I'm trying to install a new utility sink and washer hookup in my garage and am trying to plan how I'm going to run the copper supply lines. The most direct path I can think of is to notch probably 5 or so studs of an exterior wall to reach the existing drain I'm going to use for the sink. I know that I can't notch a load bearing 2x4 more than 7/8" but I can't find any guidelines as to how many studs in a row I can safely notch. Is this a question for an engineer? I don't want to go notch crazy but I think 5 or so in a row should be ok? I'm also planning on putting stud shoes on the studs i do notch.
There is no specific limit on the number of sequential studs, as the 7/8" limit is intended to reduce the potential stresses, however, given the choice, I would rather drill than notch:
2308.9.11 Bored holes. A hole not greater in diameter than 40 percent of the stud width is permitted to be bored in any wood stud. [...]
In no case shall the edge of the bored hole be nearer than 5/8 inch (15.9 mm) to the edge of the stud.
So 40% of 3.5 in gives you ~1 3/8" to use, often much more than you need for supply lines.
My concern though, is that you're thinking of notching for a waste line, and notching 7/8" to add a 1 1/2 or 2" drain line is... I'll just say that I'm with @JohnSmith in that I wouldn't bother, but then I don't know your specific situation.
This is a hard question to answer, mainly because there may be local building code that changes the answer depending on the region. From what I've read, I have not seen any number associated with the maximum number of bearing studs that can be notched. I have seen limitation on boring a hole in the same section as the notch which is not allowed.
WWPA put out Notching and Boring Guide which covers some of the common code requirements for notching. On a bearing wall, you cannot notch more than 25% of the width of the stud, which is as you said, 7/8" max on 2x4 construction. Other areas have similar requirements.
Personally, if its just a hookup in the garage, I don't know that I would notch. I would probably leave it exposed. (mostly because my garage is pretty rough as it is.)
This varies by code, and with how big your notches are. The safest answer is to limit yourself to 2 consecutive studs. Other codes will say 3 for specific situations. And if the wall isn't load bearing, or you keep the notches small enough, there isn't a limit. The best option is to go through the joists in either the ceiling or floor so that no studs need to be drilled.
Here's one from the Florida codes that gives specific limits for their location:
2318.1.9 Notching. 23220.127.116.11 Studs that carry loads in excess of 75 percent of their capacity shall not be notched or cut. 2318.104.22.168 Studs that carry loads 75 percent or less of their capacity may be notched to one-third of the depth without limit of the number of consecutive studs.