Water Pressure Physics Problem--And Lessons Learned On The House Project

It turns out that the cost of the 290 foot well came to about $9200--$19 per foot to drill, and then $11 a foot for steel casing in the first 127 feet (to prevent wall collapse into the well) and then perforated pipe for the rest of the length, so that all water coming out of this 163 foot layer of sandstone ends up in the well.

Now comes the next set of learning experiences. What my builder calls the "Dinosaur" method is to put a pressurization tank in the garage. (I think he enjoys working with me because I keep looking for a cheaper, more elegant, or simpler way to do things--and I think he hopes to pour some of this learning into future houses.) The water coming from the well pump fills this tank, and then shuts down until there is more demand for water. Pressurization tanks require electricity, and usually store about 120 gallons--although only 30 gallons are available on immediate demand. (I'm not clear on exactly why this is.)

There are many types of well pumps, but deep submersibles are what we need in this application. The hot new fad is variable speed well pumps, and Grundfos, a German company, apparently makes the Mercedes of variable speed well pumps (with a Mercedes price tag--$1900). The traditional well pump is constant speed, and for our needs, under $500.

So why would you want a variable speed pump? Every time you fill the pressurization tank, it turns off the pump. When the pressurization tank needs more water, it turns the pump back on again. Apparently, turning on a pump is the greatest strain; the more times a day that a pump gets turned on, the more quickly it will wear out.

A variable speed well pump adjusts its speed for demand, so it is often turning at very low speed, pumping a very small amount of water; as demand increases, speed increases as well, and it pumps more water. With the traditional model--a small pressurization tank--this may be the difference between turning on the pump 20 times a day, and turning it on once or twice a day. I would also expect that at low speeds the variable speed pump draws less power than at high speeds.

Anyway, one of my goals for this property was to have a large water storage tank. The original hope was to have it high enough up the hill to skip the pressurization tank, as well as to keep a water supply adequate for fire suppression in the event we lost electric power.

It turns out that every 2.31 feet of elevation gives you one PSI water pressure. Alas, the top of the hill is only about 35 feet above the house floor level, so this wouldn't be enough pressure.

Instead of pumping water from the well to a pressurization tank--and having to confront the variable speed versus constant speed well pump choice--we may just pump it to an 800 gallon water tank, a few feet up the hill. This gives us our fire suppression water supply. It also means that even without electricity, water will still flow (and apparently, through the pressurization tank). It won't fill the toilets very fast at 5 PSI, but you can at least flush, take a bath, wash dishes by hand in the sink, hose down the house and surrounding property in the event of a forest fire, and have drinking water.

Best of all, the primary reason for a variable speed well pump goes away. We have the constant speed well pump stop when the 800 gallon water tank is full; we have it turn on when the tank is down to 600 gallons. The five gallon per minute pump runs for 40 minutes to fill the tank, and then shuts off. Since a typical house consumes 300 gallons per day, this means the pump cycles about 1.5 times a day--a bit more in summer, and a bit less in winter. We may change the settings to keep the water tank at 700 gallons in summer, and perhaps less in winter, when fire hazard isn't such an issue.

With a little care, it is cheaper to have an 800 gallon water tank than to spend the extra $1500 for a variable speed well pump.

There is one annoying plumbing problem that we still need to solve. How many gallons a minute will a 1.25" water pipe move with a particular pressure at the input? The concern here is that the water tank needs to refill the pressurization tank--and hopefully, refill it fast enough that even if two people are taking showers, and the dishwasher is running, that we won't run out of water in the pressurization tank in less than 15 minutes.

I've searched around the web for a formula--because it seems like it ought to be simple--but all the pages that I have read either give formulas based on water velocity, or assert that the problem can't be simplified this much.

So, if you know how to calculate from an input PSI, and a pipe diameter, how gallons per minute will be transported, please let me know immediately. This may determine how high up the hill we have to put the water tank.

UPDATE: I seem to have found the solution--or rather, a friend of mine with a Ph.D. in Mechanical Engineering pointed me to this page. It would appear that if I have the units right, that five feet of water drop through a 1.25" pipe will flow about 42 gallons per minute--more than enough to keep the pressurization tank happy.

The formal term for a government approved water tank is a "cistern." The 500 gallon cistern is $591; the 1400 gallon cistern is $1036. This is a no-brainer--we'll spend the extra $400+ and have enough water capacity to solve any fire problem, take us through many days of interrupted electricity, and enough water that if Rhonda decides she wants the fountain in the middle of the circular driveway, we'll have the water to do it.