Vent pitch question

[DIYluke]

Is it acceptable that the vent leave the kitchen sink and pitch up away from it for about half the run, then turn down and pitches towards the washing machine & utility sink vent pipe?
Any liquid in the vent will gravity drain, but some of the kitchen "vent liquid" (condensation) may end up in the laundry room drain.
I ask because I'm looking at IPC 905.2 and maybe I'm being too literal in its interpretation by thinking the vent pipe can only drain back to the fixture it serves.
The red dot in the picture is a new structural beam that I have to leap keeping me from maintaining the continuous pitch up away from the kitchen sink.


Thanks in advance.

 

[Terry]

I've never had a plumbing inspector let me do that.
Also, any horizontal over 1/3 the vertical goes up a pipe size. I would run the kitchen vent up and out the roof as close as you can.

 

[Sponsor]

 

[DIYluke]

The drawing is misleading. It looks like I'm following the roof pitch with the horizontal, but there are two floors above the kitchen. I'm just jogging around other things.
The vent pipe to the roof goes out above the third floor and these fixtures are on the first.
Total horizontal is about 16', vertical is about 30'
That said and I'm still running it out the third floor roof, are you saying to bump it to 2"?
I'll figure out what to do about the pitch otherwise.