[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Physiology](https://durgical.com/en/physiology/) › [Cardiovascular](https://durgical.com/en/physiology/#s-cardio) › Flow, pressure and resistance: Poiseuille and turbulent flow [Physiology](https://durgical.com/en/physiology/) · [Cardiovascular](https://durgical.com/en/physiology/#s-cardio) # Flow, pressure and resistance: Poiseuille and turbulent flow - Concept - Exam priority: medium Blood flows from high to low pressure; narrow vessels resist flow enormously, and fast, disturbed flow becomes noisy and turbulent. Updated 2026-11-01 Also called: Poiseuille's law, Reynolds number **See it in 3D:** [Ascending aorta](https://durgical.com/en/anatomy/ascending-aorta/) · [Abdominal aorta](https://durgical.com/en/anatomy/abdominal-aorta/) · [Carotid arteries](https://durgical.com/en/anatomy/common-carotid-artery/) ## Key points - Q = ΔP / R; for the whole circulation, MAP − RAP = CO × SVR. - Poiseuille: R = 8ηL / (πr⁴). Halving the radius raises resistance 16-fold. - Resistances in series add (R = R1 + R2…); in parallel the reciprocals add, so total resistance is lower than any single branch. - Arterioles are the main resistance vessels (largest pressure drop); capillaries have the largest total cross-sectional area and slowest velocity. - Turbulence: Reynolds number Re = ρvD/η; rises with velocity and diameter, falls with viscosity. Anemia (low viscosity, high velocity) → flow murmurs. ## What it is Blood flow through a vessel equals the pressure difference divided by resistance. Resistance depends very strongly on radius (to the fourth power), and on vessel length and blood viscosity. Flow is normally smooth (laminar); at high velocity, at narrowings or with low viscosity it turns turbulent, which wastes energy and makes bruits and murmurs. ## Key facts - Viscosity rises with hematocrit: polycythemia (including high-altitude polycythemia in Bogotá residents, mild) increases resistance. - Blood behaves as less viscous in small vessels (Fåhræus–Lindqvist effect) because red cells line up in the centre. - In laminar flow, velocity is highest in the centre and zero at the wall; shear stress on the endothelium releases NO. ## Equations **Ohm's law for flow**Q = ΔP / R **Q** flow **ΔP** pressure difference **R** resistance **Poiseuille's law**R = 8ηL / (πr4) **η** viscosity **L** vessel length **r** radius Exact only for steady laminar flow of a simple fluid in a rigid tube; a good guide for blood. **Reynolds number**Re = ρ v D / η **ρ** density **v** mean velocity **D** diameter Turbulence tends to begin above ≈ 2000 in straight tubes, lower at branches. **Continuity**Q = v × A **v** velocity **A** cross-sectional area Velocity rises where the area falls (stenosis). ## Clinical notes - A 50% reduction in diameter (75% in area) begins to limit flow at high demand; a stenosis beyond ≈ 70% limits it at rest. - Carotid bruit and the murmur of aortic stenosis are turbulence at a narrowing; turbulent sites also favour atherosclerosis. ## Memory aid Radius rules: double the radius and flow goes up sixteen times. ## Test yourself Think of the answer, then tap the question to see it. ## An arteriole constricts so its radius falls by half. By how much does its resistance change? It rises about 16-fold, because resistance is inversely proportional to the radius to the fourth power. ## Why does adding a parallel vascular bed lower total resistance? In parallel the conductances (1/R) add, so total resistance is less than that of any single bed; each organ also gets the same driving pressure. ## Why can a patient with severe anemia have a systolic flow murmur without valve disease? Low viscosity and high cardiac output raise velocity and Reynolds number, so flow becomes turbulent across normal valves. ## Where in the circulation is the largest pressure drop, and why? Across the arterioles: they have the highest resistance of any segment because of their small radius and muscular tone. [Add to my cards (4)](https://durgical.app/estudiar/?add=/en/physiology/flow-pressure-and-resistance-poiseuille-and-turbulent-flow/) ## See it in 3D The structures of Durgical's 3D anatomy where it happens. - [Ascending aorta](https://durgical.com/en/anatomy/ascending-aorta/) - [Abdominal aorta](https://durgical.com/en/anatomy/abdominal-aorta/) - [Carotid arteries](https://durgical.com/en/anatomy/common-carotid-artery/) ## Related topics - [Systolic, diastolic, mean and pulse pressure](https://durgical.com/en/physiology/systolic-diastolic-mean-and-pulse-pressure/) - [Vascular compliance and capacitance](https://durgical.com/en/physiology/vascular-compliance-and-capacitance/) - [Local and humoral control of blood flow](https://durgical.com/en/physiology/local-and-humoral-control-of-blood-flow/) - [Starling forces at the capillary](https://durgical.com/en/physiology/starling-forces-at-the-capillary/) - [Murmurs and the hemodynamics of valve disease](https://durgical.com/en/physiology/murmurs-and-the-hemodynamics-of-valve-disease/) ## Related conditions - [Arterial hypertension](https://durgical.com/en/conditions/arterial-hypertension/) - [Peripheral artery disease](https://durgical.com/en/conditions/peripheral-artery-disease/) - [Aortic Valve Stenosis](https://durgical.com/en/conditions/aortic-valve-stenosis/) - [Carotid artery stenosis](https://durgical.com/en/conditions/carotid-artery-stenosis/) - [Atherosclerosis and dyslipidaemia](https://durgical.com/en/conditions/atherosclerosis-and-dyslipidaemia/) [← All of physiology](https://durgical.com/en/physiology/) Educational physiology content; not a diagnostic or treatment guide and no substitute for a health professional's advice. Values are approximate references. No doses are given. Sources: [20.2 Blood Flow, Blood Pressure, and Resistance](https://openstax.org/books/anatomy-and-physiology-2e/pages/20-2-blood-flow-blood-pressure-and-resistance) (OpenStax (Rice University), 2022); [20.1 Structure and Function of Blood Vessels](https://openstax.org/books/anatomy-and-physiology-2e/pages/20-1-structure-and-function-of-blood-vessels) (OpenStax (Rice University), 2022); [Carotid Artery Stenosis](https://www.ncbi.nlm.nih.gov/books/NBK442025/) (StatPearls (NCBI Bookshelf), 2025); Hall JE. Guyton and Hall Textbook of Medical Physiology, 13th ed. (ch. 14). Reference book used to check facts; its text and figures are not reproduced (Elsevier, 2016). ## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. 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