As a start do the following:
1- check the flow region either Turbulent or Laminar
Re= (de.*vel.* Dia / vis.)
Turbulent Re > 2000
Laminar Re < 2000
constants usually given Q, de. ,vis.
Guess Dia
vel. = Q/A where A= pi/4 Dia^2
2- A) use Fanning's equation for Re> 2000
delta P = (4*f)(L/Dia)(de.* vel.^2/2)*10^-5
B) use Hagen-Poisuille's eqaution for Re <2000:
delta p = (32)(vis.* vel.*L/Dia^2)10^-5
where L is pipe length (straight)
Note all units are in SI
3- Calculate delt P resulting from fittings i.e. elbows..etc using isometric drawing
4- Find the total pressure drop of the system that is
delt P of the straight length + delt P of the fittings
5- If the resulting pressure drop matches your system pressure drop requirement then, the guess Dia is the line Diameter
6- If step 5 is not correct try another Dia to satisfy your required pressure drop
7- Other criteria if not pressure drop is of a concern, i.e, there is no anchor point in the system, you might be limited with velocity requirements, if so, follow steps 1 to 4 and check the velocity result
I hope this would help you in understanding the piping hydraulic calculations since this is what the eng. offices are doing for designing a plant but via their own software for the whole plant with many integrated piping,
what you can do is to develop a spreadsheet with steps I mentioned and you will benefit a lot
Regards