In Lev Nelik’s September column (“Quiz: Why Did Water Flow Reduce So Drastically?”), he explored issues of watering a garden at an apartment complex. To see Nelik’s solution to the quiz, check out his column in the October issue of Pumps & Systems. The next two Ask Dr. Pump columns will look at readers’ responses prior to the publishing of the quiz solutions. The following is an interaction between Nelik and longtime reader Lee Ruiz.
Case 1
Watering from a 150-foot garden hose (3/8-inch opening) for 30 minutes, with a supply pressure of approximately 60 pounds per square inch of pressure (psig). The cost of water is approximately $1 per 100 gallons.
Case 2
Watering from the same hose attached to a third-floor shower room water spigot.
Quiz Question
Make a rough estimate of the cost of watering the garden in each case. Make any simplifying assumptions for your calculations. Hint: Shower room water is supplied from the same main water line via approximately 500 feet of pipe (assumed to be roughly the same diameter as a garden hose).
FROM: LEE RUIZ
Date: Mon, Sep 16, 2024 at 3:39 AM
Subject: September P&S Article Questions
To: Lev Nelik
Dr. Nelik,
I might as well submit my two cents’ worth of a response to your September garden watering quiz. I assumed that any flow-restricting nozzle at the garden end of the hose was wide open and contributed zero resistance. In addition, the hose and piping walls were assumed to have an approximate 0.0012-inch roughness height and any bends had insignificant effect. Room height plus floor thickness was estimated at 9 feet for each of the apartment stories.
When watering the garden from the Case 1 street-level supply, the main pressure loss is from the friction of water flowing horizontally through a 150-feet long, 3/8-inch inner diameter (ID) hose. Using the velocity obtained by a trial-and-error balance of ground-level supply pressure head less friction head loss and any elevation change (no elevation change for Case 1), a garden watering flow rate of about 2.6 gallons per minute (gpm) was obtained. The street-level supply-point pressure of 60 psig was used.
From the above calculated horizontal-hose flow rate, an estimated 157 gallons of water would be used for the garden each week. Therefore, the weekly cost would have been about $1.57 for the entire apartment building. This would have broken down to about $0.21 per month (less than $1/mo.) for each of the 32 apartments.
During non-Case 1 and non-Case 2 periods, when using a water faucet in the third floor apartment, an approximate 1.2 gpm maximum flow would normally be available during non-garden-watering times. So, the owner’s maximum in-apartment water flow rate would normally be about half of the Case 1 horizontal-hose watering rate. This is due to the third floor elevation difference plus the friction loss of flow through 500 feet of apartment piping instead of 150 feet of hose.
When watering the garden from the Case 2 owner’s third floor apartment shower connection, there would again be an approximate 1.2 gpm maximum flow. Using the energy and friction loss equations, the lower-than-Case 1 flow rate is due to the friction loss of flow through 500 feet of apartment piping plus 150 feet of hose. The third floor elevation difference is negated by the shower-connected hose dangling down to the ground level garden.
It is assumed that when the owner is using a third floor faucet or shower hose connection, no other apartments are using water at the same time. I can’t believe that a four-story apartment would be fitted with such small piping.
Regards,
Lee Ruiz
Oceanside, CA
FROM: LEV
Date: Sunday, Sep 15, 2024 10:00 PM
Subject: Fwd: September P&S Article Questions
To: Lee Ruiz
Lee,
As always, very thorough and perceptive analysis of the interesting story of the apartment building garden watering quiz. Exactly, the added length of the building piping is what does it—extra 500 feet added to the initial 150 feet—a big difference. But still, at any rate, albeit the flow was reduced in half, the ultimate water cost is negligible and should not be a point of contention to any apartment dwellers of this building.
Not all people use logic, and as Einstein said, “the only infinite thing is human stupidity.” In this case, it is also an unwillingness to listen. No matter how low the cost is, “it should not come from my pocket!” When a person is stuck in his or her ways—not much you can do, no matter how much “Bernoulli” you can bring as an argument!
And by the way, to your surprise on the piping: the original central piping system has deteriorated and was replaced several years ago. Each apartment owner connected a new hose/piping to his meter and the hoses sneak along the outside walls to the roof (solar heaters) and then back down to the apartment—all from the outside! The building looks like it is surrounded by a net of hose and looks ridiculous (new building codes do not allow this, but the five-year-old constructions are grandfathers).
I have always focused on the technical side, but over the years I appreciated my occasional opportunities to come across the “human side” of the system! It makes you wonder, at the end of the day, which side is more important?
Thanks again!
Dr. Lev Nelik, PE
Technical Director
International Center for Pumping Machinery Research and Development
Beer Sheva, Israel
FROM: LEE RUIZ
Date: Mon, Sep 16, 2024 at 8:26 PM
Subject: RE: September P&S Article Questions
To: Lev
Lev,
Reality can be unbelievable! Yes, your explanation answers my puzzlement about the use of such small-size piping. I would never have considered the use of individual pipes and hoses to solve the problems at this apartment building. In a way, it’s kind of a creative MacGyverish concept even if born out of stubbornness. I’m surprised that building codes, even five years ago, allowed this plumbing fix!
Thanks again for sharing and explaining this unusual case.
Regards,
Lee
