# Trouble with fluid dynamics

1. Mar 18, 2013

### juanitotruan77

1. The problem statement, all variables and given/known data

5. A rectangular opening on the side of a water tanks has a width of L. The upper part of the opening it's in a height of h1 underneath the water y and the bottom part it's in h2 . prove that the volume of water that leaves the tank is given by :
2/3(L)√(2g(h1³-h2³))
2. Relevant equations
Bernoulli's law

Continuity equation

Volumetric flux

both V and v are Speed.

3. The attempt at a solution
No idea so far.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 18, 2013

### tiny-tim

hi juanitotruan77! welcome to pf!

imagine the opening is divided into tiny horizontal openings of height dh, and integrate from h1 to h2

what do you get?

3. Mar 18, 2013

### juanitotruan77

I think i get it, i'll try it. But i'm not very familiar with using integrals. Can you explain me how?

thanks, btw.

4. Mar 18, 2013

### tiny-tim

try first

see how far you get

5. Mar 18, 2013

### juanitotruan77

i'm trying, but i don't know how to get to torricelli's law from bernoulli's in a rectangular area.

6. Mar 18, 2013

### tiny-tim

if dh is small enough, you can regard the pressure as constant

so find the speed v from Bernoulli's equation

7. Mar 18, 2013

### juanitotruan77

i can't, i don't understand where i have to put the differential of h. I think i should ask a teacher tomorrow.

8. Mar 18, 2013

### tiny-tim

the rectangle is length L, and starts at height h, and finishes at height h + dh

you can regard the pressure as being constant, = ρgh

find v, then multiply by the area (L*dh) to get the flow

9. Mar 18, 2013

### juanitotruan77

oh, that sounds reasonable, thanks :D

10. Mar 18, 2013

### juanitotruan77

well, i tried, but i couldn't make it work.

11. Mar 19, 2013

### tiny-tim

(just got up :zzz:)

show us what you did

hint: 2/3(L)√(2g(h1³-h2³)) = (L)√(2g) times [(2/3)h13/2 - (2/3)h23/2]

12. Mar 19, 2013

### juanitotruan77

Got it, bro, i already finished, i think i was cofused with the h terms. I used y terms instead. it's quite easy now that i did it. lol. Thanks.