The unsteady form of the Bernoulli equation for estimating pressure drop in the airways.
Previous investigators have used the steady Bernoulli equation to correct the underestimation of alveolar pressure by airway pressure observed during unsteady flow conditions. Using a simple idealized geometry, we demonstrate a method of including the unsteady term of the Bernoulli equation. Our approach was to determine the axial velocity distribution from the wave equation and employ this solution with the unsteady Bernoulli equation. In addition, we estimate the importance of inertia and viscosity and show that these effects can be quantified by the Womersley number.
Moslehi
F
F
Department of Anesthesiology, University of Connecticut School of Medicine, Farmington 06032.
Ligas
J R
JR
Pisani
M A
MA
Epstein
M A
MA
D000399:Air Pressure; D000403:Airway Resistance; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D011650:Pulmonary Alveoli / Q000502:physiology*; D012119:Respiration; D014132:Trachea / Q000502:physiology*