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I used a bucket to find out that at 1 feet high (a garden faucet) the flow rate from an half inch pipe is 1 gallon in 26 seconds At 3 feet high (face basin) the flow rate is 1 gallon in 30 seconds at 11 feet high (upstairs face basin) the flow rate is 1 gallon in 1 minute at 15 feet high (upstairs showerhead) the flow rate is 1 gallon in 2 minutes

Graphing the data I see that this flow won't make it to the 23 feet I need it to fill a rooftop water tank. Is there an equation I can use to estimate the water flow I would need, measurable from the one foot pipe (It changes daily from the water company these days, some days it is more than strong enough) to reach 23 feet? I want to know if i'll have to just save money for a pump after all, or a bigger tank. Keep in mind I'm not an engineer, tho I did try to solve myself this with a natural number e or ln in there somewhere lol. It's been much too long since college math.

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The flow rate at a particular height would depend on the pressure and flow rate at the supply end. You may use the simple formula (v^2 /2g) + h = constant (assuming supply pressure to be constant).

v=flow rate/ area of cross section of the pipe.(use SI units) g= 9.8m/s^2 h= height.

First find the value of the relation at h=1 ft and find the constant. Then equate this value to the relation with h=23ft and find v. Then flow rate= area of cross section of pipe× v

N.B: Since the supply pressure is variable, as you have mentioned you may take the average of the value calculated on every day in a week.

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  • $\begingroup$ Note also that you won’t get a perfect relation even if the pressure stays constant, because the flow is dependent on other things - like the diameter, length, and number of bends that the water goes through to reach each outlet. $\endgroup$ – Mark Aug 22 '18 at 1:20
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Flow is a function of head (=pressure) and the piping system - the longer, the thinner, the more valves etc. the less flow. This much you know.

This means you can't know from your little experiment alone if the head will suffice to reach your tank. I suggest running a hose up to your roof, if you have any flow at all the head in your water system suffices. At least sometimes.

23 feet is 6.9m, you need more than 0.7 bar. Water mains should deliver 4 bar but this will depend of course. I never took time when filling a bucket, but half a minute for a gallon does not seem too bad.

We don't know your plans etc. I suggest when you know if you can fill a tank on your roof, you sit down, think your system through, make a sketch or two and show this here to see if it will work to solve your problem.

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