Melissa wrote:
We would like to move our washer and dryer to a closet in the middle of our
house, so we can use the laundry room space to enlarge our kitchen. The
question is what to do with the exhaust vent for the dryer. This closet
runs right in the middle, under the highest point in our roof, one floor,
hip style roof.
SNIP

Years ago, it was common practice to run the dryer exh up to
a roof vent. In your case, that's not an excessively long run
and convection will help.

However.......I would first check with the local bldg inspector
to see if the practice is allowed and what vent terminal
requirements would have to be met. You will (should) be
needing a permit for the closet installation in any event;
there may be more questions to be answered about that.

Jim