Cylindrical tank vs conical tank

AI Thread Summary
The discussion centers on the drainage rates of cylindrical and conical tanks of equal height and volume, both draining through the same-sized hole. It was observed that the cylindrical tank drains faster, which is attributed to the geometry of the tanks. The conical tank has a larger base radius, increasing its surface area and affecting the water height during drainage. As the tanks empty, the cylindrical tank loses height more rapidly, contributing to its faster drainage rate. The conversation highlights the importance of tank shape in fluid dynamics, particularly in relation to Torricelli's law.
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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