I ran a few simulations over lunch today. The weight of just over 400 gallons of water is roughly 3,600 lbs. That is more weight than most cars, so its nothing to play around with.

The one thing I struggled with was getting the water weight forces to come out exactly how they would in the real world. The bottom of the tank is obviously going to see the full 3,600 lb force of the water, but what about the sides? At the bottom they'll see the most pressure, but at the top it will be less. So, I'm still searching for a formula that will help me figure that out. For now, I used 1 psi as my baseline. The base of the tank is 3,400 sq/in, so roughly 1 psi. I used this for the sides as well. Here is what I got:

This is with 15/32" thick plywood. Try to ignore the colors as they don't truely tell you the whole story. The graph on the right shows the peak stress and the scaling.

This is with 19/32" thick plywood. Again make sure to reference the graph as the scale varies.

Now with 23/32".

And once again with 3/4" thick plywood.

As you can see, the 3/4" plywood showed quite a bit more strength than the other two thicknesses. I'm not quite sure why the huge reduction in stress. But, its not really consequential. Plywood has a tensile strength of 4500 psi. So, even the 15/32" can hold up to the stress of the water (assuming my simulated pressure isn't way off). I'll guess I'll run a few more simulations with even thinner plywood. However, there is a point of diminishing returns I'm sure. The 19/32 4x8 sheet only costs $3 more than the 15/32 sheet, so there isn't huge cost savings to be had.