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U.S. 3 inch cases can be divided into two types, Navy (3 inch 50 Cal.) and army. There were 2 chamber lengths for the Army antiaircraft guns, and each had 2 slightly different case lengths due to the size of the rotating bands of the projectiles. The older projectiles from WWI late development (Shrapnel and MK 1 HE, etc.), had smaller bands, so the cases were longer for these rounds, as the chamber length went from top of rotating band to base of case. So, there are 2 case lengths and designations for the long chamber guns for fixed AA gun mounts and 2 case lengths and designations for the short chamber guns which were the mobile AA guns and the M10 open topped tank destroyer.
Case descriptions are as follows: For 3 inch AA fixed mount guns, the tallest cases are the MK 1 and MK 1A1 at 27.15 inches long, the difference between numbers being primer type. These cases were used for the shrapnel and any other older projos having a small (.5 inch high) rotating band. For the more modern projos, HE M42 and MKIX, AP Shot, and APCBCT M62, the two cases MK1 M1 and MK1 A1 were shortened up to 26.7 inches.
For 3 inch AA mobile mount guns, the longer variations for old projectiles, the MK II and MK IIA1 cases are 23.65 inches long. The cases for the newer design projos, the MKII M1 and MKII M2 are 23.08 inches long. This is your case, and it could have been used in the AA gun or the M10 tank destroyer. All of these cases can be found in brass, and there are very few remaining examples of laquered steel cases which would be MKII M2B1. In the U.S., a B1 designates a steel case.
Your case should be 3 inch inside diameter at the mouth. I hope this helps.
The steel case you show is the steel version of the case in the first posting. The B1 at the end of the case name means that its a steel case. This could have been used in the antiaircraft gun or the M10 tank destroyer.