Recently, I had the opportunity to go on a fishing trip. It was a “deep-sea” excursion from the northern tip of Plum Island in New England. The recommended method of trickery was to put some pieces of squid on a hook, weight the line with a 16-ounce hunk of lead and let it sink to the bottom of the ocean. As they say, “even a blind squirrel finds a nut once in a while.” So it was with me and fishing.
The real purpose of this short fish story isn’t to educate you about fishing in New England. The intent is to remind us about a style of engineering where we take what we’ve learned and use the lens of everyday life to design systems. The experience I had fishing that summer day makes me think about the concept of pressure and how I discuss pressure with colleagues and clients. For me, one of the keys to understanding engineering principles and concepts like pressure is through unit conversion.
Unit conversion is as basic to engineering as sweating a copper fitting is to a plumber or stripping the insulation off a wire is to an electrician. The most useful unit conversion I’ve used over the years is:
2.31 feet of water = 1 psi*
The reason this unit conversion is so practical is because we design systems for buildings where height is a primary attribute. Domestic water is conveyed to us at a certain pressure and we design systems that move the water to the top of the building at a minimum pressure in order for fixtures to operate. How do we alternate between height and pressure? We use unit conversions.
I used unit conversions to think about my fishing experience. Based on the spinning of the old rental reel as my rig raced to the bottom, I estimated it was dropping at about 5 feet per second. I made sure not to let the weight drop too fast to avoid a rat’s nest tangle of line when the weight hit the bottom. After a minute of this intense focus, listening to gulls and feeling the summer sun on my face, I figured the bottom of the ocean was about:
5 feet / second x 60 seconds = 300 feet deep
In sea-faring terms, that would be:
300 feet x 1 league / 15840 feet = .019 leagues
300 feet x 1 fathom / 6 feet = 50 fathoms
Under the sea, .02 leagues doesn’t sound too dramatic, so I prefer to say 50 fathoms. Aren’t “leagues” and “fathoms” the units of true fish stories?
Once I was confident my sinker had met the ocean floor, I waited a few moments and felt a small tug on my line, much like a child tugging on your coat when they want to show you something. I answered by testing the line. There was no resistance. It’s as if the fish was saying, “OK, pull me up now.” As the cod breached the veil between land and sea, he greeted me with an odd physiological condition. Something resembling his stomach was poking out of his mouth. I’ve come to learn that this was actually a swim bladder that fish use to regulate their depth in the deep blue.
The galley cook, who also doubled as a deckhand, came out to help me unhook the cod and help him get back home. Being conservation-minded, she held him gently and squeezed on his belly as she explained to me that by deflating the swim bladder, he would be able to dive easier to the bottom of the ocean. We named him Chuck.
Witnessing Chuck’s swim bladder coming out of his mouth reminds me of another calculation we often perform: using Boyle’s law to size expansion tanks for heating and pressure. Boyle’s law tells us that when we multiply pressure and volume together, the product is constant under two sets of conditions.
P1 x V1 (at the bottom of the ocean) = P2 x V2 (deckside)
Based on my estimated depth of 300 feet, and using my favorite unit conversion, I can calculate the pressure on Chuck’s bladder as:
300 feet x 1 psi / 2.31 feet = 129 psi
I’d estimate the swim bladder, at the bottom of the ocean, V1, to be about the size of a small juice box, say, 4 ounces. Converting 4 ounces to cubic inches:
4 ounces x 1.8 cubic inches / 1 ounce = 7.2 cubic inches
Now we have estimates for the pressure at the bottom of the ocean (P1) and the size of Chuck’s swim bladder (V1). We also know that the pressure on the deck of the boat (P2) is 14.7 psi, which just happens to be atmospheric pressure. We can rearrange Boyles law to solve for V2 and understand why a fish’s belly gets bloated when it comes up from the deep.
V2 (Chuck’s Bladder) = (P1 x V1) / P2
V2 (Chuck’s Bladder) = (179 + 14.7) psi x 7.2 in3) / 14.7 psi =
This turns out to be almost as big as a 2-liter bottle!
That explains why he looked the way he did and was happy to get back in the water.
Another example I often think of when describing pressure is swimming in a pool. If we ask ourselves how many psi we feel when our ears start to hurt, we can do a quick unit conversion and realize it’s about 4 psi.
10 feet x 1 psi / 2.31 feet = 4.3 psi
Whether we are estimating pressure at the bottom of a pool, Chuck’s happy home, or the bottom of a 3-inch cold-water riser, we can use the unit conversion of
2.31 ft of water = 1 psi.
These different scales allow us to discuss pressure for different applications. We design natural gas systems and people don’t always realize how much lower natural gas pressure operates. Natural gas operates as low as 4 inches of water column. For me, this is the amount of pressure it takes to blow bubbles in a root-beer float. That’s not even a quarter of a psi. Using unit conversion, I would represent this as follows:
4 inches x 1 foot / 12 inches x 1 psi / 2.31 feet = 0.14 psi
Keep in mind that elevated pressure for natural gas is defined as 14 inches of water column in NFPA 54. This translates to 0.5 psi.
I try to make a habit of writing my conversions out, usually on a scratch sheet somewhere. We have tables, chart and conversion applications available to us, but I suggest making a best practice of writing unit conversions longhand. There is something about the connection between writing and thought that helps reinforce concepts. While you’re at it, make a diagram!
Unit conversion helps us put everyday experiences into a perspective that helps us design engineering systems. It also helps us communicate our design intentions with other architects and engineers. While Chuck’s swim bladder exhibited behaviors of an expansion tank, I wouldn’t specify it for my next design. I might, however, be tempted to specify a tank with a Circulation over-pressurization diaphragm, or C.O.D. for short.
*Since seawater is denser than pure water, the conversion for seawater is 2.25 feet of seawater head equal to 1 psi. If you take the density of seawater as 63.9 pounds per cubic foot and convert to pounds per cubic inches, you can derive the height of that column to obtain pounds per square inch.