Volumetric flow rate of air into a tank - Fluid Mechanics

[abe_cooldude]

Hi all,

I am stuck on a problem, and it's been a while since I took fluid dynamics. I have a cylindrical tank of know capacity with an inlet, where a vent is attached, and an outlet, the fluid gets sucked. The tank has fluid in there with known volume and density. If I know the usage rate of the fluid, what equation would I use to calculate the volumetric flow rate of the air coming through the vent opening replacing the fluid fluid. Vent is exposed to the outside ambient pressure and temperature.

Unknown: Volumetric flow rate of the air going into the tank

Equation: I am pretty sure you have to use continuity equation some how, but now idea how to apply it. Or I might be completely off?

Can anyone help me get started in the right direction?

Thanks,
Abe

 

[Travis_King]

If the tank is open to atmosphere and is just sucking in air to fill the voids (i.e. the air isn't getting compressed) then the cfm (or m3/hr or whatever) of the fluid going out will equal the cfm of the air going in. Volume is volume.

 

[abe_cooldude]

Thank you! So yeah, it is a closed cylindrical tank with one port sucking the fluid in the tank, and other port with a vent exposed to the open air. The purpose of the port is to avoid vacuum inside the tank.

EDIT: How come it doesn't take into account the diameter of the vent hole? Pretty much, I am trying to find the amount of air flowing through that hole inside the tank per some unit time when the fluid is being sucked.

Thanks! And sorry for the trouble!

 

[Travis_King]

The diameter of the vent hole will affect a the flow in several ways, but none of them are the volumetric flow rate. If you are assuming that the pressure in the tank stays the same, then the volume of air entering must equal the volume of water exiting. The actual numbers may be slightly different.

Air flowing through the port will probably heat up slightly (probably not even measurably) which will change the fluid properties of the air. Air is funny stuff, when it's flowing. But if you lose 10 cfm of water (not typically a unit of volumetric flow for water, but it works) then you'll need 10 ACFM (Actual Cubic Feet per Minute) of air to maintain atmospheric pressure in the tank. Whether that's 10 SCFM (Standard Cubic Feet per Minute) is another story, but all that changes is what the state of the air is as it's flowing. As I said, volume is volume. If you lose 3 cubic feet in a minute, you'll need 3 cubic feet of air to replace the lost fluid.

Exactly what that flow looks like requires more analysis. Pulling the water out creates a partial vacuum, it could be very partial, but if the tank wasn't at a pressure below atmosphere, there wouldn't be any flow.

Take a look at this, it has some insight into this type of problem. here

Converting SCFM to ACFM and vice versa:Engineering Toolbox

Some more on orifice flow, though since you don't know the pressure differential between the outside and the inside of the tank, it's not super useful. Here

 

[Travis_King]

Also, if this is for some industry or client or public use, it should comply with the API 2000 Standard.