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CHEMISTRY / PHYSICS 
WEEK FOUR CLASS OUTLINE

I Nature of Flow

  1. States of Flow – Fluids are substances capable of flowing. "Fluids" are either liquid

or gas. Both liquid and gas have similar flow characteristics, the main difference is that a gas is compressible and liquids have greater density and viscosity.

Review- Liquids have no definite shape (take shape of container), but have size. Gas has no definite shape or size (fill space offered to them by diffusion).

Pressure must be considered in any discussion of flow, unit: dynes/cm2 (conversion table 4-3, fyi – don’t memorize)

2. Definitions:

Flow – a motion through a constraint

Units of fluid flow: volume per time, cc/min.

Density – mass/volume

Viscosity – (notes) the internal friction of molecules of a liquid or gas. Factors effecting viscosity: Temperature, Density, Mixing with something else.

(article) the internal frictional resistance between the layers of a fluid. It is an inherent physical property of the fluid. Unit of measurement dyne/cm2.

(chem book)- The movement of liquid molecules is called flow and the resistance to flow is termed viscosity and is dependent on the size of the molecules and the attraction to each other by molecular force. Blood with high hct more viscous – dehydrated, polycythemia. In general large molecules and strong intermolecular forces impede molecular flow, are more viscous. An increase in temperature decreases the viscosity of liquids by weakening molecular bonds.

*Liquids: Increase Temp, Decrease Viscosity

*Gas: Increase Temp, Increase Viscosity

Critical Flow Rate – Exists for a given diameter of a tube for a given fluid at a given temperature. When the flow rate of a fluid in a particular tube exceeds this critical flow rate, the flow is no longer laminar – it becomes turbulent.

  1. Rate of Flow Through Orifices and Tubes – fluid behaves one way when it passes

through a tube and another when it passes through an orifice.

Tube – a pathway through which a fluid may pass, the diameter which is considerably less than the length.

Flow through tube is driven via pressure gradient from high to low until pressure is equal at both ends.

Orifice – an opening through which a fluid may pass, the diameter which is considerably greater than the length. Ideal orifice has negligible length, just a perimeter.

The flow is driven by pressure gradient on either side of the orifice.

Rate of flow of gas through orifice varies with the square root of the density of the gas.

Ex – hydrogen is 1/16 as dense as oxygen, and it flows 4 times faster than oxygen.

Rate of flow of liquids not dependent on density.

 

4. Laminar and Turbulent Flow

Laminar Flow – (class) streamline flow; flow consists of a large number of concentrically arranged cylinders of fluid flowing at different rates. Cylinders on outside have lower velocity, those molecules in direct contact with outside wall have a velocity of zero. The cylinders in the middle have higher velocity.

The differences between the velocities in these cylinders depends on the viscosity of the fluid.

(article) The orderly movement of molecules in a path parallel to the walls of the tube, as a fluid streams through a tube at a steady flow.

Reynold’s Number:

Density of Fluid x Linear Velocity x Diameter of Tube

Viscosity of Fluid

Reynolds # different for each fluid!!

**At what number does Laminar Flow become Turbulent? 2300 and above.

(In a long, straight, rigid tube)

During laminar flow, the pressure gradient necessary to generate a particular flow is directly proportional to the product of the flow and resistance

Turbulent Flow – (class) don’t have orderly flow, breakdown of cylinders, vortices and eddy currents form.

According to the Reynold’s equation, turbulent flow is likely to occur when the fluid density and linear velocity are high, when the diameter is large, or when the viscosity it low.

During turbulent flow, the pressure gradient necessary to generate a particular flow is proportional to the square of the flow times the resistance.

Reasons why flow can become turbulent:

Kinks or bends >25 degree

Flow velocity is too high

Vessel wall is nonuniform/rough

Flow through orifice (ie. Iv catheter to vein)

The resistance is increased when you go from laminar flow to turbulent. Once the flow becomes turbulent the DENSITY of your fluid determines the flow.

Transitional Flow – When laminar becomes turbulent at this "transitional area". This mixture of laminar and turbulent usually occurs at branch points, narrowing, or partial obstruction of vessels.

5. Effects of Friction and Resistance ?used interchangeably

In order to maintain flow you must overcome resistance.

