a larger distance will generate a strong force over a short distance
Also the greater distance over a smaller Area compensates for smaller distance and a larger area
ALL are part of the conservation of energy--- energy cannot be created not destroyed simply transferred
Work (in) = Work (out)
F(1)d(1) = F(2)d(2)
Buoyancy Force (Fb)
Force that supports a body in water or other fluid
F(b) = Density of Fluid x Volume of Fluid displaced x g
*also be written
Density of Fluid x volume of fluid submerged x g
--the volume submerged is the same as the fluid displaced
When determining whether object will float or sink is determining the SG
-- where the SG >> 1 the object will sink
--the SG is <<< 1 the object will float ( the objects decimal point is the amount of that is submerged the remaining is the part of the object out of the liquid
-- when 1 =1 indicates that the object is fully submerged but will not sink at the surface)
adhesion vs cohesion
Adhesion- the attraction among molecules of DIFFERENT substances (stronger for water)
Cohesion- the attraction among molecules of SAME substances
(both help plants transport water)
Viscosity
A liquid's resistance to flowing
-some fluids contain more viscosity drag than others
-Represented as (n)
Units (Pa x s) = N x s / m^2
Fluids that have no viscosity = Inviscid ( Ideal Fluids)
Laminar vs. Turbulent Flow
laminar flow: smooth and orderly; layers of fluid flow in parallel -- low to none viscous drag
turbulent flow: rough and disorderly; formation of eddy currents (swirls of fluid)
critical speed of a fluid
Rise of Turbulence flow when the certain speed pf a fluid is greater than the Critical Speed
-dependent of Fluid Properties
-Only on the edges , adjacent to the wall (Boundary Layers) can there be found Laminar Flow
Bernoulli's Equation
P₁+ρv₁²/2+ρgy₁=P₂+ρv₂²/2+ρgy₂, where P=absolute pressure, ρ=density, and y=height relative to reference height
Increased Velocity = Reduction in Pressure
Increase in Pressure = Reduction in Velocity (Speed)
Units for pressure can be ( J/ m^3) = N/m^2
continuity equation
A1V1=A2V2
Compensation of Area and Velocity where if the Area is Increased the Speed Reduces; and Vise Versa
STP vs standard state
STP: 0ºC/273K & 1 atm pressure
Standard State: 25ºC/298K, 1atm, 1 mol of gas
-STP is used for Gas Law Calculations
_Standard State is used Enthalpy, entropy, Free energy change, and electrochemical cell voltage
Ideal Gas Law
the relationship PV=nRT, which describes the behavior of an ideal gas
There are assumptions that follow ideal gas
-The gas particles contain no volume -- point masses making gases compressible
-There are no intermolecular forces within the gas particles
-ALL collision are Elastic---- the momentum and the energy is conserved
Calculating Density of Gas
2 Forms of calculating Density of Gas
Derivation of ideal gas law equation
n = mass / Molar Mass
mass/volume = density
m/v= PM/RT
m = mass , v= Volume, P= pressure, M= molar mass, R gas constant, T= temperature
OR
V(2) = V(1) x P(1)/ P(2) x T(2) / T(1)
- when the conditions change from STP --- P(1), T(1) and V(1) at STP
Calculating Molar Mass of Unknown Gas
MW = Density of Gas (Volume at STP)
V at STP = 22.4 L/ mol
Density is mass/Volume = g/L
MW Units are g/mol
Dalton's Law of Partial Pressures
at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases
Mole fraction is obtained = Moles of Gas/ total moles of gases
Mole fraction x Total Pressure = Partial Pressure
Henry's law states that
the solubility of a gas in a liquid is directly related to the pressure of that gas above the liquid
at higher pressures, more gas molecules dissolve in the liquid
-Pressure is directly proportional to Gas solubility
-Biological Example; Exchange of CO2 and O2 in the Capillaries and Alveoli
-Change in Pressure will cause the Solubility to be altered
Kinetic Molecular Theory
an explanation of how particles in matter behave (explain how gases behaved) -- the other laws only described
- Relationship of Gases where Temperature and KE are directly related as one increases so does the other respectively
-However, an Increased in MW will cause the gas particles to travel at a slower speed
-The assumptions for the ideal gases is applied here too ---
1. Gas particles have NO intermolecular Forces -- no attraction of repulsion
2. Gas particles have no Volume ( mass point) and makes them compressible
3. all collisions are Elastic
Graham Law of Diffusion/Effusion
Diffusion: the movement of molecules from HIGH concentration to LOW in a medium (air, water) under Isothermal and Isobaric conditions ( constant Pressure and Temperature)
-in diffusion gasses mix
-as the MW of the gas particle Increases; the Diffusion rate Decreases -- an inverse relationship
v = Square root of (2 x KE (avg) / mass
-shows the inverse relationship of Velocity and Mass of gas particle
effusion
A process by which gas particles pass through a tiny opening-- under pressure
- The higher the MW of the Particle ; the Slower the effusion rate
(Similar concept to Diffusion regarding the size and mass of gas particle)
Also, higher KE(avg) the higher the Effusion rate which would indicate a smaller mass -- a higher speed -- isothermal conditions
Conditions of High Pressure Real Gasses and Its effects?
High Pressure , Low Temperature , Low Volume
Ideal gases deviate from ideal behavior
-At high pressures --- Gas particles contain Low Volume and gas particle takes up space in the container making them not compressible (a contradiction of ideal behavior)
-When Gas particles are bought closer Low volume, high pressure---- causes them to come closer together and interact with each other -- (Another Contradiction of Ideal behavior Gas particles not containing Intermolecular forces)
Conditions of Low Temperature and its effects on ideal behavior?
Low temperatures causes the Gas particles to lose KE and interact with each other more through intermolecular forces
-the decrease in Temperature causes for the gas to lose KE and condense back to Liquid state
- Lower KE causes gases to behave LESS ideally,
- the intermolecular forces causes for gas particles to take up volume making them incompressible -- another sign of not ideal behavior
Van der Waals equation of state
used to correct the ideal gas law for intermolecular attractions (a) and molecular volume (b)
a is small value when gas is small -- less polarized
a is larger when gas is larger -- more polarized
b = small when volume of molecules is smaller volume
b is larger when molecules of gas bigger volume
typically a>>> b
When a & b = 0 then the gas behaves ideally
This equation used for correcting the deviations caused by the molecular interactions and volume
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