black water tank -- I see toilet paper

Let me clarify...I took a little pipe and poked the toilet paper...I think it was toilet paper that was just in the tank...How "deep" is the black tank, typically? 5-6"? If that is the case, then I think I just am not getting everything out when I'm draining at the dump station. I have the built in spigot that I can connect the hose to.

1. When I am dumping, how long should I run the hose?
2. How long should I let this solution in my tank before I try dumping everything out again?

Thanks for your help guys!