Sizing horizontal run from island stand-alone dishwasher

[beancurd]

Re-plumbing a previous owner's jack-leg solution. Concrete countertop island dishwasher with no sink.

Was going to waste DW into 18" 1-1/2" standpipe with Johnson-T at the top and the Johnson-T vent sticking out back of island, to avoid warm moist air dumping into cabinet space. San-T and vent will be in adjacent wall. (see attached image)

The only thing I had a question on is the required size of DWV for the horizontal run under the floor, since it's only for the Dishwasher waste and nothing else. Is 2" required? Or will 1-1/2" pass code? (my concern is that with 2", the water may outrun any solids)

Thanks in advance for your time.

 

[Terry]

The Johnson tee used in the Seattle area, named after inspector Johnson, needs to be above the flood level of the sink, not below it.
There are no solids to worry about from a dishwasher line.

The Johnson tee standpipe is 1.5" and past the vent it's been 2".

The air-gap drawing is kind of funny. It goes on the sink or countertop so that it's higher than the counter.

 

[Sponsor]

 

[beancurd]

the island with the dishwasher has no sink. The first diagram of yours is what I was attempting.

But to clarify, the Johnson-T has to be above the flood level of the sink on the opposite side of the room? If so, should I move the 1-1/2" P-trap and Johnson-T into the adjacent wall to the island and have the Johnson-T vent above the island countertop.? (Sorry that my original drawing didn't clarify that the P-Trap & standpipe was in the cabinet space.)

I'll go with 2" after the San-T

Thanks again.

 

[Terry]

I've pointed the Johnson Tee both ways. In many apartments where the sink isn't close to an outside wall, it's turned inward. Normally outside in case it has a flow from it, which is extremely rare. It takes a lot for them to overflow.