In Poiseuille flow, the flow rate is directly proportional to:
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The Power of the 4th Power in Hemodynamics:
Because flow rate ($Q$) is directly proportional to $d^4$, even tiny adjustments to a blood vessel's diameter have a massive impact on blood flow.
- For example, doubling a vessel's diameter ($2^4$) increases the volumetric flow rate by 16 times, assuming pressure remains constant! This relationship explains how the body uses vasoconstriction and vasodilation to easily regulate localized blood distribution.