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) ;

something alike.