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I'm in the process of designing a water system for our regenerative agricultural project in the Horn of Africa.

I'm looking to install a ≈1000L water tank on a 3 meter stand which will gravity supply a secondary ≈1000L water tank ≈320 meters downhill with a ≈5.8m elevation drop. Piping connecting the two tanks will be PVC, probably 1"-1.25" as anything larger would be uneconomical.

I am trying to determine if this setup will work by gravity without an inline pump between the two tanks, and if the lower tank can also be on a 2-3m stand or if it needs to be lower. If necessary, an inline pump can be added but will be difficult as the project is off-grid.

Using multiple Omni calculators (velocity, flow rate, friction loss) , I've determined, if using a 1" pipe:

  • The flow velocity would be 0.603 m/s
  • The flow rate would be 18.33 L/min
  • The friction head loss would be 5.787 meters of water.

I'm not sure where to go from here with these calculations, what this determines, or if I'm even on the right path! I haven't done any calculations with water head yet, which I'm assuming would be 3 meters (the height of the upper water tank stand) as the upper tank will not always be full, so better to design as if the water level is low (?).

I appreciate any insights!

Thanks in advance,

Jonathan

EDIT: Revisiting this, I initially wrote the drop at 5.8m, but thinking I should add the 3m from the height of the tank stand? To a total drop of 8.8m. Either way, it appears the friction loss leaves me with less than 15cm of static head at the lower tank (when subtracting the friction head loss from the head/drop).

If I incorporate a ball valve at the upper tank to regulate/lower the flow rate, that seems to fix the problem? If I halve the flow rate in the friction loss calculator, the friction head loss drops drastically. Is this a proper workaround?

With a drop of 8.8m from the top of the upper tank stand, using a 1" plastic pipe, the friction head loss is 8.785m... basically unusable when after subtracting this from the head/drop, right? But halving the flow rate from 22.77(L/min) (the new flow rate with a drop of 8.8 instead of 5.8), the friction head loss is only 2.28m, leaving 6.52m of static head (8.8m - 2.28m).

Can anyone confirm my math is right? Or am I totally doing these calculations wrong? Thanks

Height profile of proposed setup

Jonathan Ciccarone
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  • Only thing that might affect your setup is that the pipe will probably not be straight, so it will effectively be a little bit longer. And in the long term, you may have problems with fouling. – Tomáš Létal Jan 16 '23 at 18:35
  • See new edit. Is my math right? – Jonathan Ciccarone Jan 17 '23 at 06:53
  • Could you add a height profile of the setup? I am not sure if I get it right. – Tomáš Létal Jan 17 '23 at 09:10
  • Are both tanks open to the atmosphere? What is your actual design requirement and what is this calculation meant to help you with? If you wanted to know if a pump is needed, it seems you've answered that question. Your edit makes it seem you are more concerned with static head for some reason. – J. Ari Jan 17 '23 at 14:14
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    Added a height profile image as requested – Jonathan Ciccarone Jan 21 '23 at 05:05
  • J. Ari, I am looking to make sure the setup will work with a decent flow, and that I'm not left with just a trickle of water at the lower tank due to friction head loss. It's fine if the lower tank takes a couple hours to fill, but if it will take a day or two, then I'll need to readjust the setup. At present, the lower tank will mainly be for filling a watering trough for livestock. – Jonathan Ciccarone Jan 21 '23 at 05:11
  • With slow flow rate, just takes water longer for the same amount to move... – Abel Jan 21 '23 at 20:28
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    Do you have a minimum flow rate requirement? – Tomáš Létal Jan 23 '23 at 09:15
  • At what height from the ground will the inlet connection be for the tank at the bottom of the hill? Is it a smooth hill down to the bottom tank or are there intervening height changes (e.g. large ditches)? – J. Ari Jan 23 '23 at 12:12
  • I think there's some circular reasoning involved in the use of the online calculations to predict both flow rate and friction head loss. The static head difference between the two ends of the pipe will be equal to the (instantaneous) height difference between the atmosphere-touching (and therefore equal-pressure) surfaces in the two tanks. The flow rate will automatically adjust itself so that the friction head loss in the pipe is just right to make this so. – Daniel Hatton Jan 24 '23 at 16:29
  • Regarding a minimum flow rate, I'd say I can't really go below 3 L/min as this would cause logistical challenges for the agriculture operation. Ideally would have a much higher flow rate though. The inlet connection at the lower tank is shaping up to be 3 meters. 2 meter tank stand and a ≈1 meter tall tank. Smooth gradual decline in elevation, no big ditches. – Jonathan Ciccarone Jan 25 '23 at 04:43
  • Daniel, would love to better understand what you are communicating as it is new for me. – Jonathan Ciccarone Jan 25 '23 at 04:45
  • To calculate friction losses, you need to know a velocity. In this case of incompressible flow, if you supplied a velocity to the calculators then you implicitly defined a flow rate since that's just velocity x cross sectional area of the pipe. I think that's the circular reasoning Daniel Hatton is pointing out. Daniel is also explaining that in gravity driven flow, the system will use all available energy and the flow rate will change corresponding to change in driving force over time. In your case, the driving force is the height of the water in the top tank. – J. Ari Jan 27 '23 at 21:41
  • Take a look at this resource, I think you need to do some further design development. https://www.pseau.org/outils/ouvrages/acf_gravity_fed_system_2_sizing_en.pdff – J. Ari Jan 30 '23 at 03:41

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