Friction must be overcome via application of additional energy in the not so "ideal" system.

Total Resistance is equal to sum of the individual.

Resistance to laminar flow depends mainly on viscosity of fluid.

Resistance to turbulent flow mainly depends on the density of fluid.

Resistance = Change in pressure or Flow = Change in pressure

Flow Resistance

We discussed in class a "RAE" tube which is an oral or nasal ETT that is curved slightly for oral & nasal cases, but the Resistance is high.

We discussed cutting OETT to decrease the length and decrease resistance.

Try to use Largest diameter approp. For patient to reduce resistance.

These examples can be discussed further using Poisseulle’s Equation (#11).

Resistance as it relates to the Anesthesia Machine (class) – valves on inhalation, exhalation side. Resistance is 2-5 cm water pressure.

Peep valve decrease, increase resistance

Dead space as it relates to extension tubing

When you intubate someone you decrease the deadspace by ˝.

6. Airway Factors Affecting Flow - (class) ETT size, airway anatomy, tumors. What kind of tumor and where it is located is essential – some tumors flop over airway when positive pressure is applied. Also discussed Reactive Airway Disease, where there is a resistance to flow. Sometimes an inhalation agent can break status asthmaticus.

 

7. Effects of Speed and Pressure

Law of continuity – (disregard friction) in a fluid propelled by a force in a tube of varying cross-sectional diameter, the velocity varies with the cross-section diameter. The velocity is greatest at the constricted portion. The volume is proportional to the cross-section area times the velocity.

More energy is necessary to force a fluid through a tube to overcome friction (this is not accounted for by law of continuity). A decline in pressure occurs as a fluid flows through a tube, this decline in pressure is proportional to the rate of flow if flow laminar, if turbulent the decline in pressure is much greater..

Rate of flow through a tube does not depend on density (viscosity is a factor)

 

  1. Bernoulli’s Theorem – (notes) pressure flowing though a tube will vary depending
  2. on the cross-sectional diameter. The constricted area has increased velocity and decreased pressure. The wider area has decreased velocity and increased pressure.

     

    (Hall) in ideal system with no friction and nonviscous fluid, no resistance to fluid flow, the total energy of the system should be constant, so the total energy in the narrowed section of tube should be equal to that in the wider section.

     

  3. Venturi System – Venturi principle extends Bernoulii’s work on the relationship

between the velocity of the flow of a fluid and its lateral pressure in several ways.

Venturi tube is used with manometer/pressure gauges to determine the flow rate and volumes through a tube. The quantity of fluid delivered in unit of time could be figured out (not often used).

Another use of venturi principle: if the diameter of a section of tube through which fluid is flowing is considerable less than that of the section preceding it, and the tube gradually widens, the lateral pressure at the constriction is much less than that before or after the constriction. The lateral pressure in a tube of rapidly flowing pressure can be subatmospheric at the severe constriction. A side arm at this constricted area can be used to draw in/aspirate another fluid into the tube. Such a device is known as an injector. Entrainment is the aspiration of a gas into a gas mixture. A liquid aspirated into gas used in nebulizer, and atomizers.

 

10. Viscosity and Flow – (chem/phys article) all fluids exhibit a certain degree of internal friction, the term viscosity is used to designate this internal friction of a fluid. When a fluid moves through a tube of uniform diameter the velocity of the molecules is not uniform throughout its mass. Those adjacent to and in contact with wall appear to be almost at rest, the next layer is sluggish, until in the middle the molecules move rapidly. The forward advance of a row of molecules is represented by a parabolic curve.

 

11. Poiseulle’s Law – describes the relationship between the pressure and the flow of a "fluid" flowing through a tube. This law is valid strictly for pure/ideal fluid undergoing steady, nonpulsatile flow (laminar flow) through a rigid vessel.

 

F= Flow

R= Resistance to flow

^P= pressure gradient

F = ^P
      R

Note: ^P = F x R (Ohm’s Law for electricity)

The volume of fluid discharged through a tube varies with the length of the tube, the diameter of the tube, the decline in pressure as the fluid is propelled along the tube and the viscosity of the fluid.

(notes) The volume of fluid through a tube can vary.

