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?


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

  • $\begingroup$ So conservation of mass: what goes in must come out, unless there is another hole... $\endgroup$
    – Solar Mike
    Jul 3, 2023 at 14:00
  • $\begingroup$ i added more information why im confused about this $\endgroup$
    – Ali
    Jul 3, 2023 at 14:05

1 Answer 1


Flow (speed or mass flow rate) is dependent on the TOTAL head loss.

Clearly flow can't change inside the system - the same fluid that goes into the series portion also goes into the parallel section. You can either calculate the flow from the total pressure drop or the pressure drop if you know the flow.

You can use equations to do this, but most engineers are going to use tables based on the type of pipe and add equivalent lengths of transitions, and elbows.

  • $\begingroup$ calculation of pressure loss for each pipe requires first the calculation of the average flow speed in that pipe. for example in this case the the flow speed ind R2 is different than in R1 therefor the exit speed from R1 should be taken as input speed in R2. how can one calculate this for a whole set ? $\endgroup$
    – Ali
    Jul 3, 2023 at 14:54
  • $\begingroup$ If you are choosing the hard way to use equations then it's a set of simultaneous equations with P-out for the 1st equal to p-in for the second. $\endgroup$
    – Tiger Guy
    Jul 3, 2023 at 14:58
  • $\begingroup$ I'm trying to calculate this for a large network (50 parts). i couldn't find a free software which could do this. neither an excel sheet so ive been developing my own. but for that im stuck in the first step of bernouli equation because i dont know what proportion of pressure loss affects speed and how much affects the static pressure loss $\endgroup$
    – Ali
    Jul 3, 2023 at 15:03
  • $\begingroup$ Then set it up using CFD. $\endgroup$
    – Solar Mike
    Jul 3, 2023 at 15:21
  • $\begingroup$ If you don't know either total pressure drop or the flow rate you will have to iterate your way there. I promise you don't have to use software to do this, people built oil refineries before flow calc software. $\endgroup$
    – Tiger Guy
    Jul 3, 2023 at 15:27

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