For an incompressible fluid flowing in a line of pipes and pumps in series

Bernoullis equation can be effectively applied to solve any particular flow problem. When the pipe system consists of a number of complicated branches and cycles

a systematic method for the analysis of the flow system is yet in need. In this article

by transforming the general formula of the pressure drop in pipes into the form

of linear element with respect to flow rate

and further

by introducing the idea of a "complete stream"

a set of simultaneous linear equations can be obtained. Such equations can then be represented in the form of matrix

which

besides presenting the equations in a regular form

also makes possible the solution by using digital computers.