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Case (a) series

This case can be solved by considering the quantities shown in the figure below:

Therefore,

which means

Case (b) parallel

The approach is similar to case (a). With reference to the figure below,

Considering the flow law,

which gives

or also

which means

Case (c) series–parallel

In this case, the reference schematic is shown below:

Pipe A is in series with B and C, which are in parallel. Using the relations derived above:

which means