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 ri4 (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 ri3) = (ΔP/l)·(ri/2). Resistance can be calculated as R = ΔP/Q = 8 ηl/π ri4.
Laminar flow Fourth-power law Parabolic flow profile Wall shear stress
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Weibel ER. Symmorphosis. Cambridge, MA: Harvard University Press; 2000.Google Scholar
Womersley JR. The mathematical analysis of the arterial circulation in a state of oscillatory motion. 1957, Wright Air Dev. Center, Tech Report WADC-TR-56-614.Google Scholar
Cheng C, Helderman F, Tempel D, Segers D, Hierck B, Poelmann R, et al. Large variations in absolute wall shear stress levels within one species and between species. Atherosclerosis. 2007;195:225–35.CrossRefPubMedGoogle Scholar