For my ROV project, I am considering using a flat acrylic disk instead of a dome for the front "window".
So I needed to calculate if a disk of a certain diameter and thickness would hold up to the pressure exterted at a specific depth.
A couple of hours of Googling led me to these calculations and constants:
The maximum stress a uniformly supported disk is subjected to (of a given material and of a given thickness and radius) is calculated as follows (from here):
σ = | 3(3 + ν)pr² |
—————— | |
8t² |
Where
σ | is the maximum stress in Pa |
ν | is Poisson's ratio for the material (0.37 for acrylic from here) |
p | is the pressure the disk is subjected to in Pa |
r | is the disk's radius in meters |
t | is the thickness in meters |
If the maximum stress exceeds the material's flexural strength, the disk will break.
For acrylic the flexural strength is 100 MPa (from here).
I entered the values for a 6 mm thick 110 mm diameter disk at a pressure equal to 25 meters depth and the result is that the max stress on the disk is 37 MPa. So it will hold.
You can enter your own values in the InstaCalc formula I made here: http://instacalc.com/9335.