Bronze 3-pdrs rather than iron 3-pdrs were used as field artillery. Iron guns were used by the Navy and for Garrison use. There were a few iron 3-pdrs in use in some countries where copper and tin was expensive or difficult to obtain for field artillery. These included Sweden and USA. Iron 3-pdrs as mountain guns were used by Piedmont [capital Turin, Italy].
The 3-pdr was used in small ships and as swivels. Their portability made them useful for point defence. Now the lengths is an interesting issue.
Can you indicate the nationality and the type of carriage. A mountain gun would be about 3 foot long whereas they may range up to 6 feet for a naval gun. Also the date of the gun and the type of carriage.
A little bit more information would be useful. Venice was conquered by the French in the late 1790s. Most of their artillery was influenced by the Austrians.