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

Question

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?

kamran · Answer

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 $
$t=thickness, alpha= length$
$And deflection = Y$
$$sigma_{ max  center}=frac{beta* q*alpha^2}{t^2}
$$
$$Y_{max}=frac{-qalpha^5}{Et^3}$$
We need to have the datasheet on the acrylic to plug in E and allowable stress.

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

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