HELP! Free Gooseneck Vent Sizing

[Kinemenematics]

Hi,

I've attached my calculations for an atmospheric EN14015 1000m3 steel tank with an emptying rate of 1440m3/hr.

The trouble is with the sizing of the vents (read some of the other threads on this, and have been trying to find a suitable equation to determine the actual flow capacity of a free vent).

So under Part 8.3.5 of the attachment, I've sized the free vent(gooseneck) at 10", trying to find the corresponding max velocity of air being vented. Can anyone verify the formula? This same formula was used by two other designers and I'm sure this was derived from Darcy. So I've looked up this formula: (Equation 4, HERE with the assumption that λ = 0 for a short and smooth vent, and then applied ΔP = hΔρ , and I arrived at what the designers got. Is there any literature to back the stuff on this webpage?

Also, I doubt the answer because the dimensional analysis doesn't add up- I'll show it on the next attachment

One more thing,
I've also designed the set pressure (1.5") as 75% MAWP (2") with the - with a venting pressure max differential as 10% of the set pressure (0.15"). Pretty sure I'm doing this wrongly - anyone have any idea on what the best practice is for a tank like this?

Thanks a lot

 

[Kinemenematics]

I've attached the dimensional analysis.

Something I missed out:
Can someone comment on the area reduction due to bird screens/meshes? Is this a logical calculation? I mean having a screen just restricts the flow of air at that point. Since air is compressible, is there even a need to use "effective area of vent"??

 

[IFRs]

The flow area should be the area net of the screens. Typically, vents need to have certified flow characteristics and vendors are the only ones motivated to set up and test such devices. You may be over-thinking this, if it is a free vent to relieve pressure and vacuum from filling and emptying, using a multiple of the fill/suction pipe may be sufficient.

 

[Kinemenematics]

okay, what kind of typical multiple of the fill pipe may be used? 1:1?