Physics Help Forum Fluid-dynamics of water between two containers

 Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum

 Feb 25th 2018, 10:03 AM #1 Junior Member   Join Date: Feb 2018 Posts: 4 Fluid-dynamics of water between two containers I have a rigid container connected to a soft bag as in the picture below. Water is pumped with a peristaltic pump in the rigid reservoir through a pipe of 6 mm diameter on the top. From the rigid container, water goes in the soft bag through a hole of 9.5 mm. The rigid container has a small hole on the top (not indicated in the picture) so it's at atmospheric pressure. Max pump flow is 3 Lpm. Depending on the flow rate, in the rigid container I see a water level whose height is h. I would like to avoid this level of water in the upper rigid container ... I would like ALL the water to go directly in the soft bag. Which should be the diameter of the hole between the upper and lower containers (or how many holes of the same diameter should I add)? Attached Thumbnails
 Feb 25th 2018, 10:25 PM #2 Senior Member   Join Date: Apr 2017 Posts: 427 My answer is designed to cause the minimum amount of work and trouble ... First I would try and connect a tube from the exit of the ridged tank down into the bottom of the soft bag . Make this of a diameter that is easy to connect , but fairly large dia , about 10mm ..... when this is filled with water it will help 'pull', siphon , the water from the ridged tank at a faster rate ... This should do it ... but if it doesn't you have to make the hole bigger or add more exits , whichever is more convenient.
 Feb 26th 2018, 10:52 AM #3 Junior Member   Join Date: Feb 2018 Posts: 4 This is good idea but I've tried and unfortunately it's not sufficient to avoid the water level. Is there any way I can calculate which is the needed diameter?
Feb 26th 2018, 07:48 PM   #4
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Join Date: Apr 2017
Posts: 427
 Originally Posted by Corrado Is there any way I can calculate which is the needed diameter?
Not to my knowledge ...

But experience tells me 20mm must almost certainly be enough.

 Feb 27th 2018, 02:38 AM #5 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 I once had an argument (I won, when his site flooded) with a civil engineering contractor about this subject. It's called the backwater curve. Basically you require a minimum static head of water to force water from a wide channel or duct into a narrower one. What you are asking can't be done. There will always be a small standing level of water in the upper tank. Any plumber will tell you that to empty a water tank you have to tilt it down towards the outlet. Otherwise there is always be a layer of water that will only clear through evaporation. Tilting the bottom of your tank may be the best you will achieve. Last edited by studiot; Feb 27th 2018 at 04:20 AM.
 Feb 28th 2018, 02:39 AM #6 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 Good morning corrado. I see that you have been online here at least a couple of times since I offered you my thoughts on fluid mechanics but you have not responded. ??? Last edited by studiot; Feb 28th 2018 at 02:42 AM.
 Mar 2nd 2018, 02:34 AM #7 Junior Member   Join Date: Feb 2018 Posts: 4 This is the "real object" ... my drawing was not 100% correct because, as you can see, the bottom part of the upper container is already inclined. Despite this, I have a water level. The only solution seems to be to increase the diameter of the hole ... going back to my first post, I was tring to understand if there is any way to calculate this diameter. As oz93666 suggested, probably 20 mm is sufficient. Thx Attached Thumbnails
 Mar 2nd 2018, 04:04 AM #8 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 Thanks, it's much clearer now. Does the tank discharge straight into the bag through a hole or is there a short pipe? I will post my thoughts and explanation later, I am clearing last night's snow this morning. Meanwhile try this experiment. Part fill a flat bottomed ordinary basin/sink/bath with water. Now check different ways of letting that water out. If you just pull the plug it will take longer to empty than if you swirl the water so it creates a vortex around the plughole, particularly if there is not water (just air) in the centre of the vortex.
 Mar 2nd 2018, 10:25 AM #9 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 OK so here are my thoughts. I did ask about the connection between the tank and the bag and here's why. Toricelli's theorem. Referring to my attachment, the picture shows the outflow from the bottom of a tank of water and Toricelli's theorem shows that the exit velocity of that water is independent of the size of the hole. Now the volumetric flow rate = Q = velocity times area of hole = $\displaystyle \sqrt {2gh} A$ or the flow rate is proportional to the square root of the head of water above the outlet. Hence my comment in post#5 since that make the flow rate zero at zero head. This is made worse if there is a pipe connection since a further pressure head must be added to h to compensate for the pressure drop in the pipe. Obviously this is all theory and if you make the hole large enough (ultimately removing the tank bottom) the water will just drop straight through into the bag. So you are on the right lines by making the oulet diameter larger than the inlet, but the water enters the tank under pressure from the pump so whether a 20mm hole will be large enough is really a matter of experiment. Attached Thumbnails
 Mar 3rd 2018, 03:13 AM #10 Junior Member   Join Date: Feb 2018 Posts: 4 [QUOTE=studiot;39447]Thanks, it's much clearer now. Does the tank discharge straight into the bag through a hole or is there a short pipe? Yes, there is PVC pipe of 6cm lenght. Attached Thumbnails

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