I use Dawn in my black tank all the time! Dump the tank at the dump station completely. Flush it out if you have the time. Close all the outside valves, add about 4 gallons of water to the empty black tank, pour about a 1/3 cup of Dawn dishwashing liquid down the toilet, and drive away!
It cleans the tank, cleans the sensors, and keeps it smelling good. At your destination, you don't need to drain the dawn, just use your toilet until the tank is full. Contents will just "slide" right out. No fuss.
Not traveling, put some Dawn in the black tank anyway. Use your toilet as normal. When full, drain, and do it again. I've been doing this for the last 14 years.
Dawn is a great grease cutter.
The first time I ever used Dawn was when I worked at McDonalds in Morganton, NC (about 1980 ish). I was the maintenance man (glorified janitor). One day we ran out of the McD's floor soap and the manager had someone run over to the grocery store across the parking lot. He came back with Dawn, add it to the mop bucket water and proceeded to mop the floor. It cut all the grease, and left the floor spotless! That was the first time I'd ever, even heard of Dawn.
It's fantastic for washing motor oil and motor grease from your hands, clothing, and pets. It's great for removing bug goo on from the grill of your car or truck and from your camper nose. Although it does strip the wax.
Any kind of grease, oil, cooking or motor, slime, sludge, goo, or poo, it cuts through it all.
OK. Do I sound like a commercial now! Anyway.... I've been using Dawn since at least 1980, and I'm STILL impressed what all it can do.
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