Calculating Pressure on Tank Walls

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Discussion Overview

The discussion revolves around calculating the pressure exerted on the walls of an aquarium tank, particularly focusing on how the dimensions of the tank influence the required thickness of the glass used to construct it. Participants explore various formulas related to pressure in liquids and their applications in different contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant introduces the formula p = d*h for calculating pressure at a point in a liquid, noting that it does not account for the tank's width and length.
  • Another participant clarifies that pressure in a static fluid is determined solely by fluid density and depth, and that total force on a surface requires knowledge of the area.
  • A participant shares a personal observation about their aquarium tank's glass curving under pressure, raising concerns about the structural integrity of the tank.
  • Several participants present different formulas related to pressure in liquids, such as p = dh and p = hpg, and seek clarification on their differences and applications.
  • One participant explains the distinction between gravitational and coherent systems of units in the context of pressure calculations, emphasizing the importance of integrating pressure over the area of interest.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of tank dimensions in pressure calculations. While some emphasize that pressure is independent of surface area, others raise concerns about how this impacts structural requirements, indicating that multiple competing views remain unresolved.

Contextual Notes

Participants reference various formulas and systems of units, but there are limitations in understanding how these apply across different contexts and configurations of tanks. The discussion does not resolve the implications of these formulas on practical applications.

Who May Find This Useful

This discussion may be useful for individuals interested in fluid mechanics, aquarium design, or those studying the principles of pressure in static fluids.

banhbo_tt
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Hi all,

A problem pops up while I was trying to calculate the pressure impacts on my aquarium tank walls.

The first formula comes up to my mind was: p = d*h

where d is pressure at one point inside the liquid
d is density of the liquid (assume it's pure water)
h is the height or distance from that point to liquid's surface.

However, the formula DOES NOT take into account the WIDTH and LENGTH of the tank. To illustrate my problem, i make a comparison between my tank and a test tube.

Assume I want to build a aquarium tank (10 x 10 x 10 meters ) and a test tube with the same height 10 meters but with normal radius (about 1 cm) just like normal test tubes. Measurement system does not matter here, the importance is that they have the same height. So if I want to build a tank that's (10x10x10) I probably need to use 3-centimeter-thick-toughened glass in order to withstand the pressure created by that amount of water. However, with the 10 meters high test tube, I just could use a normal glass with much less thin (let's say 1-centimeter-thick is enough right?).

So my point is eventhough both have the same height but the aquarium tank requires much stronger glass, compared to the test tube does,to withstand the maximum capacity of water contained. Therefore, I believe the Width and Length ( or simply surface's area) should come in somewhere in the calculation.

Can anyone help me point out where i went wrong or what i have missed out?

Many thanks in advance!
 
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The pressure at any point in a static fluid depends only on the density of the fluid and the depth of the fluid above the point of interest. Remember, pressure has units of force / area.

However, if you want to calculate the total force acting on one end of the aquarium, then you must know something about the area of the end of the aquarium, or the side, or whatever. The force can be determined by integrating the pressure gradient over the area of interest of the aquarium.

In other words, the pressure at a depth of 10 meters does not differ whether the water is in a long thin tube or acting on a broad rectangular surface.
 
In fact, my house has a aquarium tank about (3 x 3 x 1 meters) = (H x L x W) made of 3 cm thick toughened glass. When water is pump in at 75% capacity, the side glass is clearly curved. I just could not believe.
 
Last edited by a moderator:
banhbo_tt said:
so far I have found 3 formulas related to pressure in liquids:

p = dh

This is a formula for pressure as a function of depth when using a "gravitational" system of units such as the U.S. traditional system. In such a system the distinction between force and mass is blurred.

For instance, pressure (p) in pounds per square foot is the product of density (d) in pounds per cubic foot and height (h) in feet.

p = hpg

This is a formula for pressure as a function of depth using a "coherent" system of units such as SI where a distinction is made between your mass and the force required to support your weight.

For instance, pressure (p) in Pascals is the product of height (h) in meters, density (rho) in kilograms per cubic meter and gravity (g) in meters per second squared.http://00.edu-cdn.com/files/static/mcgrawhill-images/9780071393089/e0248-02.jpg

This is not a formula for "pressure". It is a formula for total force on the side of an aquarium in a gravitational system of units (note how the acceleration of gravity is not used).

The force F on the [vertical] side of an aquarium is given by the integral of the force on each horizontal strip from top (a) to bottom (b).

The force on each horizontal strip is given by the fluid pressure at the depth of that strip multiplied by the area of the strip.

The pressure at the depth of the strip is computed by the first formula above [pressure = height (h) times density (rho)].

The area of each strip is given by its width (w(h)) multiplied by its incremental height (dh).

The article in which this appeared was using height and width in feet, density in pounds per cubic foot and was computing total force in pounds.
 
Last edited by a moderator:
It's clear now. Thanks you a a lot !
 

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