Blood pressure, blood flow, and resistance

Pressure is a force over an area, so with blood pressure, we’re measuring the force that the blood exerts on the surface area of the walls of the blood vessels. Differences in blood pressure throughout the body keep blood flowing from high-pressure areas, like the arteries, to low-pressure areas, like the veins. When we say “blood flow,” we’re referring to the volume of blood that flows through a vessel or an organ over some period of time. Now, the amount of blood flow from one end of a blood vessel to another is affected by the blood pressure, and by the resistance, which comes from the vessels themselves. Vasoconstriction, where the vessels constrict, decreases blood flow, and vasodilation, where the blood vessels expand, increases blood flow.

Now, blood flow is not the same thing as the velocity of blood. Blood flow is the volume of blood that moves by a point over some period of time. So let’s say this chunk of blood has a volume of 83 cm^3, and it took 1 second for this much to flow past the blue circle—this is the blood flow, represented by the variable capital Q.

Now, velocity on the other hand, is the distance traveled in a certain amount of time. So maybe in the same one second, a red blood cell at the very edge here traveled a distance of 27 cm, then it’d be moving 27 cm/s, represented by lowercase v. Even though these aren’t equal, they are related, and the last piece is area, specifically the cross-sectional area of the blood vessel, which in reality is the same as the blood cross section like this. So, based on units, since area’s going to be expressed in cm^2, we see that flow rate equals area times velocity! Alright, so for example, let’s say we want to calculate blood velocity, and we have a person’s cardiac output of 5L/min, which is average for an adult, and the diameter of their aorta, which is 2cm.

First off, using the equation for the area of a circle, (D/2)^2 x pi, we get (2 / 2)^2 x pi = 3.14 cm^2. Next, since cardiac output is the same as blood flow, we just need to convert this L/min to cubic cm per second, so there are 1000 cubic cm in a L, and 60 seconds in a minute, so multiplying those out we get 83 cubic cm per second. Then, rearranging our little formula, velocity equals flow rate divided by area, and we get about 26 cm per second! Which is also about 1 km / hr!

Going back to blood pressure, blood flow, and resistance, that relationship can be written out mathematically as well. So, to start, you have an initial, higher pressure at one end, and a final, lower pressure at the other. The difference between these, or the initial minus the final pressure, sometimes expressed as delta P, equals blood flow through that vessel multiplied by resistance. This can be also written as Q equals change in pressure over resistance. So, for example, let’s say the the blood vessel narrows, which increases the resistance, in order to keep the flow of blood to organs the same, the pressure difference has to increase, and this is typically what happens. This equation might look familiar to a similar equation, where change in voltage V equals current I times resistance R, also known as ohm’s law!