If I have a very long (say, 1km) pipe in my garden (under the sun) with a small slope and put water at one end, will I receive exactly the same amount of water at the other end, with the same pressure that it was put in (if there is a motor to force the water into the pipe)?

And if not, where did that water or pressure go? Is there some kind of formula to express where the water / pressure went?

  • 1
    $\begingroup$ Bernouillis Principle is what you want. $\endgroup$ – JMac May 26 '17 at 16:08
  • $\begingroup$ thanks, and since i'm not very scientific, in english terms, what would be the answer to the question ? $\endgroup$ – jdoesnt May 26 '17 at 16:09
  • $\begingroup$ What are your thoughts on this? $\endgroup$ – Chet Miller May 26 '17 at 16:22

Assuming that the pipe is not porous, you will receive the same amount of water at the other end. However, there will be two things that make the pressure lower:

  1. If the water is not flowing, there will be a pressure difference due to gravity: if the inlet is a distance $h$ lower than the outlet (measured vertically), then the pressure at the outlet will be $\rho g h$ lower than at the inlet. The corollary is that if you have an inlet pressure $P_0$, the greatest height you can reach with your hose is when $P_0 = \rho g h$, so $h = \frac{P_0}{g \rho}$. For water, the rule of thumb is "10 meters per bar of pressure" (or "2 feet* per psi" - ).
  2. If the water is flowing, you will get losses from the friction with the wall. This depends on the flow velocity - as you increase the pressure, you will get more water per unit time. There is a nice chart on engineeringtoolbox.com that shows the relationship: enter image description here As you can see, as you increase the flow rate by 10x, the pressure drop increases by almost 100x. That is typical of turbulent flow. As the flow rates go down, the relationship becomes linear (eventually). And these things depend quite a bit on the viscosity of the water (a strong function of temperature) and the smoothness of the interior surface of the hose.

* 28 inches if you want to be more precise

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