To select a single partitioning the SQL just use something like this:
SELECT * FROM orders PARTITION (p3) ;
but there is not a where condition that could you to hit the p3.
the point is that mysqldump support a where condition with the option --where
but WHERE condition can not be use to select a single partition, the use of the key and the value can be complicate and explain seems check all the partition anyway.
The Future request is to have a where condition to be used as well on mysqldump to dump just a partition directly:
mysqldump... --where= PARTITION (p3) ;