Factors Affecting Blood Flow

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Reynolds number is an important indicator of how smoothly blood is flowing through blood vessels. is determined by the length of accumulated plaque , the vessel radius and the blood velocity . If the Reynolds number is below 2300, the flow is laminar, shown by straight arrows exiting the area of congestion (yellow) in the graphic. But if rises above 2300, blood flow can turn turbulent, as shown by curly arrows exiting the congestion. Laminar flow is considered healthy, while turbulent flow can have grave consequences such as heart attacks if occurring in inappropriate regions. This Demonstration shows how important, seemingly small changes can affect our health.


The Reynolds number=(length of congestion)×(blood density)×(flow rate in congested area)/viscosity.

Flow rate is determined as a function of effective vessel radius and incoming velocity due to the conservation relation: (=area of the cross section).


Contributed by: Juliet Foote and Mihir Surapaneni (April 2018)
Additional contributions by: Eitan Geva (University of Michigan)
Open content licensed under CC BY-NC-SA


See citations for blood density and viscosity.


[1] G. Elert, ed. The Physics Factbook: Density of Blood. hypertextbook.com/facts/2004/MichaelShmukler.shtml.

[2] G. Elert, ed. The Physics Hypertextbook: Viscosity. physics.info/viscosity.

[3] R. Erbel and H. Eggebrecht, “Aortic Dimensions and the Risk of Dissection,” Education in Heart, 92(1), 2006 pp. 137–142. doi:10.1136/hrt.2004.055111.

[4] J. A. Jensen. "Blood Flow in the Human Body." Technical University of Denmark. (Apr 2, 2018) bme.elektro.dtu.dk/31545/notes/lecture_4_ 4_per _page.pdf.

[5] S. S. Mao, N. Ahmadi, B. Shah, D. Beckmann, A. Chen, L. Ngo, F. R. Flores, Y. L. Gau and M. J. Budoff, "Normal Thoracic Aorta Diameter on Cardiac Computed Tomography in Healthy Asymptomatic Adult; Impact of Age and Gender," Academic Radiology, 15(7), 2008 pp. 827–834. doi:10.1016/j.acra.2008.02.001.

[6] L. Segadal and K. Matre, “Blood Velocity Distribution in the Human Ascending Aorta,” Diagnostic Methods, 76(1), 1987 pp. 90–100. circ.ahajournals.org/content/circulationaha/76/1/90.full.pdf.

Submission from the Compute-to-Learn course at the University of Michigan.


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.