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.
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.
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!
So if we wanted to plot shear, near the wall where velocity is changing the most, shear’s
actually the highest, and in the middle shear is very low and actually drops to zero.
Shear goes hand-in-hand with viscosity, because the higher the shear, the lower the viscosity
of the blood.
This is because shear 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 pretty easy...since there’s no change in velocity there’s
no shear, 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 causes shear.