Timeline for Flow equation for system of coupled tanks
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2019 at 2:33 | comment | added | Gert | Yes, I've seen it, thank you. | |
| Apr 26, 2019 at 0:30 | comment | added | Pantelis Sopasakis | Thanks again. I posted a separate question about the derivation of Equation (*) at physics.stackexchange.com/questions/476061/… in case you would like to have a look. | |
| Apr 26, 2019 at 0:28 | vote | accept | Pantelis Sopasakis | ||
| Apr 25, 2019 at 22:19 | comment | added | Gert | The motion doesn't have to be 'linear'. The EoM is basically Newton's Second Law:$\Sigma F=ma$, here $-\rho g(2h_1A_1-2h_0A_1)=M\ddot{h_1}$. $M$ is the total mass of the system, in both tanks. Thanks for the upvote! | |
| Apr 25, 2019 at 21:33 | comment | added | Pantelis Sopasakis | Apart from negligible viscosity they also assume that the length of the pipe is negligible, otherwise the length of the pipe affects the system dynamics (see this article). Could you just elaborate on the application of Newton's law? The motion of the liquid overall is not linear. What are the underlying assumptions? | |
| Apr 25, 2019 at 20:44 | comment | added | Gert | That's a great reference and confirms some of my derivation (although mine is simpler). They too find a SHO where $a$ doesn't feature. It doesn't feature because we assume a perfectly inviscid liquid ('ideal liquid'). Such a liquid experiences no resistance to flow at all: pipe diameter or length have no handle on it whatsoever. This is of course unrealistic. A real system would be damped due to viscous friction. If you're interested in 'real world' system of communicating vessels (the reference doesn't cover it either) then I suggest you pose another question, with specifics re. the pipe. | |
| Apr 25, 2019 at 20:04 | comment | added | Pantelis Sopasakis | I'm not able to derive (*) using Bernoulli's principle (unless I am justified to assume that $P_{y'}\approx \rho g h_2 + P_{atm}$). By the way, I found this article scielo.br/… - the authors propose the use of Euler's equation and the mass balance equation for each tank. I feel however that they don't justify their assumptions much. | |
| Apr 25, 2019 at 20:01 | history | edited | Gert | CC BY-SA 4.0 |
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| Apr 25, 2019 at 19:56 | comment | added | Gert | $F_1 = \rho a \sqrt{2g(h_1-h_2)}.\tag{*}$ is only true if $h_1-h_2=\text{Constant}$ OR if $h_2=0$. But it must be possible to develop a 'dynamic' version of it. In dynamic conditions, you need to apply Euler's version of Bernoulli. It also bothers me that in my derivation $a$ (the hole or pipe diameter) doesn't feature, I'm looking into that now. I will also clarify the EoM a little. | |
| Apr 25, 2019 at 17:44 | comment | added | Pantelis Sopasakis | Let me rephrase my questions: (i) Under what assumptions can we derive Equation (*) (if it's at all correct), (ii) Can we use Bernoulli's equations? (iii) Should we resort to Euler's equation for non-steady flows? | |
| Apr 25, 2019 at 17:29 | comment | added | Pantelis Sopasakis | Thank you for the answer. I wonder why the cross-section area of the hole does not appear in your solution? For example, if the second vessel were empty, we would have $F = \rho A_{\mathrm{hole}} \sqrt{2gh}$. It's also not clear to me how you used Newton's second law of motion. We have a system of changing mass, so there should be a term of the form $\dot{m}$. | |
| Apr 25, 2019 at 15:48 | history | edited | Gert | CC BY-SA 4.0 |
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| Apr 25, 2019 at 15:17 | history | edited | Gert | CC BY-SA 4.0 |
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| Apr 25, 2019 at 15:04 | history | answered | Gert | CC BY-SA 4.0 |