Cylindrical tank vs conical tank

Click For Summary

Discussion Overview

The discussion revolves around the comparison of drainage times between cylindrical and conical tanks, both having the same height, volume, and outlet dimensions. Participants explore the implications of tank shape on drainage rates, referencing Torricelli's law.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the cylindrical tank drains faster than the conical tank, as determined through calculations using Torricelli's law.
  • Another participant suggests that the difference in drainage rates may be due to the radius at the base of the conical tank being larger than that of the cylindrical tank, specifically sqrt(3) times larger.
  • A further contribution indicates that the increased radius of the conical tank leads to a larger surface area, which may affect the rate of drainage as evidenced by the graph's slope.
  • Participants question the relationship between the height loss of the tanks and the impact on drainage rates, prompting further exploration of this aspect.

Areas of Agreement / Disagreement

Participants express differing hypotheses regarding the reasons for the differences in drainage rates, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

The discussion does not resolve the underlying assumptions about the relationship between surface area, height loss, and drainage rates, leaving these aspects open for further exploration.

Fat Dapper Cat
Messages
4
Reaction score
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?
 
Physics news on Phys.org
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?
 

Similar threads

Undergrad Maintaining a constant volume of water in a tank
  • · Replies 7 ·
Replies
7
Views
3K
Measuring the water volume in a small tank with a manometer
  • · Replies 26 ·
Replies
26
Views
2K
Undergrad Hydostatic pressure at bottom of a cylindrical and conical tanks
  • · Replies 9 ·
Replies
9
Views
22K
Undergrad Solving the Mystery: Which Tank Fills First?
  • · Replies 139 ·
5
Replies
139
Views
53K
Undergrad Creating a High-Pressure Fire Hose: Conical vs. Cylindrical Tank Design
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Pressure drop across a valve in tank
  • · Replies 4 ·
Replies
4
Views
3K
How Much Work to Fill a Cylindrical Tank with Water?
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Mass conservation in a conical tank
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Density Siphoning? Solve Problem Now
  • · Replies 6 ·
Replies
6
Views
2K
Fluid dynamics problem: Equalize the volume of water in tanks at differing heights
  • · Replies 50 ·
2
Replies
50
Views
8K