formula for pressure on glass?

[salty joe]

Does anyone know how to calculate the pressure aquarium water exerts on the glass? The tank I am building is 39" deep, 96" long and 45" wide so the psi on the bottom is about 1.25 psi. (.44 psi/foot of depth)

For instance, if the tank were the same except the width was only 1/16" rather than 45", the psi on the bottom would be the same but there would be a lot less pressure on the viewing panel of glass.

My guess is that a graph showing the increase in pressure as the tank gets wider would not be a straight line.

 

[kurt_n]

You've already answered your own question, really. The only thing that effects the water pressure is the depth that you want to know it at. At the bottom of your tank, the pressure on the bottom is the same as it is on the sides. When you move half way up the side of your tank, the pressure is half of what it was on the bottom.

 

[Opcn]

My guess is that the OP is looking not for the water pressure but for the force exerted.

 

[disc1]

The pressure will be related only to depth. Sea water weighs 1.02g / mL. There's 2.56 ^3 = 16.7 ml in one cubic inch. So sea water weighs 1.02 * 16.7 = 17.1g / cubic inch. Divide by 454 g / lb and we have .037 lbs per cubic inch of water.

So the formula would be:

psi = 0.037 * (depth in inches)


For the total force on the bottom, you would multiply by the area in square inches. All of this would be easier if we used the metric system.

Really, the easier way if you know the total water volume is the total force on the bottom is just the weight of the total volume of water. The pressure on the bottom is that force divided by the surface area.

Now for the sides of the tank, the force is a little trickier. The pressure changes as we go up the side. At the bottom, the pressure is the most, but at the top of the water surface, there is no pressure on the glass.

So to find the force on the side of the tank, we would need to use calculus and integrate from 0 to the depth.

 

[disc1]

For example, to find the amount of force on the front glass of a tank that is 48" x 24" (That's the front of a standard 75 or 55)

So we integrate: h * (density) * (width) dh over the whole depth of the water. Where h = depth

Let's plug it in.

We're goin to integrate from 0 to 24" { h (0.037)(48")dh

That's 1.776h dh

so the antiderivative is:

0.888 (h^2)

And we'll evaluate from 0 to 24".


At 24" we have 0.888 * 24^2 = 511.5

At 0" we get 0.

511.5 - 0 = 511.5.

So the total force on the front glass of a standard 55 or 75 gallon tank (or anything with a 48" x 24" front) that is completely full to a depth of 48" is 511.5 lbs.


QED

 

[salty joe]

My guess is that the OP is looking not for the water pressure but for the force exerted.

Yes, thank you.
What I am interested in is a formula for the force exerted on the viewing panel. There must be one that I could plug my dimensions into and arrive at a number. I could then determine the factor of safety of 1/2" glass compared to 3/4" glass. Tanks this size that are braced have been built with 1/2" glass, I would like to know the safety factor.

 

[disc1]

The math I just posted will give you total force on the viewing pane. I'm not sure how you would then rate the glass.

 

[salty joe]

disc1, I did not see your last post until after my last response. I don't understand the calculus.

Is there any way that you would be willing to run the numbers for my build? The water height is 34", (not 39" as my first post says) the width is 45" and the length is 96". The viewing panel opening is 29"x90", and very well braced. The top of the glass is just about at the 34" water height. There is epoxied plywood and bracing above that.

 

[disc1]

I'll do this. I'll condense it into a formula. Assuming the glass is rectangular. Bowfront would be a little different.

h = depth of the water in inches
w = width of the glass in inches

use this:

0.5 * 0.037 * w * h^2

That will give you the total force from the top to bottom in lbs.

 

[salty joe]

That's impressive to be able to come up with a formula like that. And very generous to share it. Thank you very much.

 

[Opcn]

There are separate formulas for the static loads on the glass. Surely someone has them...

 

[salty joe]

Is the static load on the glass different from the total force from the top to bottom?

 

[Opcn]

My language was imprecise because I am a biologist, not an engineer.

Obviously knowing that the water pushes on the tank front with X pounds of force is not the same as knowing that that X pounds of force is going to cause Y inches of deflection in glass z mm thick. However I'm sure that there is a set of standard equations for this sort of thing.