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## Fluid Dynamics

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**Fluid Dynamics**RT 21**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.**Under conditions of laminar flow in a viscous fluid, the**velocity increases toward the center of a tube.**Fluid Dynamics**• Examples of fluid dynamics in respiratory: • Mechanical Ventilation • Mechanical devices that deliver flow to patients • Flow of blood through the pulmonary and systemic systems**Law of Continuity**• Explains the relationship between the cross-sectional area of a tube through which fluid is flowing and the velocity of the flowing fluid when the flow rate is constant • Cross-sectional area and velocity are inversely related (meaning as the area is decreased, the velocity increases) A2 V2 A1 V1 If gas flow is held constant (liquid or gas), the velocity of the gas increases as the area decreases in circumference. Cross Sectional area x velocity = flow rate**Tracheobronchial Tree Air Flow**• Example of the continuity law is air flow through the tracheobronchial tree. • The airway differs in length, diameter and cross sectional area as it descends from the trachea. • The diameter decreases, airway length decreases BUT the cross sectional area increases as the airway branches out (like a upside down tree)**The airway anatomy results in an asymmetrical pattern of**branching, called irregular dichotomous branching • The branching although smaller in diameter from the previous branch possesses a greater cumulated surface area. This keeps occurring until you reach the alveolous**Gas Velocity through the tracheobronchial tree**• The velocity of gas decreases through the tracheobronchial tree since velocity is inversely related with cross sectional area • The cross sectional area of the lungs increase as you descend towards the alveolus (the diameter decreases, but the area increases); this causes the gas flow to distribute into these branches (area) which slows the velocity • Initially gas enters the lungs via pressure gradients; however towards the alveolus, since velocity is slow, gas moves via molecular diffusion (kinetic energy imparted by body temperature)**Pulmonary Capillary Blood Flow**• Continuity law also applies to blood flow. The lungs are covered in a vast network of capillaries, with a large cross sectional area (surrounding each cluster of alveoli). • The heart expels blood from the right heart into the pulmonary vascular at a high velocity, where it then slows due to the large cross sectional area. • The reduction in velocity allows for proper gas exchange as the contact time between the alveolus and the capillary blood is increases • This can be altered with a constriction of a capillary from hypoxemia**Velocity 2**V1 = V2 However during the branching of the capillary bed, the velocity slows Velocity 1**Review on Continuity Law**• http://www.youtube.com/watch?v=wykn-JTnacE**Laminar vs Turbulent flow**• As gas travels down the tracheobronchial tree it takes on a distinct flow characteristic • Laminar (lower airway) • Turbulent (upper airway) • Transitional (bifurcation of bronchi) • Natural flow patterns: Nose/trachea = turbulent, this allows entrapment of particles in the nasal concha • As the airway increase in cross sectional area, the velocity decreases turning the flow into laminar. The transition of turbulent to laminar is called transitional flow**Laminar Flow**• Laminar flow patterns depend on the airway size and resistance to flow • Obstructions to flow (mucus, swelling…) cause turbulent flow patterns • Laminar flow turns into turbulent flow when the velocity of flow exceeds a certain value (critical velocity) which is a function of the viscosity and density of the fluid • So, laminar can turn into turbulent with constrictions of the airway in the absence of increase cross sectional area (mucus plug occluding distal lung areas for example)**Laminar Flow**• Streamed lined horizontally moving molecules • Laminar Flow in a tube has its greatest velocity in the center of the tube and least on the edges of the tube • This is called Parabolic velocity**Patterns of Flow**• Patterns of flow • Laminar flowfluid moving in discrete cylindrical layers or streamlines • Poiseuille’slawpredicts 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**Turbulent Flow**• Non linear patterns of eddies. The velocity of the flow is equal through the tube everywhere in the tube unlike laminar**Reynolds Number**• In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations. • defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions. • They are also used to characterize different flow regimes within a similar fluid, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion; turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.**Reynolds Number**• The changeover from laminar to turbulent flow depends on several factors including: • Fluid density • Viscosity • Linear velocity • Tubing length • In a smooth bore tube, laminar flow becomes turbulent when the Reynolds Number > 2000 • Factors that favor turbulent flow include: • High gas velocity • High gas density • Low gas viscosity • Large tube diameter**Patterns of flow**• Turbulent flowloss 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**Review of flow patterns**• http://www.youtube.com/watch?v=R7Fz8q0lOSo**Viscosity**• The internal force that opposes the flow of fluids (equivalent to the frictional forces between solid substances) • The greater the viscosity, the greater the opposition to flow • The stronger the cohesive forces, the greater the viscosity**POISEUILLE’S LAW**• Mucous plug removed from a patient’s airway.**POISEUILLE’S LAW**• Fluid viscosity, tube length and radius determine resistance to flow. • As the radius of a tube decreases by ½, resistance increases 16 times. • Increased resistance to flow can be caused by a decreased airway size secondary to an increase in airway secretions, bronchospasm, intubation, etc.**Poiseuille’s Law:**• Poiseuille’s Law: the law that the velocity of a liquid flowing through a capillary is directly proportional to the presence of the liquid and the fourth power of the radius of the capillary and is inversely proportional to the viscosity of the liquid and the length of the capillary. • The variables in Poiseuille’s Law are: • The driving pressure gradient (the heart pumping) • Viscosity of the fluid (a person who is anemic can affect the viscosity of his/her blood) • Tube length (the veins and arteries) • Fluid flow (depending on the pressure and viscosity) • Tube radius (can be affected by clogged arteries) • And the constants (8 and 3.14)**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**Poiseuille’s Law**• Respiratory Care Application: ETT**Poiseuille’s Law**• Asthma**Review of Poiseulle’s Law**• http://www.youtube.com/watch?v=wTnI_kfPBhQ**Bernoulli Principle**• Describes relationship between lateral wall pressure and velocity form an incompressible fluid flowing through a tube in laminar fashion**The Bernoulli Principle**• When a fluid flows through a tube of uniform diameter, pressure decreases progressively over the tube length. • As fluid passes thru a constriction, the pressure drop is much greater**The Bernoulli Principle**Jet Entrainment Source Gas Area of negative pressure**The Venturi Principle**• States: “The pressure drop that occurs as the fluid flows thru a constriction in the tube can be restored to the preconstriction pressure if there is a gradual dilation of the tube”. • http://www.youtube.com/watch?v=Wokswr_KHXQ**The Venturi Principle**Va = Flow before restriction. Vc = Flow from entrainment plus driving flow. Pa = Original lateral pressure Pb = Falling lateral pressure at the restriction. Pc = Restored lateral pressure passed the restriction.**Venturi Mask**• The reduced pressure within the restriction may be used to introduce gases (usually air) into a low-pressure region of gas flow.**Fluid Dynamics (cont.)**• 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.**Coanda Wall Effect**• Basis for fluidic devices used in several mechanical ventilators. • Main advantage: fewer valves and moving parts that can break.