Physical Principles of Respiratory Care States of Matter Change of State Gas Behavior Under Changing Conditions Fluid Dynamics

Fluid Dynamics Pressure in Flowing Fluids Patterns of Flow Laminar Flow Turbulent Flow Transitional Flow Flow, Velocity, and Cross-Sectional Area Bernoulli Effect Fluid Entrainment Fluidics and the Coanda Effect

Fluid Dynamics The study of fluids in motion is called hydrodynamics. The pressure exerted by a liquid in motion depends on the nature of the flow itself. A progressive decrease in fluid pressure occurs as the fluid flows through a tube due to resistance.

Patterns of Flow Patterns of flow Laminar flowfluid moving in discrete cylindrical layers or streamlines Poiseuille’s lawpredicts pressure required to produce given flow using ΔP = 8nl V./ πr4

Conditions that cause laminar flow to become turbulent High linear gas velocity High gas density Low gas viscosity Large tube diameter

Patterns of flow Turbulent flowloss of regular streamlines; fluid molecules form irregular eddy currents in chaotic pattern. Predicted by using Reynold`s number (NR) NR = v d2r / h

Patterns of Flow Transitional Flow Transitional Flow: A mixture of laminar and turbulent flow Occurs at points where tubes divide into one or more branches Where airways divide

Poiseuille’s Law (only applies to laminar flow) Flow of fluid through a tube: Driving pressure Resistance Viscosity Length of the tube Radius of the tube

Poiseuille’s Law The more viscous the fluid the more pressure is required to cause it to move through a given tube

Poiseuille’s Law Resistance to flow is directly proportional to the length of the tube If the length of a tube is increased four times, the driving pressure to maintain a given flow must be increased four times

Poiseuille’s Law Resistance to flow is inversely proportional to the fourth power of the radius of the tube If the inside diameter of the tube is decreased by one half, the driving pressure must be increased 16 times to maintain original flow

Respiratory Care Application: ETT Poiseuille’s Law Respiratory Care Application: ETT

Poiseuille’s Law Asthma

Pressure in Flowing Fluids

Law of Continuity The speed of flow in a closed system will be inversely proportional to the area of the tubes through which it flows

Law of Continuity 2.54 If the area of flow is decreased, then the velocity must increase If the area of flow in increased, then the velocity must decrease This fact is based upon the observation that the total fluid flowing through the system remains constant For example: if 5 L/min flows past point A, 5 L/min must flow past point B, and point C Since the area at point B is one-half that of point A, the fluid must flow twice as fast. If the area of flow is decreased, then the velocity must increase. At point C, the total area is five times as large as at point A, so the average speed is slower by a factor of 5. If the area of flow is increased, then the speed must decrease A garden hose is a good example of this phenomenon

Law of Continuity

Review We already know that when a fluid flows through a tube of uniform diameter, there will be a gradual drop in pressure We also know that as the area of flow is decreased, then the speed must increase (Law of Continuity)

As the speed of the fluid increases, the pressure in a fluid decreases The Bernoulli Effect As the speed of the fluid increases, the pressure in a fluid decreases The first three columns in this figure demonstrate this gradual pressure drop. As the pressure drops, the height of the liquid in the column will decrease Notice that as the fluid flows through a constriction in the tube, the pressure of the fourth tube shows an even greater drop in pressure. If it is assumed that the total flow of liquid is the same before and after the constriction, then the flow of liquid must accelerate as it enters the constriction According to the Law of Continuity, flow must increase in order to transport the same volume of fluid in a given time Thus it is reasonable to assume that the drop in fluid pressure is directly related to the increase in fluid speed. When the fluid passes through a constriction, the pressure drop is much greater. As can be observed in the fourth column. This drop in fluid pressure is directly related to the increase in fluid speed. The strict proportions between fluid speed and area is true only for incompressible fluids in a closed system, but the qualitative features are similar for flow in open systems, and also for gas flow.

Review We already know from the Law of Continuity that when a flowing fluid encounters a narrow passage the velocity increases. We also know from Bernoulli’s Principle that this increase in velocity causes a decrease in pressure

Venturi Principle of Fluid Entrainment If the increase in velocity at a constriction is so great that is causes the pressure of the fluid to fall below atmospheric (becoming negative) it can pull another fluid into the primary flow If we place an open tube distal to such a constriction, this negative pressure can actually pull another fluid into the primary flow system, this effect is called fluid entrainment

Respiratory Care Application: Air injector Fluid Entrainment Respiratory Care Application: Air injector A, The basic design. B, Greater entrainment and total flow occurs with larger entrainment ports. C, Alternatively, a smaller jet increases source gas velocity and entrains more air

Respiratory Care Application: Entrainment mask Fluid Entrainment Respiratory Care Application: Entrainment mask

Respiratory Care Application: Small Volume Nebulizer Fluid Entrainment Respiratory Care Application: Small Volume Nebulizer This is a typical small volume nebulizer which is powered by a high-pressure stream of gas directed through a restricted orifice (or jet). The gas stream leaving the jet passes by the opening of a capillary tube immersed in solution. Because the high jet velocity produces low lateral pressure at its outlet, it draws the liquid up the capillary tube and into the gas stream, where it is sheared apart into droplets. These droplets are directed toward a baffle (a baffle is a surface upon which large particles impact and fall out of suspension) so that only small particles are sent to the patient’s airways allowing for better deposition

Respiratory Care Application: Large volume jet nebulizer Fluid Entrainment Respiratory Care Application: Large volume jet nebulizer

Fluid Dynamics Fluidics and the Coanda effect Fluidics is a branch of engineering that applies hydrodynamics principles in flow circuits. The Coanda effect (wall attachment) is observed when fluid flows through a small orifice with properly contoured downstream surfaces.

Operate without moving parts, minimizing maintenance expenses Advantages Operate without moving parts, minimizing maintenance expenses Generally cost less than electronic counterparts Don’t break down as often as their electronic counterparts

Not easily interfaced with microprocessors Disadvantages Not easily interfaced with microprocessors Not as accurate as their electrical counterparts Difficult to measure tidal volume because tidal volume exits with source gas