# Laminar flow and Reynolds number

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### Laminar flow and Reynolds number

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#### Content Reviewers:

Rishi Desai, MD, MPH

#### Contributors:

Laminar means smooth, and so laminar blood flow is blood that’s flowing smoothly through the vessels. Turbulent flow, on the other hand, is when the blood’s not flowing smoothly, and we can figure out if blood is likely to be laminar or turbulent by finding its Reynolds number or Re, which is named after Osborne Reynolds, a Victorian scientist who not only studied fluid dynamics, but is a man that knows how to rock a beard and bowtie.

If everything’s moving like it should and the blood flow is laminar, the linear velocity of the blood -- how fast it’s moving in a straight line -- is greatest in the center of the blood vessel, and lowest near the walls of the vessel, dropping to zero at the wall.

Sometimes, though, blood flow is disrupted, like if it has to pass by a crusty old atherosclerotic plaque along the wall, which reduces the diameter of the blood vessel at that point and causes turbulence. There are a number of factors help predict turbulence, they include the density of the blood, usually denoted by the greek letter rho, the viscosity denoted by the greek letter nu. You can kind of think of a fluid’s viscosity as it’s thickness, like for example the viscosity of honey is greater than that of water. Alright, then there’s velocity of blood flow (v), and the diameter of the blood vessel (d)These values can all be used to come up with a single value—the reynold’s number, often denoted Re, and the equation looks like this:

NR = pdv/

Generally speaking, if the Reynolds number is low - below 2000, then blood flow will be laminar - think “low” and “laminar”, and if the Reynolds number is above 3000 it’ll be turbulent. A Reynolds number between 2000 and 3000 is somewhere in between. As a real-life example, a person with anemia has a low red blood cell count, and in general has a lower hematocrit, the ratio of red blood cells to total blood volume. This essentially means the blood’s less thick or viscous, which means based on our equation, if viscosity decreases, reynolds number increases. Also, these individuals often have an increased cardiac output, which means increased blood velocity and therefore increased reynolds number.

Summary
The Hagen–Poiseuille equation is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. The equation states that flow rate is proportional to the radius to the fourth power, meaning that a small increase in the internal diameter yields a significant increase in flow rate.
Sources
1. "Medical Physiology" Elsevier (2016)
2. "Physiology" Elsevier (2017)
3. "Principles of Anatomy and Physiology" Wiley (2014)
4. "Human Anatomy & Physiology" Pearson (2018)