If you have both a garbage disposal and a dishwasher, then they are connected. The flexible drain hose from the dishwasher feeds into the dishwasher inlet port, which is on the side of garbage disposal near the top. When everything is working as it should, the drain water from the dishwasher passes through the garbage disposal canister, and from there it goes into the drain P-trap and down to the sewer.
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If you find the garbage disposal leaking when the dishwasher is draining, the leak could occur at the connection of the drain hose or P-trap, the flange that connects the garbage disposal to the sink, or somewhere on the garbage disposal itself. Your first job, when you see water on the bottom of the cabinet, is to determine from which of these places the water is leaking. Once you know that, it's pretty easy to figure out what to do next.
Disposal Leaking from Flange
When water overflows from the garbage disposal flange, it means the canister is filling with water. The reason is probably because of a clog in the P-trap or waste line. The best way to bust the clog is to disassemble the P-trap and clean it out, then snake the waste line.
There's another problem you have to address, and that is that the flange shouldn't leak, even if the canister is full. The water should all go into the sink. Try turning the disposal clockwise to tighten the connection or, if that doesn't work, remove it and replace the rubber washer on the flange.
Disposal Leaking from Pipe Connections
If the disposal isn't backing up into the sink, get a flashlight and watch the garbage disposal while the dishwasher is draining to find out where the water is coming from. If it's coming from the connection between the drain hose and the garbage disposal or from the P-trap or drain pipes, the fix is usually fairly easy. You just have to tighten the leaking pipe.
The drain hose is often held by a steel clip. If that's where the leak is, try repositioning the hose on the connector and resetting the clip. It may help to replace the clip with a pipe clamp that you can tighten with a screwdriver.
If water is coming from any part of the drain assembly, note the connector from which it's leaking and tighten that connector with locking pliers or a pipe wrench. The connectors are designed to be hand tightened, but hand tightening doesn't always work, especially if the pipes are slightly offset, so go ahead and use a tool to make sure the connectors are secure.
Disposal Leaking from Bottom
If you have a garbage disposal leaking from the bottom or from any part of the body, it means a seal inside the machine has worn out. This definitely shouldn't happen to a new unit, and the warranty should cover repair or replacement.
It's a different story if the unit is old, corroded or past its warranty period. In that case, it's time for a new garbage disposal. It's technically possible to disassemble the garbage disposal and replace the worn parts, but it will probably cost more to do that than it will to buy an new one. Besides, if the unit is old enough to have worn parts, it's probably just a matter of time before something else goes wrong, so go ahead and treat yourself to a brand new garbage disposal.