Question: Draining Tank problem

[matthewslaby]

A cylidrical tank (R= tank radius) filled with a liquid with an opening for the insertion of pressurized gas on top and an exit hole on bottom (r=exit hole radius).

Plot the Height of the liquid as a function of time and exit radius.

Gas pressure=const.
No swirl (1D analysis)

Any advice is welcome: matthewslaby1645@comcast.net

 

[matthewslaby]

I want to make this problem more realistic by adding friction at the fluid exit plan and possibly swirl of the fluid (3D flow), and maybe even non-adiabatic conditions.

Please let me know if you could guide me on this. At least the solution for the simple form of this problem should be known and documented.

 

[Rayquesto]

sounds like a calculus problem I had. Except, I'm clueless in terms of adding that gas factor into the equation.

so, volume of a cylinder is pie r^2 h and deriving that you get

the change in volume over the change in time=2 pie r dr/dt + pie r^2 dh/dt but dr/dt=0 since the radius is constant in a cylinder.

I mean to me, the only way that I can picture an exit hole is by adding a cone into the equation, or something cut out, but if it were cut out, then the rate going through that small opening will depend on that small opening's radius squared times the change in height referring to the speed of the volume of the liquid.

 

[Rayquesto]

well radius is constant in the cylindrical tank.