The calculation of flow rates in the piping-network is ordinarily made by Hardy-Cross' method or by the analog computer which is set specially for these purposes. Such a treatment is unconfortable when the losses at branches can not be neglected any more. The analog computer must have a plenty of function generators which characterize the pipe branches and we must also recognize that the analog computer has the lower accuracy compared with the digital-computer. In the calculation with the Hardy-Cross' method we must assume the direction of current in the mesh of the network. For the case where the branch-losses are included the character of branches can not be determined. But the treatment which is made here analogous to the knodeanalalysis in the electronics fits for such a case where the branch-losses are included in the network. The setting of the equations and the calculations are done very simply and systematically and by using the digital computer we can save the time and labor even if we must have a complication by the iteration method.