Not my write up but I find it to be true as well.
"Tanks don't need to be level. I make the following assumptions that can be verified by any physics book.
1. The pressure exerted by a liquid on a container's walls is equal in all directions at any given distance from the surface of the liquid.
2. The maximum pressure in a liquid filled container occurs at the bottom of the container
3. The depth of the liquid in a rectangular container will be maximized when the bottom is level with the surface of the liquid and the container filled to just shy of overflowing.
It follows that if a container is tilted such that the bottom of the container is not level with the surface of the liquid some portion of the container is unused as the liquid will spill out of the low side of the container before the container can be completely filled. The actual pressure at the bottom of the container is somewhat less than the pressure of a level container completely filled. Because the pressure is equal in all directions that means that the pressure can't be described as pushing down on the glass, rather it is pushing perpendicular to the wall of the container at any point, if you turn that container in any direction the direction of the force remains the same. I assume that any aquarium is capable of holding water indefinitely when perfectly level and filled to overflowing, this is when the maximum amount of stress would be seen at the bottom of the aquarium. Tilting the aquarium slightly would reduce the depth of the water and reduce the pressure, if the aquarium was designed to hold water with more pressure it won't break with less pressure.
I've been through this before and I already know there are a million websites that say an aquarium needs to be perfectly level. Go ask one of your professors how you would calculate the pressure on a container holding a liquid, then ask him what happens when the container is tilted, walk through the calculations yourself and come back and show me how you arrive at the conclusion that there is more stress on an aquarium that isn't perfectly level. Honestly I'd like to know, I've got an engineering degree and this is one of those things that no professor or text book could help me understand. ...
The model is accurate, the maximum pressure is on the seams at the bottom of an aquarium with the maximum height of water above the seam, see statement #1, it says exactly what you do about pressure being related to water depth. The maximum water height occurs when the tank is level, if the tank is not level the maximum water height is decreased which decreases the pressure on the seams. All vertical seams have a pressure gradient from zero at the water line increasing to a maximum at the bottom of the seam, these seams don't have any trouble resisting the unequal pressure. Again the largest gradient occurs when the water height is maximized as in a perfectly level aquarium, tipping the aquarium will reduce the water height and decrease the maximum pressure at the bottom of the seam.
I graduated 5 years ago, it's been a while since I've been close to anyone in the academic community who might be able to give me some additional insight as to why a level container sees less stress. The basic assumption I make is that unequal pressures are always present on vertical seams and they will withstand the pressure gradient without incident for 10 or more years, the seams at the bottom should be no less capable of carrying a load that is unequal especially considering the net impact of a reduced water height potential of a tank that is not level. The difference in pressure from one end of an aquarium to the other in an aquarium that has 1" drop over 48" would be equal to one inch of water or .03612 PSI (1 inch water = 3.612x10^-2 PSI at sea level) a fairly negligible amount of pressure. A water balloon with a latex wall of only a few thousandths of an inch thick will easily contain that amount of pressure without rupture. In my years of keeping fish I've never had a tank leak at the seams on the bottom where the maximum pressure is experienced, I've always had leaks somewhere in a vertical seam, every leak I've had was somewhere 3-6 inches from the bottom."