- #1
Pepealej
- 20
- 0
I've rencently been thinking about several systems related to fluid mechanics, and I've asked myself the following question:
If I have a cylidrical tank with a small hole in the bottom (the surface area of the hole is small in comparison with that from the tank) and I'm filling the tank with water at a constant flow, how can I determine the speed of the water both coming from the whole and rising up the tank: (A) with respect to the height of the water in the tank, (B) with respect to time.
(This is not homework, although it sounds like so)
I know how to determine the maximum height of a system like this one with a specific flow Q. If the surface area of the cylinder is A and that from the hole is S, we have:
[tex]Av_A=Q=Sv_S[/tex] thus [tex]v_S=\frac{Q}{S}[/tex]
And, using Bernouilli's equation:
[tex]P_{at}+\rho g h=p_{at}+ \frac{1}{2}\rho v_S^2[/tex]
[tex]h=\frac{v_S^2}{2g}[/tex]
But that is considering the end point. Where the system is 'at rest' (there's the same amount of fluid in the tank and we can treat it like a pipe), but I don't know how to study the intermediate steps.
Thanks for your help :)
If I have a cylidrical tank with a small hole in the bottom (the surface area of the hole is small in comparison with that from the tank) and I'm filling the tank with water at a constant flow, how can I determine the speed of the water both coming from the whole and rising up the tank: (A) with respect to the height of the water in the tank, (B) with respect to time.
(This is not homework, although it sounds like so)
I know how to determine the maximum height of a system like this one with a specific flow Q. If the surface area of the cylinder is A and that from the hole is S, we have:
[tex]Av_A=Q=Sv_S[/tex] thus [tex]v_S=\frac{Q}{S}[/tex]
And, using Bernouilli's equation:
[tex]P_{at}+\rho g h=p_{at}+ \frac{1}{2}\rho v_S^2[/tex]
[tex]h=\frac{v_S^2}{2g}[/tex]
But that is considering the end point. Where the system is 'at rest' (there's the same amount of fluid in the tank and we can treat it like a pipe), but I don't know how to study the intermediate steps.
Thanks for your help :)