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I have a question: the situation is as follows: There is an open pool (in blue) to which a pipe is connected. The pressure above the pool is equal to the air pressure = 1 bar. In normal configuration the valve from the pipe is closed and thus the pressure in point B is equal to the air pressure + ρgH (hydrostatic pressure). There is no flow through the pipe.

In case there is a rupture of the pipe at the height of the valve, water will siphon from the pool via the pipe at a velocity v. My question is how can you calculate the pressure in point A?

I think the pressure in point A is calculated as follows:

Pa+ $\frac{1}{2}$ρva²+ρgL=Pb+$\frac{1}{2}$ρvb²+ΔPfriction where va=vb and thus:

Pa+ρgL=Pb+ΔPfriction where Pb is equal to the air pressure (1 bar) due to the break.

PA=PB+ΔPfriction - ρgL

ΔPfriction=fD$\frac{L}{D}$$\frac{ρv²}{2}$

However, my friend does not agree with me and says that Pa is equal to Pb. So who is right?

enter image description here

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  • $\begingroup$ The driving force for fluid flow is a pressure difference. That means that you are right. $\endgroup$ – David White Jun 14 '19 at 19:27
  • $\begingroup$ P friction should not be used if we use bernoulli's theorem. Because it is conservation of energy. $\endgroup$ – Sandesh Goli Jul 11 '19 at 6:38
  • $\begingroup$ Therefore Pa=Pb-pgL. $\endgroup$ – Sandesh Goli Jul 11 '19 at 6:40
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Yes, pressures at points a and b are not equal.enter image description here

pressure at B = pressure at A + pgL

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