Cylindrical tank vs conical tank

In summary, the conversation discusses using maple to solve problems involving the time it takes for two tanks to drain. One tank is cylindrical and the other is conical, but they have the same height, volume, and circular hole for drainage. Through the use of Torricelli's law, it is discovered that the cylindrical tank drains faster than the conical tank. The question is then posed as to why this is the case, to which the hypothesis is that the larger base radius of the conical tank results in a larger surface area and a faster decrease in height.
  • #1
Fat Dapper Cat
4
0
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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  • #2
Welcome to PF!

Do you have an hypothesis?
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
  • #6
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?
 

What is a cylindrical tank?

A cylindrical tank is a type of storage container that has a circular cross-section and a flat or curved bottom. It is often used to store liquids or gases.

What is a conical tank?

A conical tank is a type of storage container that has a circular cross-section and a cone-shaped bottom. It is also commonly used to store liquids or gases.

What are the differences between a cylindrical tank and a conical tank?

The main difference between these two types of tanks is their shape. A cylindrical tank has a flat or curved bottom, while a conical tank has a cone-shaped bottom. This affects the way the tanks are filled, emptied, and cleaned, as well as their overall volume and stability.

Which type of tank is better for storing liquids?

It depends on the specific needs and application. Cylindrical tanks are better for storing large volumes of liquid, while conical tanks are better suited for applications where complete drainage is necessary, such as in the food or pharmaceutical industry.

Are there any other factors to consider when choosing between a cylindrical tank and a conical tank?

Yes, there are other factors to consider, such as cost, space availability, and the type of material being stored. Cylindrical tanks are generally more cost-effective and take up less space, while conical tanks may be more expensive but offer more efficient use of space and better drainage capabilities.

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