Physics

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Physics
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• Respiratory Care Programs
• Integrated Sciences

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Energy and Work

• Energy is the ability to do work...
• Work is defined as a force moving through a
  distance.
• Work (W) Force (F) x Distance (d)
• Mass is anything that occupies space, has weight
  (on earth), and has inertia
• Inertia is the ability of a mass to remain
  either in motion or at rest until it is acted
  upon by a force.

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Energy and Work

• Kinetic Energy is energy of motion
• Its formula is derived from the work and
  force/velocity formulas

• Potential Energy is stored energy
• It is derived from the work and force/distance
  formulas

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Kinetic and Potential Energy of Fluids

• With fluids, we must deal with energy per unit
  volume, hence, Density... therefore the KE
  equation becomes...

Where m fluid mass v fluid velocity V
fluid volume D fluid density
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Kinetic and Potential Energy of Fluids

• Again, we must address Density, and thusly the PE
  equation becomes...

Where m fluid mass g acceleration due to
gravity h vertical distance V fluid
volume D fluid density
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A reminder about fluids (liquids)

• They conform to the walls of their container
• The exert pressure on the walls of their
  container
• They have mass...therefore, INERTIA
• They have a tendency to flow when there is a
  pressure gradient
• Thus, gases are FLUIDS/LIQUIDS

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The Gas Laws

• Ideal gases conform to the relationship within
  the Ideal Gas Law Equation ...

Where R universal gas (Boltzmanns)
constant (82.1ml-atm/mole-oK) P pressure
(atm) V volume (liters) n of moles of
gas T absolute temperature (oK)

• All gas laws are tied to this Ideal Gas Law
• equation in some manner...

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The Gas Laws

• Boyles Law states--when temperature and mass are
  constant, the pressure varies inversely with the
  volume.
• The Formula
• Application(s) Body Plethysmography The lung
  interior

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The Gas Laws

• Charles Law states--when pressure and mass are
  constant, the volume varies directly the absolute
  temperature.
• The Formula
• Application(s) Gas storage Gas conversions used
  w/Combined Gas Law

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The Gas Laws

• Gay-Lussacs Law states--when volume and mass are
  constant, the pressure varies directly the
  absolute temperature.
• The Formula
• Application(s) Gas storage Gas conversions used
  w/Combined Gas Law Cooking, e.g., a pressure
  cooker.

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The Gas Laws

• Combined Gas Law applies to those situations in
  which only mass is constant...temperature, volume
  and pressure are varible. Due to this, the Ideal
  Gas Law becomes--
• The Formula

Where P pressure (atm) V volume (liters) T
absolute temperature (oK) k nR ( of moles
times Boltzmanns constant)
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The Gas Laws

• Combined Gas Law (contd)--used for gas volume
  conversions in Pulmonary Function
• (1)ATPS to STPD (2) ATPS to BTPS and (3) STPD
  to BTPS.
• Thus, the Formula

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The Gas Laws

• Daltons Law of Partial Pressures states--the
  total pressure exerted by a mixture of gases is
  equal to the sum of the partial pressures of the
  constituent gases.
• Thus, the Formula
• Applied to the lung
• 760 torr 47 torr 40 torr 573 torr 100
  torr

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The Gas Laws

• Avagadros Law states that equal temperatures and
  pressures, equal volumes of gases (regardless of
  their masses) will have an equal number of
  molecules.
• If a gas is exposed to STP (0oC and 760 torr, it
  will occupy 22.4 L.
• Finally, 6.02 x 1023 molecules of that gas
  subjected to STP. This is Avagadros Number.
• (Carbon dioxide will only occupy 22.3L under
  these conditions. It is not an ideal gas. )

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The Gas/Chemical Laws

• Henrys Law of Solubility
• The amount of gas that dissolves in a liquid is
  directly proportional to the partial pressure of
  the gas above the liquid.

