Error range in compressive strength for a sphere.

[socrunningman]

so here it is, I want to build a sphere with pressure being exerted uniformly on all sides. the sphere will be immersed in a fluid and have mass pumped out(to create buoyancy.) I have calculated the strength of the sphere to be...

C=((Pw-Pi)r)/2T
where
Pw=Pressure of the Water
Pi=Internal Pressure
r=radius of sphere
T=the thickness of the spherical skin

Buoyancy is given by a separate equation.

What I would like to know is "if the diameter of the sphere is off uniform(is built by humans) what strength is required by the sphere. I haven't ever done calculations on error ranges and I do not know where to look to learn about how to do it. Learning how would be much more helpful than just knowing this case, but I will accept either!

Thanks in advance

 

[tyroman]

Just an idea... what about going back to the basics of the strength formula (the integrals from analytic geometry) and introducing terms which allow variance in radius and thickness of the shell... then re-deriving a strength formula which would include terms for such variance?

 

[socrunningman]

I had the same idea, the problem that I run into is that every time I try and do it I make the entire sphere smaller or larger in variance. what I need it an imperfect sphere formula, where say the top portion of the sphere is a little "egg" shaped" or conversely, is indented, while the rest of the sphere is still uniform. Mathematically this is a little hard to do, as some spots become more resistive to compressive forces, and others become weaker (luckily I am only looking at the weakest points not the strongest, or the in-betweens) I just know that there should be a simple way to do this, I just do not know where to look for it or how to go about it in an exact way.

Extra note, I plan on building this buoyancy sphere, testing it, and then possibly manning it. Hence why knowledge about what will theoretically happen is tres impotant.

~socrunningman

 

[Bob S]

I would review the pressure vessel design equations for spheres like successful bathyspheres use for deep ocean exploration.
http://en.wikipedia.org/wiki/Bathysphere_(vessel )
External pressure vessels require a much thicker shell than internal pressure vessels. There is (was?) a nuclear submarine (the Thresher) lying at the bottom of the Atlantic Ocean. See
http://www.history.navy.mil/danfs/t/thresher.htm
Bob S