I would go get some 2" PVC and some couplers and one T-joint. Set the pipe all up where you want it to flow (it bends nicely). I don't believe you would even need to glue it as there will be min pressure.

Cap the down hill end temporarily and put the t-joint at the top of the arch. Fill it with a garden hose at the t-joint and then cap the T. Now remove the cap on the down hill side.

Cheap and effective.