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# Need equation clarification - API 620

## Need equation clarification - API 620

(OP)
Looking for a clarification of an equation in API 620...

When calculating the meridional and latitudinal unit forces (T1 and T2) in Section 5.10.2.5 (b) and (c) for conical roof and cylindrical walls, respectively, I noticed that there are two terms in the meridional equation (T1) that include pressure due to the weight of the fluid.

In said equation, one term is "P" and the other is (W+F)/A.  "P" is defined as "total pressure" which includes "pressure resulting from the liquid head at the level under consideration in the tank" and "gas pressure."  Well, I have an atmospheric tank so I'm not worried about the second part...I digress..."W" is defined as "total weight of that portion of the tank and its contents...includ[ing] the weight of all metal, gas, and liquid..."

So, if I'm calculating meridional stress in the lowest shell course, I've added not only the pressure due to the static head of the fluid (P) at that location, but also the weight of the fluid/internal area, i.e., static pressure due to the fluid????

Are we really adding the pressure effects due to the fluid TWICE?

Please, someone explain this to me...if I managed to make any sense at all.

Thanks!

### RE: Need equation clarification - API 620

Don't overcomplicate it.

If you calculate vertical stress at the bottom of a vertical tank- you'll have the pressure at that depth, which includes the fluid pressure.  You'll have the weight of the fluid above that point plus the roof and shell- but that will all be taken as negative, and is subtracted from the first term, not added twice (read the notes on the signs there).  Net result for a cylindrical tank would be gas pressure at top minus steel weight on the shell, and that's what those equations should work out to if the signs are right.

### RE: Need equation clarification - API 620

(OP)
Not entirely sure I'm following you.

So if I'm going to calculate stress at the point where my cone bottom meets the cylindrical sidewalls of the shell, you're saying my meridional stress (T1) is:

T1=(Rcyl/2)*[Pstatic-(Wfluid+Wshell+Wroof)/Area] ??

Meaning if up is positive, then Pstatic is acting upward and the weights are acting downward...right?  I just don't see that.

*sigh*

I don't like the "simple" equations!

### RE: Need equation clarification - API 620

The free body diagram in this case is the upper part of the tank, floating in midair.  It has a pressure force acting up on the bottom of the fluid.  It has weight of contents and tank itself acting down.  Your equation appears to be correct as written.  With no gas pressure, the Pstatic is equal to the Wfluid/A and those two terms cancel.  And you get T1 is the weight of the shell and roof divided by the circumference, as expected.

This might seem an awkward way to achieve that result, but if the shell is something other than a cylinder, then the Pstatic and the Wfluid/A will not cancel.

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