calculating forces exerted on a tank's walls

[Veri]

Hey all,

I was thinking about the forces exerted on my new-ish purchased tank - regular five flat glass panels with a fixed plastic base. I recall two important pieces of structural advice in setting up the tank: (1) make sure your base is flat (i.e. not bumpy); and (2) make sure your base is level (i.e. not sloping). I understand the danger associated with the first, but I don't quite understand the significance of the second (ignoring extreme cases). The most basic first approximation seems to be, ignoring atmospheric pressure:

Water pressure p(h) = rho * g * h, where h is height of water column
Force on side wall due to water = integrate ( p(h) * width ) dh as h varies from 0 to the depth of the tank.

But this reveals a very small percentage change in force if your tank is slightly non-level, and as long as you're not sloping enough such that one side of the tank's water exceeds the manufacturer's high water limit, I'm not sure what limit is being exceeded in mechanical terms. Yet the Internet is full of people with glass and acrylic tanks reporting leaking / bulging / cracks / etc which they suspect related to tanks with perhaps under a centimetre depth difference on either side, so I'm obviously oversimplifying.

Is there perhaps a site which analyses the forces on a fish tank in good detail (panels, seal, etc.)?

Thank you!

 

[krap101]

I'd imagine that you not only need consider the increase in height, but also all the water from the other side of the tank now pushing outward on the wall? I guess the analogy I want to use, but may not exactly apply, is for skyscrapers/bridges. I think they're built to allow a few feet of sway, but when the force is too far outside its footprint, you're not only dealing with linear forces, but also shear and sometimes torsional forces. Think about the generic physics hanging picture analogy. the more vertical the wire is, the less tension, but when the wire is horizontal (or was it at 45 degrees... anyways...) there are alot more forces acting than just gravity. The tension in the wire is now greater than the weight and the picture (and wire if you consider it...)

 

[corrado33]

I would have to say it has to do with the direction of the force. When the tank is perfectly level, the direction of the force is perpendicular to the walls. When the tank isn't level, the direction of the force pushes on the seals in a different way. Some seals will have less pressure than others, probably causing some to swell.

EDIT: This doesn't make sense. Pressure is onmi-directional, it pushes in all directions. Back to the drawing board...

And for an example of what krap is talking about do this. Take a piece of string (not wire), and pull it as tight as you can between your hands. Have someone hang a small weight in the middle. Try to make the string not bend at all. It's impossible. The forces needed to keep the string perfectly straight are astronomical. Think about it, the weight is pulling down, so the string bends so it can provide the force to keep the weight from falling. If it was perfectly level, there would be no up and down force, know what I mean? I would draw a diagram but I'm too lazy.

 

[Veri]

Thanks krap and corrado for your thoughts. I can see that the forces on an empty tank would change at an angle. Taking your wire and weight model, where a panel has an evenly distributed weight, consider tipping the empty tank so one side outer wall is facing slightly downward. Overall it is going to bend down slightly - the outer part of the wall is going to be slightly stretched, and the inner part slightly compressed, with strength and the seals keeping the panel fairly straight. I guess the bending is more obvious with acrylic. Add water and we have deformed panel and surrounding seals, already experiencing substantial tension/compression forces, enjoying a new large force.

I still think the water-ground orientation won't make a significant difference per se - water's effect can still be modelled as pressure acting in all directions from which we derive a force acting perpendicularly against the inner surfaces. It is tempting to think of the weight of water acting at an angle to the tilted side (diagram: \v), but that's not how fluid pressure works.

The key then seems to be that shear, the parallel component of force against the walls, would only be significant for gravity acting on the mass of the walls (hence above). The viscosity of the fluid and friction against the moving current would contribute to shear, but I'm assuming they're negligible.

Sound sensible? Detailed quantification still in order .

 

[Laurence]

Veri: I have a 185-gallon acrylic aquarium that tilts slightly forward because of the slight slope of the concrete floor in my bungalow. The tilt is about 1/4 inch, so the water level is slightly higher in front than at the back. I don't believe this slight tilt will affect the tank, since acrylic is strong and flexible and the tank rests on firm wool padding. If the tilt is not too extreme and the tank, even if it is made of glass, rests on a smooth surface with correct padding there should be no problem with cracking or leaking.

 

[krap101]

I finally realized just now (after like a month of not thinking about it) I'm pretty sure it's the increase in hydrostatic pressure, because one side of the tank is now higher than the other... You also have to consider the non-uniform distribution of load, and as glass is very brittle, it doesn't like this one bit.

 

[vfc]

It is the twisting force from an uneven stand that is causing many of the busted seams. Not un-level, but uneven is the tank killer.

To demonstrate, place an empty tank on a perfectly flat concrete floor. Place a nickel under one corner and fill it up. If the nickel was on the back right corner, the front right corner would be raised (unsupported) by the same amount. When you fill the tank, the weight of the water on the bottom panel will try to push the raised (unsupported) corner down. The tank's water level may not even be enough to indicate the tank is higher on right side. However, the tank seams are under tremendous shear force that could cause: a small separation in the silicon that causes a leak, sides to bulge, whole seam to suddenly give way, or one glass panel to shatter.

Another way to look at it is if you placed your tank on a 1-foot thick steel top table. You could raise or lower any one of the legs by a few inches and your tank would be fine (water may spill out if you raise a leg 2 or more inches). However, if you again placed a nickel between one corner of the tank and the 1-foot steel top, that tank is in danger of failing (even if the steel table top was perfectly level).

Finally, if you glued the tank to the steel table, and filled it with water; you could (if strong enough) lift the one side of the table causing all the water to pour out on the other side without damaging your tank. You can't get any more un-level than that!!!!