Question: Draining Tank problem

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Discussion Overview

The discussion revolves around a problem involving a cylindrical tank filled with liquid, which includes the dynamics of draining the tank through an exit hole while considering the effects of pressurized gas on top. Participants explore various factors that could influence the height of the liquid over time, including friction, swirl, and non-adiabatic conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes the basic setup of the problem, emphasizing a 1D analysis with constant gas pressure and no swirl.
  • Another participant suggests enhancing the problem's realism by incorporating friction at the fluid exit, potential swirl, and non-adiabatic conditions.
  • A third participant relates the problem to a calculus scenario, discussing the volume of a cylinder and the implications of the exit hole's radius on the flow rate, while expressing uncertainty about integrating the gas factor into the equations.
  • A later reply reiterates that the radius of the tank remains constant, affirming a key aspect of the problem's geometry.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple competing views regarding the complexity of the problem and the factors to consider in the analysis.

Contextual Notes

There are limitations in the assumptions made, particularly regarding the effects of gas pressure, friction, and the potential for swirl, which remain unresolved. The mathematical steps for integrating these factors into a cohesive solution are also not fully explored.

Who May Find This Useful

This discussion may be of interest to those studying fluid dynamics, engineering applications involving fluid flow, or anyone looking to understand the complexities of draining systems in cylindrical geometries.

matthewslaby
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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
 
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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.
 
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.
 
well radius is constant in the cylindrical tank.
 

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