Question about the units in the Wa formula 1

[vesselguy]

HI all,
I was doing the calculation in paragraph 5.11.2 for MF and I can't be sure about the units to use in that formula for the column of liquid to resist uplifting from wind moment. In the equation Wa = 4.67tb Sqr(Fby x H), my understanding is Fby, the annular plate yield stress is in psi while H, the height of the tank is in ft. I can't accept this because the units inside the square root are incompatible. Am I right?

My second question is the formulas in F.4.1 and F.4.2. F.4.1 determines the maximum allowable internal pressure, which is governed by the compression ring area. Fine, I agree with that. However, I am confused by F.4.2. which limits the max internal pressure which does not cause uplift to the tank. What if I have a tank that is anchored, then the uplift is addressed and should not the max internal pressure for the tank is by F.4.1 only? I have also found that through my calculatins to check uplift by wind and pressure from Table 5-2 and 5.11.2 that there is no uplift but then equation F.4.2 tells me I must use a lower internal pressure because anything higher will cause uplift. I'm confused. Can you help me to understand how this works? Thanks.

 

[JStephen]

The Wa equation is not dimensionally consistent. Many others in the standard are not, either. The constant incorporates the unit conversion factors.

There is some inconsistency in the uplift equations in API-650. Primarily, they added the new equations in 5.11.2, but did not make corresponding adjustments in the older equations in Appendix F. I usually assume the newer equations were intended to replace the older.

 

[IFRs]

JStephen is quite right - the constant out front is often a means to make the odd units work out. I usually program MathCAD with all the units and see what the constant needs to be and why. Often the SI equations are useful to see what the factor means.

 

[vesselguy]

Jstephen and IFR,
Thanks. I suspect it was like that with the constant but I had to be sure.