In the body, however, flow does not conform exactly to this relationship because this relationship assumes long, straight tubes (blood vessels), a Newtonian fluid (e.g., water, not blood which is non-Newtonian), and steady, laminar flow conditions.
#WHAT IS 0.3 TIMES 10 TO THE 4TH POWER FULL#
The full equation contains a constant of integration and pi, which are not included in the above proportionality. It is a description of how flow is related to perfusion pressure, radius, length, and viscosity. This relationship ( Poiseuille's equation) was first described by the 19th century French physician Poiseuille. If the above expression for resistance is combined with the equation describing the relationship between flow, pressure and resistance (F=ΔP/R), then Blood viscosity normally does not change very much however, it can be significantly altered by changes in hematocrit, temperature, and by low flow states.
Vessel length does not change appreciably in vivo and, therefore, can generally be considered constant. This figure shows how very small decreases in radius dramatically reduces flow. The relationship between flow and vessel radius to the fourth power (assuming constant ΔP, L, η and laminar flow conditions) is illustrated in the figure to the right. For example, a 2-fold increase in radius decreases resistance by 16-fold! Therefore, vessel resistance is exquisitely sensitive to changes in radius. Furthermore, the change in radius alters resistance to the fourth power of the change in radius.
In contrast, an increase in radius will reduce resistance. Similarly, if the viscosity of the blood increases 2-fold, the resistance to flow will increase 2-fold. Therefore, a vessel having twice the length of another vessel (and each having the same radius) will have twice the resistance to flow. Vessel resistance (R) is directly proportional to the length (L) of the vessel and the viscosity (η) of the blood, and inversely proportional to the radius to the fourth power (r 4).īecause changes in diameter and radius are directly proportional to each other (D = 2r therefore D ∝ r), diameter can be substituted for radius in the following expression.
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