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How Buildings Stack Up

©2014 This excerpt taken from the article of the same name which appeared in ASHRAE Journal, vol. 56, no. 2, February 2014.

By Joseph W. Lstiburek, Ph.D., P.Eng., Fellow ASHRAE

About the Authors
Joseph W. Lstiburek, Ph.D., P.Eng., is a principal of Building Science Corporation in Somerville, Mass.

We live at the bottom of an ocean of air. Each of us is carrying around 14.7 pounds per square inch when at the beach in Miami. We are powerful creatures indeed. Imagine carrying around 101,000 Pascals on that beach. Or 1,010 millibars. As elevation increases, the weight of the air we are carrying around decreases. This decrease in weight with elevation is called the lapse rate (Figure 1).

The lapse rate thing gets interesting with buildings. In a heated building, the lapse rate inside is less than the lapse rate outside. This is due to the reduced density of heated air compared to unheated air. Check out Figure 2. The assumptions in this figure are important. There is only one hole in the building enclosure, and it is at the bottom. There are also no interior floors or partitions. So we have an airtight building (except for the one hole at the bottom) with no interior flow resistance. And, the building is heated. At the hole, the pressure inside equalizes with the pressure outside. As we go up with height, the pressure difference between the inside and outside gets bigger. This difference in pressure is called the stack effect.

The stack effect gets its name from the same phenomenon that causes hot combustion gases to rise in a chimney or chimney stack. A heated house or heated building can be considered a giant chimney that we live and work inside. The taller the building, the greater the stack effect. The colder the temperature, the greater the stack effect. So, in heated buildings, the air tends to flow out of the top of the building while inducing air to flow in at the bottom.

Now let’s look at Figure 3. The hole is at the top of the building. All other assumptions are the same. Once again, at the hole, the pressure inside equalizes with the pressure outside. As we go down in height, the pressure difference between the inside and outside gets bigger—but it is in the opposite direction. Neat, eh? The interior pressure line (the interior lapse rate “line”) moves laterally—horizontally shifts to the left from Figure 2 to Figure 3. The “solid” line does not move. The “dotted” line moves. The slope of the “dotted” line does not change, it just shifts left.

What happens when we have two holes the same size? One at the top and one at the bottom? Check out Figure 4. The “dotted” line shifts right partially. It crosses the “solid” line smack dab in the center of the building elevation wise. Where the interior lapse rate line crosses the exterior lapse rate line, the pressure inside equals the pressure outside. No pressure difference exists. We call that the neutral pressure plane or neutral pressure zone. A real smart old guy wrote about this in ASHVE Journal in 1926.
Now let’s modify the assumptions a bit. Let’s assume a uniform distribution of leakage areas. All surfaces are uniformly leaky—same size holes—same distribution. Also, and this is the tricky assumption, let’s assume “no flow.” Now let’s put a vented attic on top of the box. We get Figure 5. All holes above the neutral pressure plane would have air “exfiltrating” if there was flow. All holes below the neutral pressure plane would have air “infiltrating” if there was “flow.”

How does the neutral pressure plane know where it is supposed to be? Ah, Grasshopper, it always knows. In the absence of wind and exhaust fans, supply fans and ducted HVAC systems and interior partitions—weasel words for sure—roughly half the holes are above the neutral pressure plane and roughly half the holes are below the neutral pressure plane. We are talking surface area wise, sort of. There are cracks, and there are straight through to the outside holes, and there are tortuous paths. It gets worse. Holes farther away from the neutral pressure plane are more “important” than holes closer to the neutral pressure plane. It is sort of like a “moment” calculation in structural engineering. The “effective area” of a hole is multiplied by its distance to the neutral pressure plane, and this product is added to the next product of the “effective area” of a hole multiplied by its distance to the neutral pressure plane for all of the holes above the neutral pressure plane. Yes, you all know where this is going; this sum must equal the sum of the same exercise of all of the holes below the neutral pressure plane.

 

Figure 1

 

Figures 2 and 3

 

Figures 4 and 5

 

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