Darcy's Law (Physiology)

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Equation / Last modified by KurtHeckman on 2018/03/16 14:40
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The Darcy's Law (Physiology) calculator computes the blood flow (F) through a vessel based on a change in pressure (ΔP) and a resistance factor (R).

INSTRUCTIONS;  Choose your preferred units and enter the following:

  • (ΔP) This is the change in pressure between points (P1 and P2)
  • (R) This is the resistance factor in the units of mmHg•minutes/liter.

Flow Rate:  The calculator returns the Flow Rate (R) in milliliters per minute.  However this can be automatically converted into other volumetric flow units via the pull-down menu.  PressureFlow.png

Heart / Blood Calculators:

  • Compute the Heart Chamber Pressure via the Law of Laplace
  • Compute the Heart Wall Stress via the Law of Laplace
  • Compute the Blood Flow Rate using Darcy's Law
  • Compute the Change in Vascular Pressure
  • Compute Blood Pressure
  • Compute the Blood Volume in a Human based on their weight
  • To compute change in vascular pressure, (`ΔP = P_1-P_2`), CLICK HERE.

The Science

[Physiology | Cardiology | Heart Health]  Darcy’s Law was created to describe the flow of a fluid through a porous medium, specifically the flow of water through sand.  The law has been significantly simplified for this application to Physiology here.  See Darcy's Law (Engineering) for the more explicit version of this equation as typically applied to hydrogeology and engineering applications.

In the physiology application, Darcy’s Law has been interpreted as defining blood flow against resistance, where the peripheral resistance of the circulatory system to blood flow is analogous to the resistance of a medium like sand to the flow of water.  The two inputs to this equation are:

  • Mean Arterial Pressure in units of mmHg - millimeters of mercury
  • Total Peripheral Resistance in units of mmHg * (min/L)

Darcy's Law returns the cardiac output in terms of Liters per minute.

The Math

The Darcy's Law formula was derived from experimental data by Henry Darcy has the following form:

`Q = (-k*A (P_b - P_a)) / (mu * L)`, where

  • k = the intrinsic permeability of the medium
  • A = the cross-sectional area through which the fluid will flow
  • `P_b - P_a` = the total pressure drop
  • `mu` = viscosity of the fluid
  • L =  the length over which the pressure drop occurs

As you can see in contrast, the physiology version of "Darcy's Law" is somewhat simplified:

        Cardiac Output = (Mean Arterial Pressure) / (Total Peripheral Resistance)

References