Could you be more more specific.
Which test pressures ? which section of this API?
In principle, tank will be tested with water in:
1/- incorrded condition.
2/ Whith obviously water , which has s specif gravity higher than most of the oils, products..
3/- Design stress for hydrotest is a bit higher than for design with real fluid.
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I think your 1.3 x Stress ratio)x design pressure is for new ASME VIII - div.1 vessels.
We will hear from the others!!!