imagine the scenario where two pipe groups are connected in series. RG1 and RG2
RG1 Consists of two pipes R1 and R2 in Series
RG2 consists of two pipes R3 and R4 in Parallel
the diameter and surface roughness of all four pipes are equal but the length of them varies
In this scenario, water as an incompressible fluid flows through R1 and exits the network at end at R3 and R4. The flow is subject to pressure loss in the form of friction and pressure loss at Parallel T-junction in RG2.
My question is does the Volume Flow Q hence flow speed V stay constant along RG1, and for RG2 since the diameters are the same then according to continuity equation the volume flow in R3 and R4 is half as much as in RG1 ? If so, then can we calculate pressure loss by calculating Reynolds number and then friction factor for each of the segments and then sum the pressure drop of the series pipes?
Edit:
the reason for my doubt is the bernouli equation. imagine E for entry and A for exit from a pipe.
$\frac{P_E}{\rho} + \frac{W_E^2}{2} = \frac{P_A}{\rho} + \frac{W_A^2}{2} + \Delta P$
hence the flow speed W is dependant on the pressure difference across the pipes (also friction)
if possible please provide an example for demanded pressure at R1 for desired total volume flow at R4 and R3