How Length is a Pressure

Jeff Yirakby Jeff Yirak, P.E., CPMP, LEED AP BD+C, O+M

HVAC design engineers frequently calculate pressures, flows, and temperatures of fluids, such as heating water, supply air, or exhaust flow. While atmospheric pressure is currently exerting about 15 pounds of force over every square inch of your body (15 psi), the pressure of the air handling system in the building in which you find yourself is operating at relatively small pressures, usually less than 1 psi. Rather than operate in fractions of a psi, engineers change scales and work in feet or inches of water. How can a length be a pressure, you ask? It’s all about gravity.

Grasping at Straws

Let’s use a familiar example to illustrate the concept. As you drink through a straw, it is not that you are “sucking” the soda or whatever into your mouth, it is that you’re creating lower pressure in your mouth (stay with me) and atmospheric pressure is pushing the liquid up the straw. This push is against gravity, so the pressure required to elevate the liquid in the straw is a function of the pressure difference between the open atmosphere around the soda and the pressure in your mouth, and the weight of the liquid in the straw, which is a function of density and gravity.

Since the density of water and the effect of gravity (on Earth) are constant, we can eliminate these from the measurement and simply refer to the difference in pressure as a function of the length of the column (height) of the liquid in the straw, which is a pretty convenient way of measuring pressure.

This process works with other fluids besides water; mercury is a popular liquid, since it doesn’t evaporate. Barometric pressure is often reported this way, in millimeters. Unfortunately, since it’s an environmental hazard, mercury is not a good choice in the built environment, so we use benign water instead.

The column height, H, is measured in length, but is a representation of the differential pressure.

The column height, H, is measured in length, but is a representation of the differential pressure. Image Source: https://commons.wikimedia.org/wiki/File:Utube.svg / Licensed CC BY-SA 4.0

Applications in Mechanical Engineering

In HVAC, the relationship we’re often describing is the pressure of ductwork relative to the atmosphere, since that’s where our ductwork terminates (such as at a diffuser in a room). It takes energy to move air from one place to another, and that work is a function of the pressure and flow of air that is moved. Flow is just a volume, such as cubic feet of air per minute, and the pressure is measured in inches of water. There are twelve inches of water in a foot of water (convenient, no?), and there are 2.31 feet of water per psi (or 27.72 inches per psi). The differential pressure required to create a column of water X inches tall is reported as a “X inch” pressure.

Next we need to address static, velocity, and total pressure, but that’s a whole ‘nother discussion.

 

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