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What size supply pipe must be used from a 5000 litre water tank to supply 4 bars of pressure to a house that is 20m below and 300m away from the tank?

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It's a trick question, you can never get 4 bar of pressure with only a 20 m head.

The pressure due to a vertical column of liquid is equal to the density x height of the column x the acceleration due to gravity (little g = 9.8 m/s2).

Your height is 20m

Density of water is 1000 kg/m3

g = 9.8

So, pressure is 196,000 Pascals

100,000 Pascal per bar, so you have 1.96 bar as the max pressure you could get, independent of flow rate or pipe size.

1

Pressure of the gravity fed water delivered from the overhead tank will have nothing to do with the pipe size used. The pressure is dependent only on the vertical distance between the top of the water in the tank and the delivery point.

Where pipe size does come into play is in the flow rate that is needed at the delivery point. If you only have one delivery point being used at a time you can get by with a pipe size that can deliver the desired flow rate all the way back to the tank.

If you have multiple delivery points in use at one time then the branch lines from those delivery points will have to merge into a larger pipe at some point and then this larger pipe goes the rest of the way back to the tank. You roughly work out the size of this larger pipe needing to have a cross sectional area that is the sum of the cross sectional areas of the multiple use delivery point pipes.

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Given that 20 meters of head only equates to 1.96 Bar (1m elevation = 0.0980413943 Bar), no pipe alone will do this - you'll need a pump, or you'll need to accept less than 2 Bar as all the pressure you have available.

Then you need to determine the flow rate you wish to operate at for sizing the pipe - you'll get 1.96 bar with any size pipe and no flow (static head) but as you actually use water the pressure will drop (dynamic head) in relation to to pipe size and rate of flow. That is essentially friction in the pipe resisting flow and reducing the effective head. Calculators are available and the formulas for that are adequately complex that using one is suggested. Aside from size of pipe and flow rate, pipe material enters into it as some types are smoother inside and thus have less friction for a given size of pipe than other types.

For example, if you were sizing for 12 l/min, 25mm plastic pipe would have about 2.7 m dynamic head, leaving you with 17.3m head pressure (delivery pressure = 1.7 Bar), and 50 mm pipe would only lose 0.0925m at that flow rate (delivery pressure = 1.9 Bar).

Bump the flow up to 120 l/min and the 50 mm pipe costs 6.55m head (delivery pressure = 1.3 Bar) - but the 25mm pipe cannot provide that flow rate at all with 20m head - it tops out at about 35 l/min with no pressure at the house end (20 m static head - 20m dynamic head; delivery pressure = 0 Bar)

  • Including it in the answer is more useful. – Tester101 Apr 25 '15 at 12:59
  • Thank you very much for your quick answers. So roughly speaking one needs just over a meter of elevation to get one bar of static pressure. So I would need about 50m of elevation on 300 meters of say 32mm pipe to obtain a decent amount of pressure and flow for a farm house. I could of course also use one tank to fill another tank next to the house and run a booster pump albeit on a solar powered system but then there would be a whole lot of different costs involved. Might I ask where I can get the formulas or alternatively a table for the flow rate calcs for different size pipes? – Sandy Apr 26 '15 at 13:59
  • @Sandy 10.2m per bar, roughly. Put dynamic head calculator into a search engine. Most will be from pump companies, so any entry for elevation is usually taken to be "added static head for pumping uphill" in sizing a pump - just leave it at zero and enter the pipe and flow parameters to see what the dynamic head is, then subtract that from your static head yourself. Unless you happen to have another 30m of elevation with water supply handy, living with 1.9-1.7 bar delivered water pressure (at reasonable flows) is probably the most sensible solution if this is an off-grid house. – Ecnerwal Apr 26 '15 at 15:29
  • Sorry I meant 10m per bar. Got the calculator. brilliant! Thanks a lot. – Sandy Apr 27 '15 at 22:57

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