This figure shows the pressure-flow relationship for two pipes. The blue squares represent a flow of 40 °F water through a 2 inch diameter pipe, 500 feet long with total minor loss coefficients of 25, and an elevation increase of 15 feet. The yellow diamonds represent a flow of 40 °F water through a 2 inch diameter pipe, 500 feet long with total minor loss coefficients of 5, and an elevation increase of 25 feet.
The representation of a composite pipe consisting of these two pipes connected is series is created by simply adding the pressure drop at the same flow rate since the same flow passes through both pipes. This is represented by the green circles.
As discussed in the last post, each of the original pipes can be modeled very well by an equation of the form ΔP=a*Q2 + b*Q + c. If the two models are represented by ΔP1=a1*Q2 + b1*Q + c1 and ΔP2=a2*Q2 + b2*Q + c2, then the composite (series) pipe can be easily represented by ΔPseries=(a1+a2)*Q2 + (b1+b2)*Q + (c1+c2). The red line in the figure shows the parabolic fits combined in this way.
For pipes connected in parallel, the composite representation is achieved by adding the flow rates at the same pressure. This figure shows the same data as before for the two pipes with blue squares and yellow diamonds. The green circles represent the composite parallel case where the flows are added at the same pressure. Finally, each of the original pipe data sets were modeled with equations of the form: Q= g*( ΔP)0.5 + k*(ΔP)-0.5 + s. The models were combined by adding coefficients: Qparallel= (g1+g2)*( ΔP)0.5 + (k1+k2)*( ΔP)-0.5 + (s1+s2). The red line shows the two models combined in this way. Of course, for both the original data (green circles) and combined models (red line) an “if” statement is used so that the flows aren’t added until the pressure is high enough to start flow in the pipe with the larger elevation gain. This is equivalent to having appropriate check valves in the parallel pipes.
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