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The Gas/Chemical Laws

• Grahams Law of Diffusion
• Gas within a gas--the relative rates of diffusion
  are inversely proportional to the square root of
  their densities...
• example a gas with a lower density will diffuse
  faster into another gas--oxygen will diffuse
  faster than will carbon dioxide

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The Gas/Chemical Laws

• Grahams Law of Diffusion
• Gas within a gas--the formula

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The Gas/Chemical Laws

• Grahams Law of Diffusion
• Gas within a liquid--the relative rates of
  diffusion are inversely proportional to the
  square root of their densities...and directly
  proportional to their solubility coefficients
• example a gas with a higher density will diffuse
  faster into a liquid--carbon dioxide will diffuse
  faster than will oxygen into a liquid

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The Gas/Chemical Laws

• Grahams Law of Diffusion
• Gas within a gas--the formula

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Molecular Transport Mechanisms

• DIFFUSION--the random movement of molecules from
  an area of high concentration to low
  concentration across a semi-permeable membrane.
• ACTIVE TRANSPORT--the movement of molecules
  across a semi-permeable membrane from an area of
  low concentration to high concentration,
  requiring energy.
• FACILITATED TRANSPORT-- the movement of molecules
  across a semi-permeable membrane from high to low
  concentrations requiring a carrier.

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Applied Concepts of MolecularMovement

• Hydrostatic Pressure--the force a liquid places
  on the walls of its container
• Osmotic Pressure--the movement of a solvent such
  as water across a semi-permeable membrane from an
  area of high concentration to low concentration.
• Oncotic Pressure--the pressure forces exerted by
  large, non-diffusable molecules such as proteins
  which hold certain diffusables such as the
  electrolytes in particular fluid compartments.

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Applied Concepts of Molecular Movement

• The Gibbs-Donnan Rule--(oncotic pressures)
• If a non-diffusable entity such as proteins is
  present on one side of a selectively permeable
  membrane (to other solutes), the anions and
  cations will distribute themselves unequally
  across that membrane.
• But, there are three (3) primary requirements---

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Applied Concepts of Molecular Movement---the 3
criteria for the Gibbs-Donnan Rule

• 1st--the total number of cations and anions must
  be equal on both sides of the membrane
• 2nd, on the side with the non-diffusables
  (proteins), the diffusable cation concentation
  will be higher and the diffusable anion
  concentration will be less than those anions on
  the side that has no non-diffusables.
• 3rd, the non-diffusable side will have a higher
  osmotic pressure that the side having no
  non-diffusables (proteins).

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Fluid Dynamics

• Law of Continuity--states that the product of the
  cross-sectional area times the velocity is
  constant, e.g., cross-sectional area and velocity
  are inversely related.
• Basically, this simply means as cross-sectional
  area increases, the gas velocity decreases, and
  vice versa.
• The formula
• A x v k

Where A tube cross-sectional area v fluid
velocity k a constant
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Fluid Dynamics--The Bernoulli Principle Equation

• Based upon the law of energy conservation
• Simply stated, at a constant flow rate, the sum
  of the potential energy and kinetic energy per
  unit volume of fluid and lateral wall pressure at
  one point in the system will equal the sum of
  these factors anywhere in the system.
• Remember, we are dealing with incompressible
  fluids, as well as rigid tubes...theres more...

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Fluid Dynamics--The Bernoulli Principle Equation

• If we place a restriction in this tube...note
  what happens...at the restriction...
• lateral wall pressure decreases
• central velocity increases
• central pressure increases
• PE and KE on both sides of the restriction remain
  unchanged (Energy Conservation!!)

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Fluid Dynamics--The Bernoulli Principle Equation

• The view of the tubes...and the equation

P 1
P 2
Constant Flow
v 1
v 2
P 2 lt P 1
v 2 gt v 1
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Fluid Dynamics--The Venturi Effect Fluid
Entrainment

• Venturi studied Bernoulli in detail...his
  studies
• concluded that
• There must be a way to re-establish
• prerestriction pressure...
• There must be a way to re-establish velocity
• At the point of restriction where lateral wall
• pressure is lower, then fluids will move from
• the outside to the inside, at the point of
  restriction,
• also known as the jet.
• AND HE ACCOMPLISHED JUST THAT...

