With a constant pressure difference assumed and the same length and viscosity, along the artery we have. This pressure could be supplied by an IV bottle with the surface of the saline solution 1.61 m above the entrance to the needle (this is left for you to solve in this chapter's Problems and Exercises), assuming that there is negligible pressure drop in the tubing leading to the needle. Poiseuille's law definition, the law that the velocity of a liquid flowing through a capillary is directly proportional to the pressure of the liquid and the fourth power of the radius of the capillary and is inversely proportional to the viscosity of the liquid and the length of the capillary. Blood vessels are not rigid but elastic. Motor oil has greater viscosity when cold than when warm, and so pressure must be greater to pump the same amount of cold oil. We recommend using a Poiseuille's Law (also Hagen-Poiseuille equation) calculates the fluid flow through a cylindrical pipe of length L and radius R. The poiseuille's equation is: V = π * R4 * ΔP / (8η * L) In contrast, an increase in radius will reduce resistance. v A 19% decrease in flow is caused by a 5% decrease in radius. During vigorous exercise, blood vessels are selectively dilated to important muscles and organs and blood pressure increases. For example, a 2-fold increase in radius decreases resistance by 16-fold! Â© 1999-2020, Rice University. Our mission is to improve educational access and learning for everyone. The weakest stimulus capable of producing a response produces the maximum contraction of cardiac and skeletal muscle cells, and the maximal impulse transmission rate in neurons. This decrease in radius is surprisingly small for this situation. This is given by. This is the currently selected item. 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