# Hydrostatic Pressure

# The Basics

Imagine you have a tall cylinder filled with water. If you use a pressure sensor to measure the pressure within the column of water, you will find that the further down you go the higher the pressure will be. In fact, every centimeter you move down the column the water pressure will increase by 1 cmH\(_2\)O (0.736 mmHg or 98.07 Pa). In the diagram shown below, \(P_0 < P_1 < P_2 < P_3\).

If you want to calculate the exact pressure difference between two locations (e.g., \(P_0\) and \(P_2\)), you can use the formula

$$P_2 = P_0 + \rho gh$$

where \(\rho\) is the fluid density, \(g\) is the gravitational constant, and \(h\) is the height difference between \(P_2\) and \(P_0\). Note that in this sign convention, \(h\) is positive and \(P_2\) will be larger than \(P_0\).

Here’s the rule: As you go down, there is more fluid on top of you so the pressure increases. As you go up, there is less fluid on top of you so the pressure decreases.

# Hydrostatics of Blood Pressure

Since humans are basically walking 5–6 foot tall cylinders of blood, our bodies experience hydrostatic pressure too. If you choose the heart as a reference pressure, similar to \(P_0\) in the figure above, then the hydrostatic pressure on different parts of the body is shown below. Note: the values on the gingerbread patient are approximate, not exact!

This may be confusing because if the pressure increases as you go from the head to the feet, why does the blood flow back up to the heart? The answer is that hydrostatic pressure is acting on both the arteries and veins and it cancels out during blood flow.