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Fluid Dynamics--The Venturi Effect Fluid
Entrainment
1st--distal to the restriction, he opened
the restriction at an angle of no greater than
15o. 2nd--as a result, prerestriction pressure
was almost achieved, as was prerestriction
velocity... 3rd--he inserted a tube at the point
of restriction-- as he surmised, fluids DID move
from the outside to the inside at the point of
restriction...from high to low
pressure...technically, this is the jet
principle... and not entrainment....but we do use
his effect....
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Fluid Dynamics--The Venturi Effect and Fluid
Entrainment
The view of the tubes...
P 3
P 1
P 2
v 1
v 2
v 3
Constant Flow
P 2 lt P 1
P 3 P 1
v 2 gt v 1
v 3? v 1
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Fluid Dynamics--The Venturi Effect Fluid
Entrainment
1. We use it in automobiles, those with
carbureted fuel systems to mix ambient air and
gasoline being delivered to cylinders for
power. 2. We use it in respiratory care (a)
Venturi nebulizers (b) to deliver mixtures of
gases to deliver specified oxygen
percentages...to calculate these percentges,
especially when titrating air/oxygen mixtures
the following formula is used...
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Fluid Dynamics--The Venturi Effect Fluid
Entrainment
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Fluid Dynamics--Laminar vs. Turbulent Flow
Characteristics

• Laminar Flows are characterized homogenous
• fluid layers, with the leading edge being
• parabolic in its design...
• As driving pressures and velocity of the flows
• reach critical velocity (a function of the
  density
• and viscosity of the fluid)...turbulent flow
  occurs.
• Tubulent flows are characterized by inhomogenous
• fluid layers, random movement, and loss of
  leading
• parabolic edge seen in laminar flows.

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Fluid Dynamics--Laminar vs. Turbulent Flow
Characteristics

• In order to have laminar flow, the pressure
  gradient
• needed is proportional to the flow rate times a
  constant
• related to the viscosity of the gas...

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Fluid Dynamics--Laminar vs. Turbulent Flow
Characteristics

• In order to have turbulent flow, the pressure
  gradient
• needed is proportional to the square of the
  flow rate times
• a constant related to the viscosity of the
  gas...

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Fluid Dynamics--Reynolds Number
Reynolds Number is the dimensionless result
of the relationship between kinetic forces, and
the frictional force of viscosity of homogenous
flowing fluids. If R N gt 2,000, turbulent flows
occur.

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Fluid Dynamics--Resistance

• Resistance is equal to the change in pressure
• divided by the gas flowrate...
• There are 3 components to ventilatory
  resistance---
• inertial, e.g. the system itself resists changes
  in motion
• elastic, e.g., the chest wall and the lung
  (compliance
• is the measure, a static measure.)
• airway resistance, e.g., a dynamic measure, as
  given
• in the definition...

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Fluid Dynamics--Resistance

• The formula...
• Units of measure...
• cmH2O/Liter/second

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Fluid Dynamics--Resistance

• The calculation for airways resistance (fluid
• flows), is identical to...
• Ohms Law, used in electricity...the units of
  measure are different, but the course of action
  is similar...consider the following...

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Fluid Dynamics--Resistance

• Assume we have 3 tubes gradually getting smaller
  in size...we will have greater resistance to
  overcome...because we will ADD all of these
  resistances together. This is known as a SERIES
  circuit in electricity, as well as in liquid
  systems. But we can diminish the total resistance
  by spreading the total resistance over a larger
  area...

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Fluid Dynamics--Resistance

• And we can do this by establishing what is known
  as a PARALLEL circuit...
• By doing this, we no longer ADD the total
  resistances...we add the RECIPROCALS, thereby
  reducing the total system resistance...
• This is true for electrical circuits as well as
  the lung...

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Fluid Dynamics--Resistance
Examples... Series Resistance...