Flow(Q) = ~ r4 x ^P

    1. x n x L

n = viscosity coefficient

L = length

*know the principle as it relates to radius

Discussed more below:

12. Effects of Length and Radius on Volume

According to Poiseulle’s Law – the volume of discharge is inversely proportional to the length of the tube and directly proportional to the fourth power of the radius of the tube. Thus, is the length of tube is doubled, the volume of fluid discharged is halved (if all other factors are constant).

If the radius is reduced by half the force or pressure propelling the fluid through the tube must be atleast doubled to maintain constant volume.

Ex. How much do we decrease resistance to flow if we double radius? 16x

Triple radius? 81x

13. Effects of Density and Viscosity on flow – Viscosity is independent of the density of the fluid.

Ex – Benzine and liquid petrolatum have nearly similar densities, but the petrolatum is more viscous and moves more slowly through a capillary tube.

Thus this tells us that it is viscosity that determines the rate of flow not density.

Changes in temperature and pressure alter both viscosity and density of gases.

???Density was a factor in chem/phys article with mov’t of gas through an orifice.

???Once the flow becomes turbulent density determines the rate of flow

 

14. Volume Flowmeters - Measurement of the flow of gases is based on the principle that flow past a resistance is proportional to pressure.

(Rajala article) The flowmeter is a device that measures, controls, and indicates the flow of gas passing through it. Modern flow meters know as variable orifice or Thorpe flowmeters.

Gas enters through bottom and leaves through top, elevating an indicator float or bobbin that moves and down the tapered tube freely. The indicator floats at the point of equilibrium where the downward force of gravity on the bobbin is equal to the upward force of the gas flow. A scale calibrated specifically for each gas is found along the side of the tube – indicating gas flow. The higher the float rises the greater the gas flow around it. The flowmeters are calibrated at room temp and atmospheric pressure.

Rate of gas flow through flowmeter depends on:

-Pressure change across the constriction: as gas flows around the bobbin, friction between the glass and bobbin in encountered, causing a pressure drop – this change is constant for all positions within the tube.

-Magnitude of the annular opening: the space between the float and the wall of the tube forms a channel or "annular opening. Gas flow increases with increase in annular opening.

-Physical properties of the gas – at low flows when the tube is narrow, gas flow varies according to the viscosity of the gas (Poiseille’s law). At high flows the gas flow becomes a function of the density of gas (Graham’s law)

*More simply put: (Stoelting/Miller)The proportionality between pressure and flow is determined by the shape of the tube (resistance) and the physical properties (density and viscosity) of the gas.

Flow as it relates to altitude:

At low flow rates, flow is laminar and dependent on gas viscosity (a property independent of altitude)

At high flow rates, flow becomes turbulent and flow becomes a function of density (a property that is influenced by altitude – the resulting decrease in density will increase the actual flow rate – the meter will read lower than the actual flow)

Inaccuracy – error increases inversely with the rate of flow and become clinically significant at flows less than 1L/min.

Placement of O2 flowmeter when machine used has a series arrangement: place downstream, closest to outlet; use oxygen analyzer.

15. Physics of the Circulatory System – (class) be aware of vessel rich groups.

 

16. Cardiac Output (see handout – normal resting values)

CO = HR x SV

CI = CO

BSA

EF (Ejection Fraction) = SV x 100 = ? %

NML 60-80% End diastolic volume

 

SVR = MAP – CVP x 80

CO

Circulation Time – The amount of time it takes for a substance to pass through the liver X1. This is a big factor when dealing with iv agents. The older the person, the slower the circulation time, takes a while to get to the brain.

On beta-blocker may decrease circulation time based on decreased HR

Peds/Healthy – have a faster circulation time.

We discussed Aortic Stenosis briefly, in that you may have a good EF but the volume ejected is very diminished.

Right to Left shunt – Blood is bypassing the lungs, slows induction

V/Q mismatch, pulmonary emboli

Left to Right shunt – no real effect on speed on induction, assuming that systemic blood flows normally. Theoretically, you would think that this would decrease the delivery of anesthesia to the body/tissues, BUT increased cardiac output makes up for this by compensation.

 

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Last updated 04/10/00 12:26:46 PM