# Laminar flow and Reynolds number

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## Physiology

#### Cardiovascular system

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Rishi Desai, MD, MPH#### Contributors:

Tanner Marshall, MS, Yifan Xiao, MDLaminar 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.

Laminar flow is when a fluid flows in a smooth, continuous stream. The Reynolds number is a dimensionless parameter that helps to determine whether the flow will be laminar or turbulent. When the Reynolds number is low, the flow will be laminar. When the Reynolds number is high, the flow will be turbulent.

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- "Physiology" Elsevier (2017)
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- "Human Anatomy & Physiology" Pearson (2018)