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.