Poiseuille developed an equation in 1846 to describe the steady laminar flow of a Newtonian liquid in a narrow rigid glass tube. This equation can be used to predict how a change in one variable will affect the system, assuming a nondistensible system. An alternative name is the Hagen-Poiseuille equation.
flow of fluid =
= π * (pressure difference) * ((diameter)^4) / (128 * (viscosity of fluid) * (length of tube))
Change
Effect on Flow
Effect on Pressure
Effect on Diameter
Effect on Viscosity or Length
Flow
NA
proportionate
unchanged
unchanged
Pressure
proportionate
NA
unchanged
unchanged
Diameter
proportionate, change raised to 4th power
unchanged
NA
unchanged
Viscosity or Length
inverse proportionate
unchanged
unchanged
NA
where:
• If radius is used for the equation, the 128 is changed to 8 (radius to fourth power = 1/16 diameter to the fourth power).
• In a distensible system the diameter would change with the pressure, depending on the elasticity of the material.
• In a physiologic system the viscosity might change (dilution or concentration) as an adaptive response.
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