# Vertical pipe flow

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.

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?

parameters:

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

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

• 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? Oct 4, 2022 at 20:19
• Sure, the viscosity is for 10 degrees saltwater
– KSH
Oct 4, 2022 at 20:45
• Have you checked if the initial assumption of laminar flow is correct? Oct 5, 2022 at 16:08
• No I have not but it cant be if I use the High velocity to calculate reynolds number ?
– KSH
Oct 5, 2022 at 17:47
• 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. Oct 6, 2022 at 16:51

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: $$\Delta p = \left(h_{submerged} - h_{pipe}\right)\cdot \rho\cdot g$$