I TEACH college kids this stuff... if I couldn't do the math I'd be in a world of trouble
As far as the media changing the velocity - it's hard to say. It would certainly decrease the total velocity change, but it's quite likely it would still be accelerating within the shower. It would be darn complicated to try to calculate the difference!
That's a big reason why I went with the energy-based calculation instead of acceleration. Every time the water splashes or changes direction, it loses some energy, and hence there's less kinetic energy available at the end for the velocity of the water. As I said, everything I did was a theoretical maximum - best case scenario.