- #1
Alexander350
- 36
- 1
I tried using the Bernoulli equation to solve this. I took two points at the surface of the water in both the containers and formed this equation:
[tex]gh_{b}=\frac{1}{2}v^2+gh[/tex]
This is assuming that the velocity of the water in the large tank is approximately zero and using the fact that both the surfaces are at atmospheric pressure. Then, I solved for the velocity and said that this is equal to the rate of change of the height of the water in the narrow cylinder.
[tex]\frac{dh}{dt}=\sqrt{2g(h_{b}-h)}[/tex]
Finally, solving this with the assumption that h starts at 0, I got:
[tex]h=\sqrt{2gh_{b}}t-\frac{1}{2}gt^2[/tex]
But looking at this function, it increases to the height [itex]h_{b}[/itex] and then decreases again. This obviously does not happen; it would just stay at that height forever. So what have I done wrong?