Where does this steel ventilation calculation equation come from?

[nicoga3000]

I'm looking at a vent that will be used to prevent a tank from collapsing due to vacuum pressures in a pipe burst/free drain scenario. The situation would be a container is filled with water when an inlet or an outlet pipe bursts. The water flowing out would create some pressure in the tank that would need to be balanced by some vent(s) at the top of the tank.

So here's an equation that I have on file:

Av = Q/(4005*Ce*sqrt(pressure differential))

It's not a matter of if I can plug and chug my way through this - it's a matter of finding out WHERE this equation comes from. Nobody I've spoken to has any idea, nobody around my office seems to know, and really, it's not OK to use an equation without knowing it's validity nor it's origin.

Does anyone have ANY clue if this equation will suffice or information regarding it's origin? I need some sort of legitimate reference, but I just can't find a darn thing. Much appreciation!

 

[Lok]

Av = Q/(4005*Ce*sqrt(pressure differential))

Don't want to be rude... but please explain the variables (Av,Q,Ce) as although they are common they might refer to a specific localised value taken only in your tanks case type.
The 4005 might be a value that comes from the material used, otherwise please explain it.

 

[nicoga3000]

Oh wow, yeah, sorry about that. They're pretty standard parameters:

Av = required area of the vent (ft^2)
Ce = entry coefficient (unitless)
Q = flow rate (GPM)
pressure diff = the meaning of this is still a bit fuzzy to me (" H20)

 

[Lok]

Oh wow, yeah, sorry about that. They're pretty standard parameters:

Av = required area of the vent (ft^2)
Ce = entry coefficient (unitless)
Q = flow rate (GPM)
pressure diff = the meaning of this is still a bit fuzzy to me (" H20)

Better now... Yet these formulas are derived out of a lot of calculations, something like 10 pages of them. And you end up with a simple and effective formula that works in your specific case.

One way to test it would be to do the math again, where you would need all data from your setup and see if the safety value the you get is close ( less then 10% error is still good enough).

Usually when you design a product, you get through 30 computation steps, and end up with 2 or 3 relations between it's most common variables (capacity, flow etc.). In a second product if it is similar to the first the end result will still apply.

 

[russ_watters]

That formula is just Bernoulli's equation with some standard constants and conversion factors already plugged-in and re-arranged into a convenient form.

 

[nicoga3000]

Is there any chance that anyone would be willing to help get me started on the derivation? It's been a while since I've done any hydro calcs.

What I can supply is that this is in a water tower (as I think I mentioned). The top of the tower has a vent on it which leads to the atmosphere. The tank has some height (say the head range, HR) and then has a height from the ground to the bottom of the HR (the low water line in tank lingo, LWL).

LWL + HR = HWL (high water line)

I think my issue is in the assumptions and how Q's and V's are related, such as which can be set equal (V1 = V2 = V, etc). I'm defining three points:

1) Just outside the tank, outside the vent
2) Just inside the tank, right after air would enter the vent
3) Just inside the drain pipe, which is effectively at the LWL

Again, what assumptions I can make is what I think is holding me back from making too much progress on this at the moment. Any direction/motivation/help would be awesome. :)