Laminar flow and Reynolds number

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 who 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.Another example would be a person with a thrombus, or blood clot, which just like the atherosclerotic plaque would narrow or decrease the diameter of the blood vessel...now, at first glance this seems a little weird eh?

But it turns out that blood velocity also depends on the diameter of the vessel, by the equation velocity equals flow rate over area, which after subbing for the area of the blood vessel, is 4Q over pi d^2, so plugging that in for velocity, we see that as diameter decreases, reynolds number increases!Now a related concept is shear rate.

Now, remember how the velocity of the blood depended on whether it was in the center or near the walls? Where it’s fastest in the middle and really slow near the walls, in fact at the molecular level, just outside the walls, water molecules are just sort of loitering around not moving!

If we freeze it and plot these velocities, we’ll notice that this difference in velocity is parabolic, meaning that as you move away from the walls, velocity at first jumps up pretty quick, but as you near the middle, the change in velocity is pretty low.

This difference in relative velocities is the shear rate! So if we wanted to plot shear rates, near the wall where velocity is changing the most, shear rate’s actually the highest, and in the middle shear rate is very low and actually drops to zero.Shear rate goes hand-in-hand with viscosity, because the higher the shear rate, the lower the viscosity of the blood.

This is because shear, or simply the differential velocities, helps to pull the elements in the blood apart decreasing it’s stickiness, or viscosity, making blood less viscous at the vessel walls and more viscous in the middle of the vessel.

Now, let’s say all the blood’s somehow moving at the same velocity. Well in that case, if you plot it out, there’s no change in velocity across the blood vessel, and that makes plotting shear rates pretty easy...since there’s no change in velocity there’s no shear rate, and likewise this fluid isn’t viscous!All right, as a quick recap: The Reynold’s number is written as Re = density times diameter times velocity over viscosity, and is a way to predict when fluid’s going to be either laminar or turbulent.

In general, Reynold’s numbers below 2000 will have laminar flow, and Reynolds numbers above 3000 will have turbulent flow.

Furthermore, differences in velocity across a blood vessel gives rise to the shear rate. pretty easy since there's no change in velocity there's no shear rate And likewise this fluid isn't viscous All right As a quick recap the renas number is written as re equals density times diameter times velocity over viscosity and is a way to predict when fluids either gonna be laminar or turbulent In general Reynaud numbers below 2000 will have laminar flow and Reynalds numbers above 3000 will have turbulent flow is exmoor The differences in in velocity across a blood vessel gives rise