Sitting around a chlorinated swimming pool, you usually smell the chlorine scent as the water (H20) evaporates. There's a lot more chlorine in the pool than in "normal" city water, or else you'd smell that same scent when you watered your lawn on a hot day. If you can small chlorine it's in a gaseous state. Right?
I recall reading someplace on CureZone, that if you shower for ten minutes you absorb as much chlorine as if you'd swallowed twenty gallons of water.