How long it will take flood a vertical pipe if the bottom of pipe cut

[myturns]

HI! Could anyone help me? Water Depth is about 1km. the vertical pipe is also 1km length vertically and empty but we try to cut the bottom of pipe by blade so the water will flow inside the pipe from bottom. Do you know how to calculate the time to flood fully up to a sea level? Pipe size is ID is 25in. Cutting will take 2 hours and during the cutting, the cutting pipe gap(assumed 1in.)is very small. Objective is to see how much of pipe would flood during the cutting process before tool makes the complete cut. Thanks

 

[bimr]

The flow rate that is possible through the opening will depend on the size of the opening. It is not clear from your post what size is the opening.

Water flow through pipes typically reaches a maximum velocity of 9-12 m/s. If the pipe was open on the bottom, a rough estimate is that it may take 1 1/2 minutes to fill the pipe.

 

[rconner]

This "pipe" is truly "empty", it must be AWFULLY thick as the external pressure would be tremendous -- also, not sure I'd want to be floating around real close when it was breached (are you sure this isn't prohibited homework?) [In any case be very careful at this depth!]

 

[myturns]

Thanks for reply. Sorry for wrong info. The cut will be 30m water depth and total vertical pipe length is 1km. I used Orifice Discharging Freely into Atmosphere Q=CA x SQRT(2gh) but actually when it cuts, the air will come out of the pipe. It's not atmosphere. How to calculate? Area of Orifice is 21 in^2, Coefficient 0.82, water depth=30m.

 

[bimr]

Will be very difficult to calculate since the event is not steady state. To start off with, you will create a vortex at the entrance to the pipe with will disturb the flow going into the pipe. Then, air bubbles will be rising and water falling within the pipe with periodic bursts of air through the vortex.

In water the volume of air halves for every 10m of depth. Additionally, a bubble rising through water experiences forces of fluid friction and turbulence. These create an opposing force proportional to velocity, so just as a body falling in the air reaches a terminal (maximum) velocity, so it is for a bubble when the frictional forces due to its upward velocity match the upthrust.

A rising air bubble in water reaches a velocity of approximately 2/3 * (square root(gR)) for a bubble of radius R. What this means to the sound is that whatever the bubble size it quickly reaches its final velocity. Now suppose a bunch of bubbles, some big, some small, were created deep in the water. The bigger ones will arrive at the surface first, followed by the smaller ones.

From the sea floor 800 meters down, it has been observed that it takes 20 minutes for methane bubbles to rise 300 meters. Based on that empirical data, one can guess approximately 60 minutes.

You might get a better answer in the diving forum.

 

[cvg]

if you dont release air from the top, the water wont enter through the bottom. if the air releases from the bottom, then you will have problems making the cut or getting water to go in. the flow rate will also vary with size of hole and the head pressure. it is not a steady state process and you will have to integrate if you want a reasonable estimate. I'm not sure if there is any issue with rising bubbles, still trying to visualize how that would happen.

 

[itdepends]

Why does the time to fill the pipe matter? Do you want it full? Are you trying to ensure the pipe isn't full until you've completed the cut? Are you worried about what may happen when the cut is complete and the pipe isn't full?

Why wouldn't you flood the pipe before making the cut?

As a chem eng/metallurgist the first part of any answer I give starts with "It Depends"