Gas Flow Physics

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:

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

• 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

• 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