Simulate Airflow going into a vessel

[naughtv3]

Hello all,

We're designing a new product at the moment. It's a vessel that will contain a liquid. It has two openings at the bottom; 1st opening is 1mm, 2nd is .8mm. Vessel is 120mm long and has a diameter of 55mm. The openings are separate parts that are assembled on afterwards.

See my crappy drawing for explanation.

What I would like to know is that is there any way I can calculate the flow rate of air going into the bottle and flow of liquid going out as the vessel slowly empties itself? How could you simulate this/what formulas would you use?

Thanks

Vinny

 

[BigInch]

This is not too difficult.

You have fluid pressure equal to the air pressure at the surface of the fluid. That pressure appears to be atmospheric pressure minus the pressure lost from the flow of air through the tube up to the surface. You will need a pipe flow equation (valid for low pressure) to calculate what the pressure drop will be from that air flow into the cylinder. You will have a small localized pressure drop to consider at the inlet to that tube where air is flowing in as well. That can be considered as the Cd coefficient of a circular square-edge opening (in the wall thickness' dimension. That could be 0.6 x the velocity head of the air moving into the tube. That will be relatively small in relation to total pressure drop, possibly a candidate to neglect.

At the bottom outlet where liquid is being expelled, you will also have a localized pressure drop from the fluid exiting the cylinder, also another Cd of a square-edged opening. Since the velocity head of the liquid will be larger than that of the air, you might not want to neglect that one.

The flowrate of air into the cylinder should equal the flowrate of the liquid out, to prevent a reduction of pressure inside the cylinder too much, and possibly collapse it, so I would figure the flow velocity of water out, based on its pressure imposed on the orifice now at full height, remembering that it will reduce linearly to zero as the liquid level drops to zero, making the velocity less and less until the last drop leaves.

Air being much more easy to flow in than for the water to leave, as long as you have a reasonable tube diameter, should not be the limiting feature of this system. Size the air tube for the maximum flowrate of the water leaving, calculated now when the surface level is highest.




We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer

 

[BigInch]

... If the primary mechinism of the flow driver is gravity, as it appears to be.

We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer