Lifting of submerged pipe, ventilation area calculation

[Willem_lift]

Hello all,

This is the situation: a pipe, shown in de drawing below, is lifted at a constant speed of 1m/min. The pipe is closed at the top and open at the bottom. For obvious reasons, a ventilation hole is required at the top. The intention is to lift a minimum amount of water, in other words, the height difference of the water inside the pipe and the sea level should be minimal.

Some more info:
-pipe diameter at top: 1.3 meter
-pipe diameter at bottom: 2.6 meter

I tried some things to calculate the required vent hole area, but I'm not sure if I did it right at all. Hope you can help me!

This is how I did it:

I determined that an height difference of 0.5 m was allowable. 0.5 m of water results in a pressure of P = 0.5*g*rho_saltwater = 0.5*9.81*1028 = 5042.3 N/m^2

Then I used an online calculator:

http://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html

And filled in the following variables:
-Air temperature: 10 degrees Celsius
-Primary pressure: 5042.34 Pa
-Secondary pressure: 0 Pa

For the volumetric flow I used the most unfavorable situation, which is when the pipe is almost out of the water. At that point the largest amount of water leaves the pipe.

Q = r^2*pi*lifting_speed = (2.6/2)^2 * 3.14 * 1 = 5.3 m^3/min

Then iterate the tool till you find an appropriate vent hole area. I found that an hole with a diameter of 50mm would do the job.

Is this in any way correct? And I would like to be able to calculate it myself, instead of using a tool. Anybody know how to?

Thanks in advance!

 

[DEvens]

I have not checked your arithmetic. But it looks like basically the right way to approach things. A hole size 50 mm in diameter does not seem outrageous.

If you want to calculate the air flow for yourself, the calculator page you cited gives the formulas. It looks simple enough to implement as a spreadsheet function. You could then do various things to get your answer.

Is this something to do with deep-sea oil well drilling?

 

[Willem_lift]

Thanks for your reply. Good to hear that the calculator is the right approach.

The reason I doubted it, was that I wasn't sure if it was ok to assume al the water height difference would result into a pressure difference. I thought that maybe a significant amount of the pressure would be needed to overcome any friction forces with the water and the inside of the pipe.

And yes, it has something to do with deep-sea oil well drilling! The removal of a drilling rig to be precise.