Fluid Science For School Project

[Student2001]

Hello,

 

I've been struggling with a school project for some time now.

I need to find out the speed at wich a tank is draining to make a model out of it (in simulink). The model will show a x-t graph, x being the height of the water in the tank.

The flow is laminar, but the lenght of the exittube is significant enough to enduce friciton.

A basic model that i made can already account for the diameter of the exittube, but not yet for it's lenght (and thus friction).

When i tried implementing formulas for head loss the model didn't work as i had hoped. I think i might be using the wrong (combinations) of formulas.

I hope someone can help me with finding out the problem i'm facing here. In calculating the speed of the waterlevel i used the following formulas:

 

-   Bernoulli's equation (with head loss added on the right side of the equation)

-   v2=sqrt(2gh)

-   P2=density*g*h

-   Head loss = f*L/D*(v_average/2g)

-   Friction factor = 64/Re

-   Re = (density*v_average*diameter)/viscosity

-   v_average = (dP*D^2)/(32*viscosity*L)

 

Thank you kindly for your response.

 

Greetings,

Teun

Edited February 16, 2020 by Student2001

[GAHD]

Rather than do it for you, I'll give you some tools to help you grasp

First off: lazy housekeeping in variables makes dimensional analysis difficult. Properly define all short-hand variables with their long form in a table. It's really easy to do something silly like combine different volumes instead of divide or multiply them, or to use the wrong base units, without that housekeeping.
Second off; when manipulating equations, you've really got to pay attention to exponents...You're using what looks like a broken and non-exponential version of Darcy's in there? attention to detail. Brush up on log and exp algebra, it'll do you good.

[isaac]

And "no way" for anyone to answer your question? Oh, do not be mad at the guys on the forum because they do not know the answer to your question. "Modern science" doesn't know the answer to your question either! Therefore, "modern science" suggests to you that you first build your tank, then fill it with liquid as you wish, and then drill a hole in the tank (also as you wish), and then observe (measure) what is happening. You can then map this "your model" using "similarity theory" to any "real problem". The guys at CERN do the same. They have built themselves a huge energy reservoir, so when they fill that reservoir with energy, they drain that huge energy through a small hole and watch what's going on! Well, of course, no one benefits from such "science" except for the "little ones" playing with these expensive "toys", but don't despair, as soon as they solve the "big bang" and "God's particle" problems, your problem is first on the line!

 

Since you can't rely on "modern science" right now, you have to rely on your own mind!

(temporarily forget "laminar", "turbulent", "viscosity", "reynolds" and similar "scientific" nonsense!).

So you can first create a balance of materials and energy:

E_P = E_K + E_lost, E_lost = kE_K, so E_P = (1 + k)E_K, E_P = hg, E_K = v²/2 and the energy balance per unit mass will be:

hg = (1 + k)v²/2, v = (2hg/(1 + k))^0.5 if Q=flow kg/s, D=density kg/m³, A=area of liquid in tank m², it will be:

v = f = Q/DA = (dh/dt)/(DA) = (2hg/(1 + k))^0.5 so you get the differential equation:

dh/(DAh) = ((2g/(1 + k))^0.5)dt, which you have to solve by simple integration with known initial conditions h₀, t₀, while you have to look for the constant k in the "empirical tables" for run out of the tank through a "small opening". Finding the value and name of that "variable" is a true "rashomon" because every "Mr. Professor" differently calls, labels and calculates it. So you "fire" k = 0.5, and count! Cheers!

 

(p.s. Nothing this is "true" to you, it's just a blabber of my mind, you have to use yours!)