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I am trying to calculate exit pressure of water from a pipe where the water entry is approximately 100m below ground. I know the exit flow velocity of water (20 GPM or 1.2618 litres/second); this was estimated as this is the required flow velocity to irrigate an acre of land. A centrifugal pump is used to draw the water from underground; this pump is above ground and therefore is not submerged in the water. I have made a crude illustration to visulaise my question (it is worth noting that the pipe diameter does not change throughout the length of the pipe, it remains the same even if not shown accurately in the diagram).

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So, my assumption for the pressure at point 2 is the culmination of all pressures casued by the atmosphere and teh various sediments of rocks and soil, from some preliminary research I found this to be about 5 atm (would this be a reasonable estimation for a ground depth of 100m?). However, I am getting confused by the flow velocity at point 2. I think it should be 0 m/s, as teh water is drawn from a stationary reservoir but it doesn't make much sense for the initial velocity to be 0 m/s, otherwise how would water be drawn up?

If I have the flow velocity and pressure at point 2 I could then use Bernoulli's equation to calculate pressure at point 1 (making height 0 at point 1 and -100 at point 2).

Any guidance would be greatly appreciated!

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  • $\begingroup$ Point 2 is within a porous medium, correct. Is this horizon artesian, or is it pretty close to hydrostatic? Do you know the permeability or hydraulic conductivity of rock in layer 2? You need to help of a groundwater hydrologist for this. $\endgroup$ Oct 1 at 11:58
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If the pipe is of uniform cross section, the the rate of flow must be constant for the entire length. A pump at the surface cannot be more than 33 feet above the level of the water table. Bernoulli's equation assumes conservation of energy (which you do not have in this situation). You need an equation which relates the rate of pressure loss to the pipe size and the viscosity of water.

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  • $\begingroup$ Firstly, thank you very much for your answer. I have a few questions: 1) Why can't the the pump be more than 33 feet above the water reservoir? 2) Is energy not conserved because energy is added to the system by the pump? 3)Would the pipe flow equation be useful in this situation then as Bernoulli can't be used? thank you very much. $\endgroup$
    – Tea_Cups
    Oct 1 at 14:12
  • $\begingroup$ (1) Due to the porosity of the material at the earth's surface, the pressure at the top of the ground water surface is about one atmosphere.. With a vacuum at the top of the pipe, that pressure can only support about 33 feet of water in the pipe. Deep wells require a pump down in the pipe. (2) Energy is not conserved because of the pump and because of friction in the pipe. (My son had to redo a system irrigating his lawn because the pipes were too small.) (3) A pipe flow equation which considers friction (viscosity) is what you need (on both sides of the pump?). $\endgroup$
    – R.W. Bird
    Oct 2 at 14:44

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