I want to know the flow through a vertical pipe when a valve in the bottom is opened (a disk is lowered as illustrated in the drawing) I know the heights in the drawing and the diameter of the pipe. enter image description here

I have tried to use Poiseuille's law (assuming laminar flow). Where I get the following:

Flow: <$Q_{pipe} = \frac{(p_1-p_2-\rho \cdot g \cdot h_{submerged}) \cdot \pi \cdot D_{pipe}^4}{128 \cdot \mu \cdot h_{pipe}} $> Velocity: <$Q_{pipe} = \frac{(p_1-p_2-\rho \cdot g \cdot h_{submerged}) \cdot \pi \cdot D_{pipe}^2}{32 \cdot \mu \cdot h_{pipe}} $>

where: <$p_1 = \rho \cdot g \cdot h_{submerged} \quad p_2 = p_{atm}$>

However, using this I end up with an average fluid velocity of approximately 9000 m/s.

Can anyone help me set up the equations needed?


<$\rho 1000$> <$g = 9.82$> <$h_{pipe} = 0.152 m$> <$D_{pipe} = 0.102 m$> <$\mu = 0.00141$>

the submerged height can vary in the range of 0.1 to 0.45 m.

  • $\begingroup$ Your result could be correct, depending on the input parameters. Could you add the values of all the input parameters? Also, did you use the right viscosity? $\endgroup$ Oct 4, 2022 at 20:19
  • $\begingroup$ Sure, the viscosity is for 10 degrees saltwater $\endgroup$
    – KSH
    Oct 4, 2022 at 20:45
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    $\begingroup$ Have you checked if the initial assumption of laminar flow is correct? $\endgroup$ Oct 5, 2022 at 16:08
  • 1
    $\begingroup$ No I have not but it cant be if I use the High velocity to calculate reynolds number ? $\endgroup$
    – KSH
    Oct 5, 2022 at 17:47
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    $\begingroup$ Yes, it is probably not laminar flow. If that is the case, you should use another approach. This answer to a similar problem may help. $\endgroup$ Oct 6, 2022 at 16:51

1 Answer 1


Since the pipe is vertical, the flow will have to overcome its height as well (if $h_{submerged} = h_{pipe}$, there should be no flow). So the proper pressure difference driving the flow will be: $$\Delta p = \left(h_{submerged} - h_{pipe}\right)\cdot \rho\cdot g$$

If calculated flow is not laminar, you can use the approach from this answer.

  • $\begingroup$ What if the submerged height is lower than the height of the pipe ? should I consider the gravitational force from the tank ? $\endgroup$
    – KSH
    Oct 11, 2022 at 9:36
  • $\begingroup$ @KSH In that case there would be no flow and you would just get water surface in the pipe at the same level as the connected body of water. $\endgroup$ Oct 11, 2022 at 15:45
  • $\begingroup$ okay I see thaanks $\endgroup$
    – KSH
    Oct 11, 2022 at 17:28

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