Physics in Human Body

Physics and biology are two subjects that I enjoy learning- one tasks your mind and makes it solve complex problems while the other teaches you about life and how it functions. Naturally, learning a topic that involves a great deal of both the subjects is immensely interesting, and I had the privilege to do exactly that.

As a part of my examinations I am required to submit a project in each subject I am studying. I had decided that my physics project would be on fluid dynamics, since I was going to learn about this chapter in the coming term. I was surprised to see that fluid dynamics has great application in the human body, specifically the flow of blood in blood vessels. Here are a couple of the fluid dynamic concepts that are found in the flow of blood-

1. Hagen–Poiseuille equation

The Hagen–Poiseuille equation gives us a relation between the pressure in an artery and it’s radius, length and viscosity of the fluid-

The fact that pressure is inversely proportional to radius ^4 means that even a small plaque (decreasing the radius of the artery) will have a large effect on the pressure.

2. Bernoulli’s principle

Bernoulli’s principle states that an increase in the velocity of a certain fluid is simultaneous with a decrease in pressure or a decrease in the fluids potential energy.

Bernoulli’s principle can be used to derive the pressure at different parts of the body.

As per Bernoulli’s equation

P+1/2ρv²+ρgh=constant. The kinetic energy term can be ignored as the velocities in the three arteries are small (≈ 0.1 m/s) and almost constant. Hence , the blood pressure at the brain P_b, the heart P_h and the foot P_f are related by

P_f = P_h +ρgh_h= P_b +ρgh_b

Typical values of height to the heart and the brain are h_h=1.3 m and h_b=1.7 m.

Taking ρ=1.06 x10³ kg m^-3 , P_h =13.3 kPa

P_f =26.8 kPa and P_b =9.3 kPa

Since 1mm of Hg= 0.133kPa

P_f =200 mm Hg, P_b = 70 mm Hg

Thus, the pressures in the lower and upper parts of the body are quite different when a person is standing but are almost equal when the person is lying down. In terms of mm of Hg, value of P_h is 100 mm of Hg.  

The above two concepts are both very important when it comes to determining the rate of flow to blood in an artery, blood’s viscosity, diameter of an artery, medications of blood pressure, etc.

I had great fun doing this project and certainly hope that I will get many projects like these which have a great extent of cross curricular links!