# Flow from the bottle

I made some calculations about flow from the bottle, but problems occured when the experimental data came back. Need to refine calculations, but problems occur when trying to link the angle to the flow, because volume changes constantly, and volume that has left in the bottle is governed by the force sensor. And the force sensor is governed by the algorithm that links volume with weight, and weight and volume change with the change of the flow, which again is a function of the change of the angle.

As the bottle is oppened, angle of the fluid will always be parallel to the ground, because of the free surface and $p_{a}$. But problem here is that not every bottle is the same shape, so the height and the angle will not be the same for every bottle, and pouring process will not start for at the same angle for different bottles. With some bottle necks being convex effects of the surface tension will be much grater, and the poured amount of the liquid will be different than the deisred one. Then also, expansion waves will cause turbulance within the flow, and the flow should at least remain laminar, for easier pouring and calculations, but in real time pouring this is not that easy to get, well offcourse on higher pouring speed, with lower pouring speed this is not that big of a problem, but surface tensions tends to splurge liquid under the bottle.

So for the diagram, I can put this picture, it's selfexplanatory. As I stated angle should correlate with the flow, and weight should be governed by force sensor, with this the force sensors senses the change of the weight (or volume) in the bottle, and this tells the framework on how much fluid has been poured and how much is remaining. Angles that I got from calculations and experiments differ, some of this I can contribute to surface tension. But the flow and the angle of the bottle to correlate to the change of the weight has proved different in a bigger manner.

For the geometry, different bottle types were used, so there is no specific geometry, but formulations were made for a generic bottle, so there could be some referencing points to the problem at hand.

Any suggestions on how to model this mathematically and to do it correctly.

• Please include a diagram - it is not clear what the geometry is you are trying to model, and what effects you want to include (what is the purpose of creating the model, how accurate do you expect it to be...). Without more information this question will be closed as "unclear what you are asking". So - please do yourself a favor and clarify... the "full" solution is probably chaotic and not amenable to "correct" (closed form) mathematical treatment, so you may have to be content with an approximation. – Floris Sep 12 '14 at 22:09
• Mathematical (read: analytic) models of fluid dynamics is only possible in a few cases. For you to do this, you might want to take a look at something like Comsol multiphysics (there are other similar products out there). – Kyle Kanos Sep 13 '14 at 18:32
• @KyleKanos thanks for the reply, problem is that I need to make correct mathematical formulations, but what I made is basic fluids, as a mechanical engineer I have only limited understanding of it. Been messing with this a lot, started learning higher stuff, but the problem is even when I try to put everything in the model still comes fuzzy. Experimental data is not correlating with the formulation. Don't have enough experience with CFD, did try this, but as I stated, not enough experience with it. Already my thesis is finished, but wanted to try to correct these problems. – Slavisa Galamic Sep 13 '14 at 21:45
• The "mathematical model" is the Navier-Stokes equations (plus continuity equation). There is not going to be a "simple" mathematical model you can do for this, you have to do CFD to model it in any sense. – Kyle Kanos Sep 13 '14 at 23:40
• This is a cool problem! I'm not so convinced that you will need to use CFD to get something reasonable on this. Civil engineers done a lot with open channel flow over the years. This would be similar but with higher viscosity. I'd bet that you'll mostly get a flow rate depending on: angle of the opening, diameter of the opening, height of the free surface above the bottom of the opening, fluid properties (viscosity, density). I'd be interested if you can share data on weight loss, angle and rate turning. We might be able to tease something useful out of that. – user3823992 Sep 15 '14 at 6:44