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This image roughly represents the layout of a renovation house that I am working on. Due to a few layout changes and the plumbing nightmare that I inherited (a maze of piping, inaccessible shut-off valves, sloppy soldering), I am planning on re-plumbing most of the house. I attempted to search for some easy-to-understand articles and images regarding branch systems and pipe sizing but I didn't come up with anything that I found as very helpful.

My main question here is, should I use a single supply line (as indicated by the solid darker blue line) or should I end the bathroom line and add a second supply line (indicated by the dashed dark blue line) back to the kitchen and downstairs half-bath? Dark blue represents 3/4 copper pipe and light blue represents 1/2 copper pipe.

What would be the advantages and disadvantages of each layout?

Plumbing layout

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Using sizing methods outlined in Appendix E of the IPC, either way will make very little difference as the same demand factor is applied to the supply either way. The additional friction loss through 3 reducing tees is very small. There's not enough information to say if the sizes are adequate in general. –  bcworkz Jun 28 '13 at 19:20

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Just a note that I'm not a plumber. That said -- anyone can install some pipes and have a plumbing system, but a GOOD plumbing system is a balanced system. To design one, you have to know the fundamentals.

Permit me to lightly delve into some physics (which may only be for the benefit of some other person with a similar question) --

The water in your pipes and its distribution are affected by: Gravity, Inlet Pressure, Inlet Volume, Outlet Pressure, Outlet Volume. As long as your upstream supply can provide the necessary pressure and volume, and your downstream outlet pressure and volume, accounting for gravity, doesn't exceed this, it should be fine.

That said, it is what happens when you overwhelm the system that would matter. Lets (just as an example) say that your outside faucet nearest your supply uses 75% of the available system GPM because it is on a 3/4" line, then you start to run hot water in a bath (1/2" lines) that would normally use another 50% of the available system. In a well balanced system, the faucet would drop to around 60% and the shower would use the other 40%. Now -- lets say the system is fairly balanced, except that your outside faucet is 5 feet below the supply and the shower is 5 feet above. Gravity reduces the water pressure of the bath, while increasing the pressure of the lower faucet allowing the faucet to "suck" more out of the system -- your shower may end up with only 25 or 30% of the water, while the faucet get 70 to 75%.

This is the reason the your main supply running through the house is larger, while each branch is a reduced side. The area of a 1/2" pipe, is half that of a 3/4" pipe. A 1/4" pipe is only 10% of the size of a 3/4" pipe. This is also the reason that each branch uses a T pipe, with the main pipe being the straight. This does a better job of letting each branch have a better chance of pulling from the main line equally, and why you'll often see the main line terminate with a cap after your last branch, rather than simply being an elbow directed into your last branch. There are some exceptions (2nd floor fixtures, outside faucets) where you may want this advantage. Restrictors at the fixtures can also assist in balancing your system by lowering the outlet volumes of individual fixtures.

Finally -- to answer your actual question, unless you've noticed problems with your system when more than one fixture is in use, you're probably fine in this layout with a first floor configuration, but I don't think that moving the three separate branches for the bathroom to a single branch off the main line is a bad idea by any means. But, I don't know that you're going to get a significant return on your work. If you go that route, consider making the branch to the bathroom a 1/2" off the main line, rather than a 3/4" to 1/2". Lastly, well located shutoffs for each branch are fantastic for when you're eventually want to make a repair without shutting of the water to the entire house.

Whether the 1/2" branch for the bath would be big enough -- seriously, who runs their toilet, shower and faucet at the same time in a single bathroom. :)

Hope that helped.

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"seriously, who runs their toilet, shower and faucet at the same time in a single bathroom." I do, we have a single bathroom and it is my and me girlfriend so I use the bathroom as nature calls which doesn't always miss her showers. The toilet is filling up when I wash my hands so all 3 are running simultaneously. –  Jason Jun 28 '13 at 20:57
    
Fair enough, but I pose that even doing so shouldn't be enough to overwhelm the system. Most Sinks are plumbed with 1/4" connections and many of todays toilets use lower flow of water to "quiet fill" the tank. Even so, it should only result in a slight drop in the cold water supply to the shower, which is typically being restricted or is rarely turned on completely, unless you're taking a cold shower :-). But, your point is valid. –  Jacob S Jul 1 '13 at 12:34

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