Fair enough, letââ"šÂ¬Ã¢"žÂ¢s clear up these issues. First off Iââ"šÂ¬Ã¢"žÂ¢m a currently a 3rd year Mechanical Engineering student at the University of Saskatchewan. Iââ"šÂ¬Ã¢"žÂ¢ve taken 2 courses on fluid mechanics alone, and currently completing my third. The largest tank Iââ"šÂ¬Ã¢"žÂ¢ve build is only 135gal, and it happens to be my tank, however I do see how this really that relevant. I didnââ"šÂ¬Ã¢"žÂ¢t do any calculations to calculate the glass size I recommended I was simply going on what Iââ"šÂ¬Ã¢"žÂ¢ve seen. Hereââ"šÂ¬Ã¢"žÂ¢s a link to someone who built a plywood tank (bigger than yours) and used 12mm glass for viewing panels:
http://home.online.no/~joobjoer/eng_diy/2200litre/2200litres.html
But since you asked lets do some elementary calculations to back up my claim.
In order to figure out if the glass will be strong enough we should examine the weakest point or where the greatest hydrostatic force acts. This point will be located somewhere on the front view panel. We can find this resultant hydrostatic force quite easily:
F = ã Hcg A
Where:
ã = specific weight of seawater = density x gravitational force = 1025kg/mÃ"šÃ‚³ x 9.81m/sÃ"šÃ‚² = 10055.25
Hcg = the height from the centroid to the top of the water level. In our case we can make this value equal to half the height of the glass and assume the tank will completely full.
A = the area of the plane in question = 0.762m x 2.4384m = 1.858mÃ"šÃ‚²
So F = (10055.25)(0.381m)(1.858mÃ"šÃ‚²) = 7118.09N
To balance the bending moment potion of stress the resultant force from the fluid does not act through the centroid of the glass but below it towards the higher pressure. This line of action passes through the center of pressure (CP) of the plane.
To find the coordinates (Xcp, Ycp) of the point in which the resultant hydrostatic force acts we sum the moments of the element force pdA about the centroid and equate to the moment of the resultant F. However since the other side of the glass is at atmospheric pressure the ambient pressure can be neglected because it acts on both sides. Therefore the center of pressure is independent of specific weight and this simplifies our calculations.
Xcp = 0 in our case as the glass face is perfectly rectangular, therefore the position will be directly below the centroid (not to the left or right of it).
Ycp = (Ixx sinè)/(Hcg A)
Ixx = moment of inertia with respect to the x-axis (horizontal) =
(length x heightÃ"šÃ‚³)/ 12 = (2.4384m)(0.762m)Ã"šÃ‚³/12 = 0.0899m^4
è = 90Ã"šÃ‚° since the glass plane in question is vertical.
Therefore Ycp = ((0.0899)(sin90))/((0.381)(1.858)) = 0.127m
This means the point CP is located 0.127m below the centroid.
So now we just need the reaction forces located at the bottom and top of the glass where the plywood holds the glass.
R-bottom = 4815.4N
R-top = 2372.7N
These where calculated by summing the moments about the bottom point and then the top point.
Now the maximum bending moment occurs at CP and is equal to (4815.4N)(0.254m) = 1223.1Nm.
Next we calculate the elastic section modulus (this is where glass thickness comes in):
For rectangular shapes: S = (1/6)htÃ"šÃ‚²
t = glass thickness = 12mm = 0.012m
h = tank height = 0.762m
S = (1/6)(0.762)(0.012m)Ã"šÃ‚² = 1.8288 x10^-5mÃ"šÃ‚³
Now we can finally calculate the maximum stress that will occur in the glass:
This equal to the maximum moment over the elastic section modulus:
(1223.1Nm)/(1.8288x10^-5) = 66.88 MPa
If you use 24mm glass the maximum stress would be = 16.72 MPa
So there you have it. Iââ"šÂ¬Ã¢"žÂ¢m not sure what the tensile strength of glass is but you want it to be more that the max stress calculated above. I believe itââ"šÂ¬Ã¢"žÂ¢s somewhere in between 69 and 120 MPa depending upon the type. Tempered glass would be even higher probably anywhere from 120 to 370 MPa. Not sure though on these numbers.
Side Notes:
The above calculations are only valid if both the bottom and the top of the tank have adequate bracing.
The above calculations should only be used for plywood tanks, as all glass tanks are joined with silicone which means the weakest point would be at the seams.
A safety factor was not used, however the actual water height will be lower than what was used in calculations.
Only the weakest point was examined.
There is a possibility I could have miss calculated, thereââ"šÂ¬Ã¢"žÂ¢s no guarantee the glass will experience the above stresses (could be more could be less).
All units were converted to SI units.
Work Cited:
Engineering Material Science, William D. Callister
Fluid Mechanics 5th Edition, Frank M. White