Gas Flow Physics

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Non-elastic Resistance to Breathing:

  • Work of breathing is ~65% elastic recoil of lungs/thorax and ~35% airway/tissue resistance (non-elastic resistance)
  • Non-elastic Resistance is composed of:
  • Airway flow resistance - ~80%
  • Pulmonary tissue resistance/viscous resistance - ~20%
  • Work to overcome non-elastic resistance increases markedly with rapid respiration or with narrowing of airways
  • During airflow, pressure to produce a unit increase in lung volume is greater than when there is no flow
  • Pressure required to produce a given airflow depends on whether the flow is laminar or turbulent

Laminar Flow:

  • At low flow rates, flow is laminar - stream lines are parallel to the sides of the tube.
  • Laminar flow in straight, circular tubes:

Screen shot 2012-09-13 at 5.53.19 PM.png

  • P is driving pressure, r radius, n viscosity, l length. Because P = V x R:

Screen shot 2012-09-13 at 6.01.59 PM.png

  • So if radius is halved, resistance increases 16 fold, while doubling the length only doubles resistance.
  • Gas in the center of a tube of laminar flow travels twice as fast as the average velocity. The variable velocity across a tube's diameter is called the velocity profile.

Turbulent Flow:

  • Pressure is not proportional to flow rate, but to its square P=KV2
  • Viscosity less important, but gas density increases pressure drop for a given flow
  • Slower axial flow velocity

Reynolds number:

  • Determines whether flow will be laminar or turbulent

Screen shot 2012-09-14 at 8.35.29 AM.png

  • d is density, v is average velocity, r radius and n viscosity
  • Turbulence is most likely to occur when velocity of flow is high and tube diameter is large
  • Low density gas eg. helium produces less turbulence
  • In smooth, straight tubes, turbulence is probable when Re exceeds 2000

Airflow in the lung:

  • The lung is a complicated, branching system, and applying gas flow principles to it is difficult
  • Flow is turbulent in the trachea, especially during exercise when velocities are high
  • For most of the bronchial tree, flow is transitional
  • Fully developed laminar flow probably only occurs in the very small airways