A method for the mathematical solution of the flow distribution in a parallel fluid flow system with consumption in branch pipes has been developed. Assume that the flow restriction coefficients and the consumption in any branch pipe are the same

and that the flow is laminar and the variation of hydrodynamic pressure is neglected

then the flow in the branch pipe can be expressed in the following form. (gi+1 - gi)- (gi - gi-1) = 2Rgi - Rgo By transforming it into differential equation d2y/dx2-2Ry =0 where y=gi-1/2 go

x = i we obtain the general solution as follows: gi = C1e where the constants of integration C1

C2 can be directly calculated from the following formulas: C1 = (DB - FG) / (EB - FA) C2=(DB-C1EB)/(FB) where D=R(n-1) for the downstream-system (the system with same direction at its entry and exit). D=R(n-1) (2-k) for the upstream-system (the system with opposite direction at its entry and exit). The results obtained by using the usual method and the new method are the same

while the latter is much more simple and accurate.