Derivation of API 650 Shell Thickness Eq 2

[Soln]

Can anyone help me see where the "2.6" in the US Customary shell thickness equation comes from?

Shell thickness (governed by hoop stress), t =Pressure*Dia/(2*Allowable Stress)=pD/(2S)

Where: Pressure=(density)(gravity)(liquid height), so t=(rho)ghD/(2S) = 9.81D(H-.03)/(2S)

therefore,

t=4.9D(H-0.3)/S (SI Units)

I can see that 4.9 = 9.8/2, or g/2. But I'm having a tough time finding the combination of conversions that renders the constant "2.6" given in the equation for the US Customary shell thickness equation.

Can anyone shed some light?

 

[JStephen]

Pressure at depth in PSF = 62.4 lb/cuft x H
Hoop force/ foot = 62.4H x D/2
Thickness = 62.4H x D/2 /(12"/foot)/Stress
and 62.4/2/12 = 2.6