Calculate thickness of a 1 square meter window made of acrylic in a submarine to endure 100meters

This question would have two parts:

1 - How to calculate thickness of a 1 square meter window made of acrylic in a submarine to endure 100meters of deepness in salt water?

I don't remember the procedure to calculate this, even If I have done it in the past during mechanical structure classes. So any help with the calculus, or from where to get the formulas, is appreciated.

2 - Roughly speaking, this is the same strength required for the material to endure the weight of a column of 100m tall and 1 square meter base of water? So, 100 Tons?

• is it a square/rectangular/circular window? – NMech Nov 25 '20 at 14:59
• A flat circle, or domed even? – Jonathan R Swift Nov 25 '20 at 15:21
• Pressure of 100m of sea water plus the 1 atmosphere for air.. So density of sea water is about 1023 kg/m^3 – Solar Mike Nov 25 '20 at 18:57
• Yep, a square window – pfernandez Nov 25 '20 at 19:21
• How about pressure = density * height * gravity plus atmos p, surely that’s sufficient? – Solar Mike Nov 25 '20 at 19:34

The pressure at the depth of 100m is:

$$p=\rho*h=100*1024=102400kg/m^2=10.24atm$$ Assuming 1 atm pressure inside the cabine.

As per Roark’s Formulas for Stress and Strain WARREN C. YOUNG RICHARD G. BUDYNAS Seventh Ed. pp 502 ch. 11 table 11.4, for a square plate with free edge supports.

$$\beta=0.2874 \ for\ square$$

$$q=pressure, \ p$$

$$t=thickness,\ \alpha= length$$

$$And\ deflection\ = Y$$

$$\sigma_{ max \ center}=\frac{\beta* q*\alpha^2}{t^2}$$

$$Y_{max}=\frac{-q\alpha^5}{Et^3}$$

We need to have the datasheet on the acrylic to plug in E and allowable stress.