Cylindrical tank vs conical tank

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SUMMARY

The discussion centers on the drainage rates of cylindrical and conical tanks of equal height and volume, utilizing Torricelli's law for analysis. It concludes that the cylindrical tank drains faster than the conical tank due to the geometric differences in their shapes. Specifically, the conical tank has a base radius that is sqrt(3) times larger than that of the cylindrical tank, which increases its surface area and affects the rate of height loss during drainage. This results in a steeper slope in the drainage graph for the conical tank compared to the cylindrical tank.

PREREQUISITES
  • Understanding of Torricelli's law
  • Basic knowledge of fluid dynamics
  • Familiarity with geometric properties of cylinders and cones
  • Ability to analyze graphical data
NEXT STEPS
  • Study the applications of Torricelli's law in different tank shapes
  • Explore fluid dynamics principles related to surface area and drainage rates
  • Investigate the mathematical modeling of fluid flow in conical and cylindrical tanks
  • Learn about the impact of tank geometry on fluid dynamics in engineering contexts
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Engineers, physicists, and students studying fluid dynamics, particularly those interested in the practical applications of drainage systems and tank design.

Fat Dapper Cat
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Hey everyone, I'm new to this site and I figured this would be the best place to ask this question.

We've been using maple to solve two specific problems on the time it would take two tanks to drain. One being cylindrical, and the other conical. They have the same height, the same volume, and the same circular hole at the bottom at the bottom for water to drain out of tank. We found the cylindrical tank drained faster than the conical tank by using Torricelli's law.

So my question is this, based on the shape of these two tanks, why is it that cylindrical tank drains faster?
 
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russ_watters said:
Welcome to PF!

Do you have an hypothesis?

Yes, I'm assuming this is because the radius at the base of the conical tank is larger than the that of the cylindrical tank. For ours specifically it was sqrt(3) times larger.
 
Fat Dapper Cat said:
Yes, I'm assuming this is because the radius at the base of the conical tank is larger than the that of the cylindrical tank. For ours specifically it was sqrt(3) times larger.
You are on the right track, but why does that matter?
 
russ_watters said:
You are on the right track, but why does that matter?

This would increase the surface area for the conical tank. This must be why our graph's slope decreases at a far faster rate than that of the cylindrical tank.
 
Fat Dapper Cat said:
This would increase the surface area for the conical tank. This must be why our graph's slope decreases at a far faster rate than that of the cylindrical tank.
Look at it from the other direction: As the tanks empty, which one loses height faster? What impact does that have?
 

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