Poiseuille's Law Calculator for Blood Flow
Understanding Poiseuille's Law in Hemodynamics
Poiseuille's Law, named after the French physicist Jean Léonard Marie Poiseuille, is a fundamental principle in fluid dynamics that describes the flow of a Newtonian fluid through a long cylindrical pipe. In the context of medicine and biology, it is the cornerstone of hemodynamics—the study of blood flow through the circulatory system.
The law states that the flow rate (Q) is directly proportional to the pressure gradient and the fourth power of the vessel radius, while being inversely proportional to the viscosity of the fluid and the length of the vessel. Because the radius is raised to the fourth power, even a tiny change in the diameter of an artery (such as during vasodilation or vasoconstriction) has a massive impact on blood flow.
How to Use the Blood Flow Calculator
To calculate the flow rate using our tool, you need four key parameters:
- Vessel Radius (r): The internal radius of the blood vessel (measured in millimeters).
- Pressure Difference (ΔP): The change in pressure between two points in the vessel (measured in mmHg).
- Viscosity (η): How "thick" the blood is. Normal blood viscosity is typically around 3.5 cP (centipoise).
- Vessel Length (L): The distance over which the blood is traveling.
Frequently Asked Questions (FAQs)
Because the radius is to the power of four (r⁴), doubling the radius of a blood vessel increases the flow rate by 16 times, assuming all other factors remain constant.
Higher viscosity (thicker blood) increases resistance, which decreases the flow rate. Conditions like polycythemia can increase viscosity, forcing the heart to work harder.
Strictly speaking, no. Blood is non-Newtonian because its viscosity changes with flow rate (shear rate). However, Poiseuille's Law provides a highly accurate approximation for flow in larger vessels.