Vacuum Question 1

[trev150]

Hello Everyone,

Doing a little R&D at the minute and I have come up against a wall so please help.

There will be a small tank of 50 litres and larger tank of 450 litres. I will suck out the 450 Litre so it is as close to an absolute vacuum as possible ( lets assume a perfect vacuum to keep the maths easy).

I will now connect my 50 litre tank which is full of normal air at atmospheric pressure. Once I open the valve I know that the 2 different pressures will cause the air to move from the smaller tank to the larger tank and settle at equilibrium.

I would like to know how long this will take,what the final air pressure will be and what effect on time changing the diameter of the connecting pipe will have over a distance of 10metres?

Can anyone help me?

Thanks,

Trevor


P.S. - By the way I posted this in the wrong section earlier, so my apologies for that.

 

[PEDARRIN2]

Assuming perfect gases, P1V1=P2V2, and assuming no temperature change (which might be a big assumption since expansion of the gas will likely have a change in temperature) P1 is atmospheric, V1 is 450 liters and V2 is 500 liters. This will let you calculate P2

How fast the change will take will depend on the gas properties (density, composition, expansion factoretc.), temperature, pipe size and material. Since the delta P will exceed 40% (going from atmospheric to "perfect vacuum"), you would likely need to use one of the empirical gas flow equations.

Once you have the flow rate, I would assume you would divide the volume (500 liters) by the flow rate (liters/time) to arrive at the time.

 

[LittleInch]

I think you mean V1 is 50, not 450?

How long? Depends on when you call it over. This is a transient calculation not easily done by formula calculation as the differential pressure which is the driving force for the flow from the small tank to the big one is changing every second and the flow gradually tails off. For such a short distance it will probably come to an effective 0 velocity within a relatively short time, depending on the size of your pipe. If the size of you pipe is a small fraction of the volume then increasing size will make a big difference. If its always much bigger then increase would be less effective, but will always make it better.

you may also have choked flow to start with which then changes to non choked flow.

you need to take at least 5 or possibly 10 snap shots in time after t=0 to re-calculate all the flow and pressure figures.

I would get someone to model this in a transient flow program.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[racookpe1978]

Little!

He is starting his (homework ?) problem with air in the 50 tank, and ending with that air filling both the 450 + 50 tanks = 500 total.

V1 = 50, V2 = 500. Final pressure - if no heat loss - would be 1/10 of original pressure: P1 (tank 1) = 14.7 psia. final pressure tank 1 + tank 2 = 1.47 psia.

The (homework) problem CANNOT be solved as given: No pipe length, pipe diameter and pipe wall thickness, no fitting count nor valve description (opening times will be critical) if time is needed in the "second.decimal place" level. If net time is needed only in general terms, then I'll tell him that small a tank will equalize in a 20 - 30 seconds with a 25 mm pipe with a quarter throw ball valve. A bit more if you have a 6 mm (1/4 inch) flex hose connecting the two tanks. A Still more if yo have to turn a globe valve. 50 liters of air is very, very small, but the driving d/p isn't very large either

Temperature difference? The first tank cools, the second ALSO cools (No air in there to compress!), the pipe also cools. After a long time (30 minutes), all will return to about the original temperature, presumably to ambient. Is he leaving the valve open as the tanks and pipe heat back up? Classroom temperature = 25 C? 298 K probably. Could be more in south Texas in the sun, less in Calgary in January.

 

[trev150]

Thanks for all of the comments and help so far.

If I do need to solve the problem and (this is only a R&D project so I will be collecting a lot of data of how it behaves) I just want to try and size up the correct pipe.

I was only going to use 1 quarter turn ball valve between the two tanks. The pipe would be either 15mm or 22mm domestic copper or 1/2" BSP or 1" BSP galvanised.

What is the formula that you would use to calculate this? I understand that iterative loops will be required in the calculation and I am happy to do this but just need a formula to prove my theory. I have also decided to ignore the temperature difference unless it will seriously affect the results. It only needs an accuracy of 1 decimal place unless this won't give enough resolution.

My background is in electrical and automation so some of this is new to me but I am finding very fascinating as I never fluid mechanics at University.

Also my calcs for P1V1=P2V2 gives me 1 x 50 = P2 x 500 which gives P2 @ 0.1 BAR

Once again thanks for the help so far.

 

[trev150]

I have found this on a Physics forum. Which would seem to solve it for me and I can take time steps every 0.1s until it is completed. How do I find out what the velocity of the air will be? Once I know this I can then calculate the flow rate through the different sizes of pipe. How do I know what volume the mass of air will take up in the vessels?




I would break the problem into time steps. Here is the basic procedure:

a) During the time step, assume the pressures in the two vessels are constant and figure out the flow rate.

b) Multiply the flow rate in Step 'a' by the timestep. This will be the quantity of gas that flowed during the time step.

c.1) Subtract the mass determined in Step 'b' from the higher pressure vessel.

c.2) Determine the new (lower) pressure in the higher pressure vessel with the perfect gas law. The pressure is lower since mass has left the vessel. Use the 'Z' compressibility factor if needed.

d.1) Add the mass determined in Step 'b' to the lower pressure vessel.

d.2) Determine the new (higher) pressure in the lower pressure vessel with the perfect gas law. The pressure is higher since mass has entered the vessel. Use the 'Z' compressibility factor if needed.

e) Go To Step 'a'. The difference in pressures is now lower and so will be the flow rate. Repeat until the two vessel pressures are equal. Add up all the time steps and this is the total time.



Thanks,

 

[LittleInch]

There are many equations around that for a differential pressure, pipe size (ID), density etc, will give you volumetric flowrate and or velocity. You may need to guess velocity and iterate until you get the differential pressure that you have from step a. Density of air at standard conditions is 1.225 kg/m3.

Volume will be in proportion to the pressure difference from STP (1 bar at 15C), e.g. 0.5 bar will be 0.6112kg/m3.

The air will take up the volume of the vessels - what will vary is the pressure and density so your question "what volume the mass of air will take up in the vessels?" is simple - the volume of the vessel. I think you meant pressure or density??



My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[trev150]

Hello

Thanks for the help everyone. I have managed to piece together enough information to build a small test rig. I have made some calcs that I have based the sizing on and the real test data will either prove or dis-prove my calcs.

Once again thanks everyone.

Trevor