Venting and Draining Ratios

[GrahamHepworth]

Hi All

I was wondering whether there were any governing ratios between the drainage area size and the required venting area size to prevent choking???

Many Thanks

 

[TrevorP]

I'm not sure I know exactly what you're getting at here, but I think you may mean that if you have a vessel or pipework that is being drained, what vent size do you need on top of the pipework/vessel to stop air flow back up the drain pipe? If I have understood this correctly, then I think I have come up with some answers for you. I'm a bit confused, because this is not really "choked flow", as this expression has a specific meaning in fluid mechanics, and I don't think it applies here.
The upwards pressure on the pipe is atmospheric pressure. The downwards pressure is determined from the static head of the liquid, plus the absolute pressure in the vapour space above the liquid, less the frictional losses due to flow. As long as the downwards pressure exceeds the upwards pressure, air cannot flow back up the drain pipe.
The ratio of diameters of the pipe sizes therefore depends on the properties of the liquid that is being drained, and of the gas that is displacing the liquid, i.e. going through the top vent. It also depends on the pipework for both the drain and the vent line, and on the vent gas pressure, so there is no fixed rule for this. At least none that I know of.
The worst case is at the end of draining when the liquid is just above the top of the drain. At this point, if the vent gas flowrate equals the draining liquid flowrate, air cannot flow up the pipe during draining.

I have done some number crunching to see what I could come up with regarding ratios of vent/drain pipes under a certain set of circumstances. If we assume that the liquid is water at ambient temperature, that the vent gas is air at atmospheric pressure and ambient temperature, and that the vent and drain pipework are both short, vertical, and consist of the same fittings and pipework length, then it appears that if the ID of the vent pipework is at least equal to a quarter of the ID of the drain pipework, this should be sufficient to prevent back flow of air up the drain.

 

[pleckner]

OK, that's one way of interpeting the question. Another way is that as the tank is draining, it will pull a vacuum unlesss enough air is drawn in to compensate.

To answer your question, it depends. The quickest way to get the right vent to use with a given drain is to do a little gas flow and corresponding liquid flow calculation.

Using the isothermal gas flow equation determine the amount of air required from atmosphere to some allowed vacuum you would get while draining the vessel.

Start with a drain size and determine the first instantaneouis flow through the drain nozzle. Use the Darcy equation with one entrance loss for the nozzle and the maximum volume in the tank (liquid head). This will give you the instantaneous maximum volumetric flow of liquid. This is the same volumetric flow of air you will need to compensate. Choose the maximum vacuum you are willing to tolerate. Using the isothermal gas flow equation specifying the flow and pressure drop, choose a nozzle size that will pressure balance the liquid outflow. Choose the next standard size for the vent nozzle. Don't forget to include an entrance loss for the air into the vessel.