Beam / Lintel sizing

Hi all
I'm about to start on my bathroom / laundry reno and I'm moving some rooms around. A few of the walls are load bearing, so obvious structural work needs to be done. It's fairly straight forward, just needing a beam and some support either end, but is there a table or some calculations I can use to determine the size of the beam I need?

Pics are below of the existing and then future floor plans. This whole thing is in the corner of the house (single story, hip roof). The red dot is the location of a strut supporting the hip truss (I think that's what it's called - the main structural centerpiece supporting the ridge line running down to the corner of the roof.)

So I'm guessing some kind of beam running across between the two walls and supporting the weight in the middle would be the go. Don't really want to have a bulkhead in the middle of my bathroom ceiling, but you have to do what you have to do.

So what sized beam will I need, and how much bearing on either end? Thanks. :2tsup:
Let me know if you need more info.

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