Pipe diameter & flow rate

Oh f*ck, this doesn't appear to me my day/week/mth at all does it. One of these days I will get to the bottom of this and will report back I - sorry, 'promise' just seems too strong a form of words for the effort I am likely to give it, given the effort involved and the level of satisfaction likely to be gained from a correct result :-/.

CDA site has info for copper tube. N.B., the d dimensions quoted are outside diameters (15mm, 22mm, 28mm, etc). The fluid equations mentioned above would use the inside diameters/radii.

I found a fluids textbook whilst looking for another book ( which I never did find). D'arcy equation uses an empirical factor f to describe the friction losses in turbulent flow. The difference (to Poseuille's) is due to the complexity fo turbulent flow, so that a solely analytical solution is not possible.

D'Arcy equation; h= (4fl/d) x (v^2/2g)

v = Q/area = Q/(pi d^2/4)

Substituting gives h = (4fl/d) x 16Q^2/ 2g pi^2 d^4

h = flQ^2/3.03d^5; near enough to h = flQ^2/3d^5

h = rQ^2 where r is a resistance coefficient. r =fl/3d^5.

Above gives head losses for volumetric flow rate. Pressure loss P = hg x density.

I'm sure you can figure it out further if you want to.