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Seismic Loads on Large Tanks - API 620

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I am checking the seismic design of a large tank using API 620.

In API-620 Appendix L, there is a factor "k" that is used to calculate the
period of the first mode of sloshing.  "k" is derived as a function of the
ratio of diameter to height of the tank.  A graph called figure L-4 is given
that plots "k" as a function of D/H.  The value of "k" is slightly less than
0.6 for all values of D/H less than about 1.8.

The tank suppklier has indicated that the value of "k" used in his design is
0.5783933.  Either he has much sharper eyes than I do (the graph is about 1
inch high) or he is deriving the value of 'k' numerically.  I cannot find an
equation for "k", and the value of 0.578...seems about right, but I am
curious about the derivation of the value of "k."

Any help would be appreciated.