**Module Two:**

Air Flow and Fluid Dynamics

Bulk gas flow: transport of whole groups of molecules (volume of gas) from one location to another

Air flow - the rate @ which air moves from point of higher pressure to point of lower pressure a function of the

- Magnitude of driving pressure (the difference between the pressure at the beginning of the tube and the pressure at the end of the tube)
- Resistance to gas flow in communicating pathway (influenced by radius, shape of pathway)

- Density and viscosity of gas
- Type of flow pattern:

Flow – measurement of fluid volume per unit of time (L/min or L/sec) and symbolized by

, the V representing volume, and the dot above the V representing the unit of time, and can be expressed as L/min or L/sec.

Formula for calculating resistance to flow in the airway (aw):

Resistance in the airway is equal to the difference in pressure (also called pressure gradient) divided by the flow.

Three types of flow patterns occur simulataneously in the respiratory tract, under the influence of airway resistance, which contribute to the work of breathing, and influence the distribution of gases in the lung.

Smooth unobstructed flow of gas through a tube of relatively uniform diameter

Few directional changes

Slow, steady flow through straight smooth, rigid, large caliber, cylindrical tube

Outer layer flow slower than center due to friction, results in discrete cylindrical layers, or streamlines

Double flow by doubling pressure as long as the flow pattern remains laminar.

a) A tube showing the imaginary lamina. b) A cross section of the tube shows the lamina moving at different speeds. Those closest to the edge of the tube are moving slowly while those near the center are moving quickly.

Relates factors that determine laminar flow

Indicates degree of resistance to fluid flow through a tube

The resistance, (or pressure gradient), to fluid flow through a tube is **directly** related to the length, flow, and viscosity (as length, flow, or viscosity increases the resistance will also increase) ; and **inversely** (as radius increases, resistance decreases) related to the radius of the tube **to the fourth power**. (doubling radius increases gas flow by factor of 16)

If r = 3 then r^{4} = 81

If r = 6 (radius doubles) then r^{4} = 1296 (same as multiplying 81 x 16)

If r = 1.5 (radius reduced to half original value) then r^{4} = 5.06 (1/16th of original value)

*This is very significant in disease states that cause narrowing of the airways because it can significantly increase the amount of work the patient has to do to get air into their lungs - particularly in children whose airways are small to start with! Conditions that can cause airways to narrow include asthma, croup, and edema caused by inflammation.*

Variables and constants of Poiseuille's Law:

Variables can be rearranged to solve for different components:

To solve for viscosity the equation is arranged:

To solve for flowrate the equation is arranged:

To solve for driving pressure the equation is arranged:

In general, the relationships between the variables is:

(a decrease in flowrate will result in a decrease in resistance, and decrease driving pressure)

(a decrease in the radius of the tube, will cause an increase in the resistance to flow - exponentially by a power of 4, if driving pressure is constant, flow will decrease; to maintain flow will need to increase pressure)

(an increase in the length of the tube will result in an increase in resistance, if driving pressure is unchanged then flow will decrease; to maintain constant flow pressure will have to be increased)

(if all other factors are held constant, and increase in the driving pressure will increase flowrate

Key Points:

The more viscous a fluid, the greater the pressure gradient required to cause it to move through a given tube.

The resistance offered by a tube is directly proportional to its length; the pressure required to achieve a given flow through a tube must increase in direct proportion to the length of the tube.

Because the resistance of the flow is inversely proportional to the fourth power of the radius, small decreases in the radius of a tube cause **profound** decreases in the flow of the fluid through the tube.

Rough with much eddy current formation

Generated by sudden changes in direction or acute reduction in diameter

90% of turbulent flow in the airways occurs in the nose and trachea

Gas advances along tube at the same velocity at the center as at the periphery

Driving pressure to produce given gas flow proportional to the **square of volumetric flow rate**

Double flow by fourfold increase in pressure

A way of combining the factors to detemine a number that can be used to indicate the presence of turbulent flow. It can be in as a varilable expression as:

velocity of gas flow

density of gas

radius of the tube

viscosity of the gas

[Velocity – the measure of linear distance traveled by the fluid per unit of time (cm/sec) which differs from flowrate which is volume/time]

NOTE: Egan's uses h for the symbol for viscosity and give the equation as which mathematically works the same.

