The model simulates fluid flow, F, through a rigid vessel of resistance, R, given a pressure drop across the length of the vessel Delta_P.
Description
The model simulates fluid flow, F, through a rigid vessel with resistance to flow, R, given a pressure drop across the length of the vessel delta P. This is simply the fluid analog of Ohm's Law where F is equivalent to electrical current, I, delta P is equivalent to the voltage difference, V, and the fluid resistance, R, is equivalent to the electrical resistance. R is derived from the Hagen-Poiseuille law and depends on vessel length, L, fluid viscosity, u, and the vessel diameter, D.
Equations
The fluid analog to Ohm's Law is given by:
and R is determined from the Hagen-Poiseuille relation and becomes:
where all variables are as previously defined.
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Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827
Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.