A copper 90deg elbow has a fitting insertion loss equal to 1" of straight copper pipe, therefore if you have 6 elbows it would have the same effect as adding another 6" on a straight run of pipe.

At the flow rates of a shower head the friction head loss would be almost negligible.

Thanks lazypup.

Just out of curiosity I worked it out.

Each elbow is has an insertion loss equivalent to 1" of 1/2" copper pipe so 6 elbows would be equivalent to adding 6" or 1/2foot of pipe.

At 3gpm the "Friction Head Loss" is 3.2psi/100ft of pipe which then equals 0.032psi/ft.

1/2ft of pipe would then cause a friction head loss of 0.16psi.

By contrast, if you were to raise the shower head 6" that would cause a "Vertical static head loss" of 0.2195psi so the 6 elbows would only cause approximately 1/13 as much loss as raising the shower head 6".

Very interesting. I WAS going to raise the shower head a few inches. Practically-speaking, do I need to rethink that? This is a first floor bathroom, if that helps.

The Vertical Static Head Loss is 0.434psi per foot of vertical rise and here again, the loss is so slight that it doesn't bear consideration.

For 1/2" pipe, the equivalent length is about one foot per 90, which will give you under 0.4psi loss at 3gpm for your 6 elbows.

Here is a link that might be useful: Copper.org tubing handbook