- #31
Cyrus
- 3,237
- 17
Dear god yes! upload it to some webhosting site.
Need desperate help on fluid dynamics
- Thread starter gtabmx
- Start date
Click For Summary
The discussion revolves around a fluid dynamics experiment involving a 2L bottle with a slot, where data shows an inverse relationship between the time for water to reach the slot and the slot area, represented by T=0.0169/A. The experiment aims to derive a formula for the time to empty the bottle based on initial volume, bottle radius, and slot area, but the participant struggles with understanding the underlying principles, including Bernoulli's law and fluid dynamics equations. Suggestions include using differential equations to model the flow rate and incorporating pressure gradients, but confusion persists regarding how to account for changing water height over time. The participant has gathered data that fits a parabolic function for water height versus time but is unsure how to manipulate this into a usable flow rate equation. Overall, the conversation highlights the complexities of fluid dynamics and the challenges of applying theoretical principles to practical experiments.
- #32
gtabmx
- 56
- 0
http://www.yousendit.com/transfer.php?action=download&ufid=37914B012881DD86
may not be the neatest thing
may not be the neatest thing
- #33
gtabmx
- 56
- 0
Alright, I ahve a differential equation set up that my linear algebra professor at school had set up and i have finished solving it from what I know and it gives a quadratic equation, which is not pretty and gives more info but still lacks some stuff as there are still two unknown constants and I have yet to verify if it corresponds to the data, I wil post it as soon as I fugure out how to tyoe it properly as it is not pretty.
- #34
Cyrus
- 3,237
- 17
Well, for one thing, your graph is volume vs time that equation is NOT volume vs time.
- #35
gtabmx
- 56
- 0
h(t) = -((Surf Area of Bottle)(accel due to gravity)(t^2))/((2)(Surf Area of Slot)) - (accel dur to gravity)(konstant)(t) - ((Surf Area of Bottle)(accel due to gravity)(konstant^2))/((2)(Surf Area of Slot)) + (Constant)/(accel due to gravity)
where Konstant is a constant produced by general integration
and
where Constant is the C in Bernoulli's equation found on http://plus.maths.org/issue2/bottle/index.html
and my linear algebra proffessor set the intial differential equation using that Bernoulli's equation and some crazy stuff...
thing is I do not know if it fits the data, which i wil try soon, and I do not knwo how to find Constant or Konstant; however, it is easy to see that the last two terms have no time variable so they make up initial height h(o) so Constant is no longer a problem, however, Komstant is as it appears in the second term
where Konstant is a constant produced by general integration
and
where Constant is the C in Bernoulli's equation found on http://plus.maths.org/issue2/bottle/index.html
and my linear algebra proffessor set the intial differential equation using that Bernoulli's equation and some crazy stuff...
thing is I do not know if it fits the data, which i wil try soon, and I do not knwo how to find Constant or Konstant; however, it is easy to see that the last two terms have no time variable so they make up initial height h(o) so Constant is no longer a problem, however, Komstant is as it appears in the second term
Last edited:
- #36
Cyrus
- 3,237
- 17
Looking at your data, your equation matches very well to what vanesche gave.
Look over your work with more care.
Look over your work with more care.
- #37
gtabmx
- 56
- 0
Wait, which equation, the one provided on the site or the one i have just posted?
- #38
Cyrus
- 3,237
- 17
The one on the site. I don't know what that mess you posted is, sorry.
- #39
gtabmx
- 56
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So you manipulated the equation ont he site into something useful where velocity is not included or did you use the equation as is?
- #40
gtabmx
- 56
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How can that be, I plug 25seconds into that equationa nd get -2.3meters?
- #41
Cyrus
- 3,237
- 17
what do you mean velocity, where do you see velocity anywhere?
- #42
gtabmx
- 56
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"The symbol u stands for the fluid velocity"
on site
on site
- #43
Cyrus
- 3,237
- 17
Yes, and where do you see it in the final equation?
Think about conservation of energy.
Think about conservation of energy.
- #44
gtabmx
- 56
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Nowhere, ok so your are using the last equation, I thought you rederived another equation from Bernouilli's equation. Yes, I am using that last equation and it does not fit, perhaps my values for lambda are worng. I solved for them and got around 4.0E-3. Correct?
- #45
Cyrus
- 3,237
- 17
I got your graph to match, you better redo those calculations boy, or I am going to smack you!
- #46
gtabmx
- 56
- 0
OKOKOK i will gimme a sec
- #47
gtabmx
- 56
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OK, i get lambda is either equal to 9.251E-3 or 3.526E-3 with inconsistent units, correct?
- #48
Cyrus
- 3,237
- 17
Nope. Check your work some more. You are close though.
- #49
gtabmx
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Oh god, look I know you are trying to do this for my own good but I looked over it and found nothing wrong and I have fired up maple to triple check and here.
{x = 0.003525914211}, {x = 0.009251617087}
{x = 0.003525914211}, {x = 0.009251617087}
- #50
Cyrus
- 3,237
- 17
Can you write me your equation your using to solve for lambda?
It might be that its rounding off, but I want to be sure its not what I think it might be.
It might be that its rounding off, but I want to be sure its not what I think it might be.
- #51
gtabmx
- 56
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0.0251 = 3062.500000 x - 39.13118960 x + 0.125
0.0251 = 3062.500000 x - 39.13118960 x + 0.125
"->"
{x = 0.003525914211}, {x = 0.009251617087}
0.0251 = 3062.500000 x - 39.13118960 x + 0.125
"->"
{x = 0.003525914211}, {x = 0.009251617087}
- #52
Cyrus
- 3,237
- 17
No, this is not correct.
Where did you get these numbers?
Intercept is ok, but the rest are wrong.
Where did this come from?
0.0251?
3062.500000 ??
39.13118960 ??
Where did you get these numbers?
Intercept is ok, but the rest are wrong.
Where did this come from?
0.0251?
3062.500000 ??
39.13118960 ??
- #53
gtabmx
- 56
- 0
I used the equation and i plugged 25s into time and the corresponding height 0.0251m from my results and i simplified.
- #54
Cyrus
- 3,237
- 17
Ah, this is fine.
BUTTT, you should use data points as far as possible, i.e. use 35.
You will find that you get:
0.0035822
0.00551068
BUTTT, you should use data points as far as possible, i.e. use 35.
You will find that you get:
0.0035822
0.00551068
- #55
gtabmx
- 56
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ok, so wat a couple of decmals 
so, wat are the units of lumbda?
and now wat? there must be a way to find the values before even doing the experiment?
so, wat are the units of lumbda?and now wat? there must be a way to find the values before even doing the experiment?
- #56
Cyrus
- 3,237
- 17
You tell me.
Not a couple of decimals, a factor of 2.
Not a couple of decimals, a factor of 2.
- #57
gtabmx
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It was a joke, i understand.
- #58
gtabmx
- 56
- 0
No units, makes me feel better i think
- #59
gtabmx
- 56
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So now i know lambda has no units and u must do the experient to find it, that's not taht good since its not a general formula yet
- #60
gtabmx
- 56
- 0
Wait, lambda is not consistent, it has not units is in first term and units in second
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