Law of Poiseuille

Abstract

The law of Poiseuille describes the relation between pressure drop, ΔP/l, and blood flow, Q, in a stiff tube under steady flow conditions. For a tube with circular cross-section and when the blood flows in a laminar fashion, i.e., each fluid layer stays at the same constant distance from the center, the flow depends strongly on the radius of the tube (fourth power), the pressure drop over the tube length (ΔP/l) and viscosity of blood (η) as Q = π r _i ⁴ (ΔP/l)/8η. The velocity profile, v(r), is parabolic. The wall shear stress, τ, acting on the intimal layer (endothelium) equals τ = 4 η Q/(π r _i ³) = (ΔP/l)·(r _i /2). Resistance can be calculated as R = ΔP/Q = 8 ηl/π r _i ⁴.