SS Flow Dynamics - Fall23.pptx

Fluid Dynamics Clay Freeman, DNP, CRNA Science in Anesthesia 1 Objectives Readings: Nagelhout: Chap. 15 Davis: Chap 2 • Describe various fluid mechanics • Detail Poiseuille’s Law • Detail Reynold’s Number • Discuss Laminar vs Turbulent Flow • Detail Bernoulli’s Principle • Discuss Venturi Effec...

Fluid Dynamics Clay Freeman, DNP, CRNA Science in Anesthesia 1 Objectives Readings: Nagelhout: Chap. 15 Davis: Chap 2 • Describe various fluid mechanics • Detail Poiseuille’s Law • Detail Reynold’s Number • Discuss Laminar vs Turbulent Flow • Detail Bernoulli’s Principle • Discuss Venturi Effect 2 Hydrostatics Both LIQUIDS & GASES Are FLUIDS Fluids are all susceptible to gravity, pressure, and friction Static Fluids are defined by density and pressure P= pgh P – fluid pressure p – fluid density g – gravity h – fluid depth Fluids can be categorized by their response to Perpendicular stress: Liquids resist compression Gases become compressible and expandable Strain is the deformation of fluid in response to stress 3 Fluid Dynamics Dynamics of Fluids are defined by their response to stress Fluids change shape in response to stress, or succumb to strain Response to Tangential (Shear) stress: Friction is resistance to flow from surface interaction Viscosity is the inherent property of a fluid that resists flow 4 Fluid Mechanics All flow moves from higher pressure to lower pressure Flow (F) is defined as the quantity (Q) of fluid passing a point per unit of time (t) F=Q/t Px P< x 5 Flow Rate F=Q/t Volume of a fluid per unit of time flowing through an area SI units is cubic meters per second m3/s But we will be focused on… 6 Types of Flow LAMINAR TRANSITION AL TURBULENT 7 Laminar Flow All molecules travel in a parallel path within the tube • Molecules in the center of the tube encounter less tangential force and flow at velocity twice that of mean flow • Flow decreases near the walls until it ceases 8 Hagen-Poiseuille’s Law Mathematical Expression of Laminar Flow F = (p r4 DP) / (8 h l) Flow (F) is exponentially proportional to the Radius (r) (F) is directly proportional to the Pressure Gradient (DP) (F) is inversely proportional to fluid Viscosity (h) (F) is inversely proportional to Length (l) of tube 9 Poiseuille’s Law F = (p r4 DP) / (8 h l) - FLOW RELATIONSHIPS Flow (F) is exponentially proportional to Radius (r) 20 ga 1.65 mm 16 ga Decreasing radius by 1/2 decreases flow to 1/16 RADIUS (r) 0.89 mm FLOW RATE (Q) Doubling the radius increases flow by factor of 16 10 Poiseuille’s Law CLINICAL APPLICATION 7.0mm ETT has twice the resistance compared to 8.0mm 11 Thorpe Tube 12 Poiseuille’s Law F = (p r4 DP) / (8 h l) PRESSURE GRADIENT (DP) Flow (F) is directly proportional to the Pressure Gradient (DP) FLOW RATE (Q) DP = PInflow - 13 Poiseuille’s Law F = (p r4 DP) / (8 h l) VISCOSITY (h) Flow (F) is inversely proportional to fluid Viscosity (h) Polycythemia FLOW RATE (Q) Anemia 14 Poiseuille’s Law F = (p r4 DP) / (8 h l) 16 ga 1” LENGTH (l) Flow (F) is inversely proportional to Length (l) of tube Decreasing the length by 1/2 doubles the flow 16 ga FLOW RATE (Q) 2” 15 Poiseuille’s Law Versus CLINICAL APPLICATION Versus 16 Poiseuille’s Law Resistance For Laminar flow: R = (8 h l) / (p r4) Resistance = D Pressure / Flow (Q) 17 Poiseuille’s Law CLINICAL APPLICATION Resistance = D Pressure / Flow (Q) Systemic Vascular Resistance Use of pressure gradients and hemodynamic flow to determine Resistance or “Vascular Tone” 18 Poiseuille’s Law CLINICAL APPLICATION Anesthesia machine flow sensors consider aspects of Poiseuille’s Law while compensating for differences in gas density and temperature 19 Turbulent Flow • Consists of irregular swirls or eddies • Occurs at high velocities • Occurs at sharp bends, angles, and irregularities 20 Reynolds Number Index that uses Poiseuille’s Law and fluid Density to determine whether a given flow will be laminar or Turbulent Directly proportional to: Velocity Density Diameter Inversely proportional to: Viscosity Re = (vpd) /h v= Velocity p= Density d= Diameter h= Viscosity Reynolds Number Laminar flow < 2000 Turbulent Flow > 2000 21 Reynolds Number CRITICAL Flow is the point at which laminar flow becomes Turbulent 22 Reynolds Number CLINICAL APPLICATION Viscosity is highly valuable in determining Laminar flow ( “stickiness” or resistance to shear stress) Density is highly valuable in determining Turbulent flow 23 Turbulent Flow CLINICAL APPLICATIONS Flow becomes Turbulent if: • Velocity of flow is high o Speaking, coughing, deep breathing • Tube wall is rough o Corrugated tubing • Kinks, bends, narrowing, or branches in the tube o Especially if angle > 25° encountered • Fluids flow through an orifice  Turbulent flow increases resistance  Flow through smaller and terminal bronchioles is low-velocity and laminar Respiratory gasses include water vapor and CO2, which affect 24 Bernoulli’s Principle As flow passes through a narrowing in a tube, the Velocity of that flow increases with a corresponding decrease of Pressure at the area of narrowing VELOCITY PRESSURE 25 Bernoulli’s Principle Velocity & Pressure exhibit an inverse relationship to one another which is explained by the Conservation of Energy Law The increase in Velocity can be shown through consideration of: 4 L/min 2L 1L Velocity1 = (4 L/min) / (2 L) = 2 L/min Velocity2 = (4 L/min) / (1 L) = 4 L/min The energy required to increase Velocity is borrowed from the kinetic energy of the fluid exerting Pressure • thus as Velocity increases, Pressure must decrease 26 Bernoulli’s Theorem CLINICAL APPLICATIONS Useful in Echocardiography: • Estimate cardiac output • Cardiac valve area can be determined (mitral vs aortic stenosis) 27 Venturi Effect Because of the decrease in Pressure, placing opening in the narrowing of a tube causes surrounding fluid to be entrained with the flow AIR ENTRAINMENT VELOCITY PRESSURE 28 Venturi Effect CLINICAL APPLICATIONS VENTU RI MASK NEBULIZER 29 Venturi Effect CLINICAL APPLICATIONS JET VENTILATION 30 Coanda Effect Occurs with constrictions prior to bifurcations This could cause preferential fluid flow at a bifurcation as the Pressure of the fluid increases and the Velocity decreases beyond the narrowing Constricti on VELOCITY 31