Pipe A and B have a known and identical length and diameter, and are in parallel. I'm assuming the flow trough pipes A and B are also identical, as is the roughness of the pipes. Pipe C also has a known length and diameter (which is different from the diameter of pipe A/B).
I'm interested in the total head loss at the end of Pipe C. I am aware of the following Darcy-Weisbach equations that are relevant in this case (parallel and series):
Here the total headloss is the sum of the headloss per pipe, placed in series.
Here the total headloss over set of 2 parallel pipes is equal to the headloss of one of them.
But, how do I combine these two equations to retrieve the total headloss over pipes A, B and C?