• P

R 1
FLOW
R2
R 3
R 1 R 2 R3 Raw or 2cmH2O/L/sec
2cmH2O/L/sec 2cmH2O/L/sec 6cmH2O/L/sec
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Fluid Dynamics--Resistance
Examples... Parallel Resistance...(using the
reciprocal)

• P

R 1
R 2
FLOW
R 3
1/R 1 1/R 2 1/R3 1/Raw or 1/2cmH2O/L/sec
1/2cmH2O/L/sec 1/2cmH2O/L/sec 1.5
L/sec/cmH2O or 1/1.5 L/sec/cmH2O 0.67 cm
H2O/L/sec
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Fluid Dynamics--Viscosity Poiseuilles Law of
Laminar Flow

• Viscosity--the opposition of fluid movement
  through an conduit due to molecular interaction
• With liquids, this is caused by cohesive (Van der
  Waals) forces
• With gases, molecular interaction
• Viscosity is temperature dependent--
• w/liquids, viscosity decreases w/incresed
  temperature
• w/ gases, viscosity increases w/increased temps

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Fluid Dynamics--Poiseuilles Law of Laminar Flow

• The mathematical relationship--
• Flow is directly proportional to (1)the pressure
  gradient (2) the tube radius raised to the 4th
  power
• Flow is inversely proportional to (1) fluid
  viscosity (2) length of the tube and (3) the
  mathematical constant ?/8.

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Fluid Dynamics--Poiseuilles Law of Laminar Flow

• The Formula

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Fluid Dynamics--Poiseuilles Law of Laminar Flow
Rearrangement of The Formula shows that airway
resistance is inversely proportional to the
radius raised to the 4th power!!!!!!!!!
Basically, this means if we halve the radius of
the tube, we will increase the resistance 16
fold!!!!!!!!!!!!!!!
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Fluid Dynamics--Poiseuilles Law of Laminar Flow
Further rearrangement of The Formula shows that
flow is equal to driving pressure divided by the
resistance...again, we are touched by Ohms Law
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Fluid Dynamics-- Conditions on Poiseuilles Law
of Laminar Flow

• Fluid flow must be nonpulsatile and laminar
• the single conducting tube must be rigid and
  cylindrical
• the fluid must be homogenous and Newtonian
• Newtonian fluids maintain constant viscosity.

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Ventilatory Mechanics

• Hookes Law (The Law of Elastance)--a substance
  is said to be elastic if, after being deformed
  (or stretched), it returns to its normal shape...
• It can be applied to the lung, but the law must
  be modified...
• If we substitute pressure for force, and volume
  for length, we can plot pressure/volume curves.

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Ventilatory Mechanics--Compliance and Elastance

• Compliance--the ease of distensibility or
  stretch
• Elastance--is the reciprocal of compliance
• THEREFORE--compliance indirectly measures
  elastance
• While the lungs have a natural tendency to be
  elastic and collapse, the chest wall has a
  natural tendency to compliance expansion

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Ventilatory Mechanics--Compliance and Elastance
The Formulae
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Ventilatory Mechanics

• Compliance measures of the lungs and chest
  combined are less than the compliance of the
  lungs and chest, separately measured

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Ventilatory Mechanics--The Law of LaPlace

• Applied to geometric spheres, its mathematical
  relationship indicates
• That driving pressure is directly related to
  surface tension of the sphere and
• Is inversely related to the spheres radius
• P 2ST
• r

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Ventilatory Mechanics--The Law of LaPlace

• However, because of the surface active agent
  produced by the alveoli, this law actually has
  little significance in alveolar mechanics.
• Remember, Critical Volume, is that volume
  required to keep alveoli inflated--surfactant,
  effectively lowers critical volume, so that
  alveoli can remain inflated longer...

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Ventilatory Mechanics
r
r
If we open the one-way valve and allow these
alveoli to communicate--airflow will move away
from the small alveolus to the larger one,
simply because, it takes a higher driving
pressure to keep the small alveolus inflated...
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Myocardial Mechanics-- Frank-Starling
Relationship

• A modification of Hookes Law, it states that the
  amount of contraction of myocardium is directly
  proportional to the amount of stretch prior to
  that contraction