Anesthesia Pharmacology:  Physics and Anesthesiology

Fluid and Gas Flow Principles

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  • An important clinical consideration has to do with a change in the relationship between flow and pressure as flow transitions from laminar to turbulent.  

    • In particular, for turbulence flow inside pathways that have rough internal edges, flow appears about proportional to the square root of pressure or a doubling of flow requires a quadrupling of pressure.

    • Furthermore, with turbulent flow, since pressure to flow relationships do not exhibit linearity, resistance will not be constant.  

    • In the turbulent flow case, resistance measurements must be specified in terms of the particular flow rate.

    • Physiologically, during breathing, airflow resistance will depend on the air flow rate assuming turbulence.

  • For turbulent flow, a nonlinear relationship exists between flow and pressure as shown below:

 

 

 

Occusion, Resistance and Pressure (courtesy of Dr. Rod Nave, Georgia State University)

  • The  equation = Pd4 / (128 l ) (Hagen-Poiseulle equation) illustrates the important relationship between flow rate and pressure.  Note the direct proportionality-that is, if all other things are equal, to increased flow rate requires a directly proportional increase in pressure.

  • Now, using an example provided by Rod Nave, Ph.D., consider the case in which the areas the need for a significant increase in blood volume flow rate in a so-called "flight or flight" situation.  

    • If a 5-fold increase in blood flow were required in this could be accomplished only by increasing blood pressure, then the pressure would have to be increased from a nominal 120 mm Hg to 600 mm Hg, a clearly impossible physiological response.

  • By contrast, vasodilation of only 50% is sufficient to accomplish the fivefold increase in flow.  Note in the equation above the fourth-power dependency of diameter (or radius); so, going from 1r to 1.5r would provide (1.5)4 or 5.06 increase in volume flow rate.  Furthermore, a 50% vasodilation is physiologically reasonable.

  • Calculations

 

The  figures and Poiseuille's Law material below, courtesy of Dr. Rod Nave, Georgia State University

Calculations

 

 

Bernoulli's theorem


  

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