Water Pressure in Box: Calculating Perspex Thickness

[Crazy Person]

Dear All

I have approximately 300liters of water that I would like to house in a box. However I would like to check up on my water every now and again so I would like to make it out of clear perspex/acrylic. I could make it out of glass, but perspex is cheaper and easier for me to handle.

What would be the perspex thickness versus height of the water in equation form, given a maximum deviation of 1mm; P=[itex]\textit{ρ}[/itex]*g*h

I have found that for approx 600mm height that a perspex thickness of 13mm is recommended, though perspex is very strong. Most of the problem appears to come from the bending of the perspex under pressure, causing the joints to experiencing not only sheer by rotational stress (Im an Elec Eng, so forgive my miss use of basic Mech Eng principles). Is there no cool engineering design that could accommodate this as part of the normal design (Design for bending?) by, for example, extending the back and front faces and using square vertical perspex rods to hold the front and side faces together? This could place the 'bending' stress on the shorter side face, which could be thicker. This scheme does neglect the bottom and, potentially top face effects.

Am I asking the wrong question and would the right question be "Where can I find cheap FDTD software"?

Thanks
CP

 

[edgepflow]

If you can find a copy of "Design of Welded Structures" by Blodgett, there is an outstanding treatment of tank design (steel tanks but same ideas). I have a copy at work.

It shows you how to analyze stress and deflection is the square tanks and add stiffiners as needed. It turns out that a horizontal stiffiner all around the top cuts most stress and deflection problems. If more is needed an additional horizontal stiffiner all around about 40% from the bottom may be used. A simple angle ('L') shaped stiffiner is acceptable.

 

[AlephZero]

Is there no cool engineering design that could accommodate this as part of the normal design (Design for bending?)

This is why most real-life large tanks are cylindrical not rectangular. This fixes the problem by getting rid of the flat panels and "corners" completely. Spherical tanks are even better, for high pressures.

A good principle for designing any mechanical structure is to use material in tension or compression, not bending. Even for beams, where the basic functions is to resist bending, the cross section is often an I or T shaped rather than a solid rectangle, or the beam is are built from a network of struts each of which is in tension or compression, but the structure as a whole resists bending (for example tower cranes and some bridge designs).

 

[Crazy Person]

"Design of Welded Structures" by Blodgett

Thanks, Ill see if the local Univ library has it.

It turns out that a horizontal stiffiner all around the top cuts most stress and deflection problems. If more is needed an additional horizontal stiffiner all around about 40% from the bottom may be used. A simple angle ('L') shaped stiffiner is acceptable.

Nice, now that’s what I am talking about. I had a chat to my brother in law, who does mechanical modeling, however he has little experience in designing something to accommodate bending, as Aleph mentioned. He does have modeling software which may help, but I am worried he's more interested in this experiment to see if it fails.

This is why most real-life large tanks are cylindrical not rectangular.

Thinking about it, I have never really seen a very large other than circular shape tank. They are difficult to build out of Perspex though, as I believe that the seems may be weaker than what I could manage to cement in a square tank. I did pick up prices of circular tubes of Perspex but, as the larger sizes are imported, the price literally is exponential verses diameter.

A good principle for designing any mechanical structure is to use material in tension or compression, not bending. Even for beams, where the basic functions is to resist bending, the cross section is often an I or T shaped rather than a solid rectangle, or the beam is are built from a network of struts each of which is in tension or compression, but the structure as a whole resists bending (for example tower cranes and some bridge designs).

My first year mecha is coming back to me – I remember most of the forces being along struts. And to add – the Eiffel Tower was built similarly. Apparently if you melt it down and fill its base with the melted materials, it would only be a meter or so high.

As I am and Elec Eng and know no limits in Mech Eng, Ill attempt a design on a rectangular tank. Ill look into that book, and others – I am glad its not all axial design. Ill post some results once its done.

Thanks
CP

 

[alphy]

Dear CP,

Thank you for your question. I can provide you with some insight on the water pressure in a box and how to calculate the appropriate perspex thickness.

Firstly, the equation you have provided is correct - P=\textit{ρ}*g*h - where P is the pressure, ρ is the density of water, g is the gravitational acceleration, and h is the height of the water column. In order to ensure a maximum deviation of 1mm, you would need to consider the maximum pressure that the perspex can withstand without bending or breaking. This can vary depending on the type and quality of perspex, so it is important to consult with the manufacturer or do some research to determine the appropriate thickness.

In regards to your idea for a design that can accommodate bending stress, it is definitely a valid consideration. Using square vertical perspex rods to hold the front and side faces together can distribute the pressure more evenly, reducing the risk of bending in the joints. However, as you mentioned, this design may neglect the bottom and potentially top faces. It would be important to also consider the pressure on these faces and ensure they are thick enough to withstand it.

In terms of finding cheap FDTD software, it may be helpful to consult with a mechanical engineer or do some research online to find a suitable software that fits your budget and needs.

I hope this helps answer your question and provides some guidance for your project. Best of luck!

Sincerely,