Reynold's Number thus is:

(1) Determined mathematically from velocity of flow, radius of tube, density and viscosity of gas

(2) A unitless number

(3) Indicates that turbulent flow occurs when N_{R} > 2000 (assuming tube is smooth and regular - can occur at a lower number if surface of the tube is rough or irregular)

(4) Reynold's number increases if there is an

(a) Increase in linear velocity of gas, density of gas, or radius of tube

(b) Reduction in viscosity of gas

The above chart indicates that with increasing velocity the Reynold's number also increases - breathing in quickly creates more turbulent flow throughout the tracheobronchial tree and significantly increases the work of breathing. Getting a patient to take a slow breath could help reduce the effort and anxiety of breathing.

Mixture of laminar and turbulent

At the same volumetric flow rate (volume of flow / amount of time) linear flow velocity is lower in small airways because of greater cross-sectional area.

FIGURE 6-23 Fluid velocity, at a constant flow, varies inversely with the cross-sectional area of the tube. (Modified from Nave CR, Nave BC: Physics for the health sciences, ed 3, Philadelphia, 1985, WB Saunders.)

Velocity of a fluid moving through a tube at a constant flow varies inversely with the available cross-sectional area

Exhalation- laminar pattern in bronchioles changes to turbulent in large airways

Inspiration – reverse occurs - turbulence in large airways changes to laminar in bronchioles

Bernoulli Effect (Daniel Bernoulli)

As velocity increases, lateral pressure (the force applied to the sides of the tube) decreases

As gas flows through a stricture (obstruction), its velocity increases and lateral pressure decreases

Magnitude of pressure drop is proportional to the increase in the square of the velocity.

Lung pathophysiology – COPD: increased mucus in airways can cause partial obstruction, the increased velocity of gas passing by the narrowing causes a decrease in lateral pressure, and combined with the destructive changes in the lung tissue, augments airway collapse and air trapping on exhalation.

Bernoulli's Priniciple or Effect has practical applications in the field of respiratory care in that it allows us to deliver precise oxygen concentration levels with simple devices by mixing oxygen with entrained room air. It also is applied in the process of delivering aerosol treatments with medications. When entrainining air the effect is applied through the use of air injectors and venturi devices.

Drop in pressure caused by increased velocity through restriction (jet) pulls in (entrains) additional air through open port.

Influenced by diameter of jet orifice (restriction), and size of entrainment port

B) Fixed jet size – changing size of opening of entrainment port influences amount of air entrained and resulting total flow. Gas velocity and pressure drop remains constant so increasing opening of port allows more air to be entrained, decreasing size of port decreases the amount of air that can be entrained.

C) Fixed entrainment port – changing size of jet diameter - the smaller the opening of the jet the faster the gas velocity, causing a greater drop in pressure, and thus more entrained volume and total flow. The larger the opening of the jet, the slower the gas velocity, less drop in pressure, less air entrained.

Most common device for air or fluid entrainment in respiratory care equipement

modification of the Bernoulli effect (Giovanni Venturi)

Venturi device includes a dilation of the gas passage just distal to obstruction, and if the angulation of the funnel is not over 15^{o}, the gas pressure will be restored nearly to its pre-restriction level.

Advantages of a venturi over an air injector:

greater entrainment and therefore higher total flow output

Stable oxygen % even with variations in total flow (as opposed to an injector where velocity would decrease with flow, and cause a decrease in entrainment of air)

Major limitation: Back-pressure (obstruction downstream from Venturi) reduces entrainment - resulting in a higher oxygen concentration than expected.

Used with early ventilators for adjusting oxygen concentrations (F_{I}O_{2}), or decreasing pressures within circuits to facilitate exhalation.

Fluidics is the branch of engineering that applies hydordynamic principles in flow circuits for purposes such as switching, pressure and flow sensing, and amplification.

Principle of fluidic circuitry is the phenomenon of **wall attachment**, known as the **Coanda Effect.**

Based on the Bernoulli effect (A) coupled with curved wall on one side of jet (B).

Can actually deflect fluidic stream through a 180^{o} turn by carefully extending the wall contour

Subatmospheric pressure along wall directs flow until interrupted by counterforce (pulse of gas).

Gas flow pathway can be changed by side jets in devices called gates; pulses of air from the side jet cause an increase in pressure at the wall, breaks the attachment and allows the gas stream to attach to the other wall, which will stay adhered to that wall until a pulse of air from below causes it to switch back.

Advantages: Fewer valves and moving parts that can break

Disadvantage: Consume more gas

Fluidics – no moving parts required for switching, pressure and flow sensing.