I'm doing a remodel which includes a new master bath. My wife picked out a spa type shower that pumps upward of 10 gallons per minute. Does anyone know what size drain pipe I will need? Standard shower drain in these parts is 2", but I'm worried that it won't be able to keep up.

In my application the shower will drain from the p trap, travel ~2" then turn 90 degrees down where it will travel approximately 9' down vertically before it has to make 3 more 90 degree turns before it connects with the 4" main sewer line.