This study has explained a method of solution of general flow problem by mathematics. The flow-problem is the Darcy-Weisbach formula of the head-loss, i.e., HL=KQx. This equation has been transformed into the Leibnitz’s form of the differential equation & then solved subsequently, considering suitable functionary variables for the derivation as applicable. This way of solution takes the feature of inner variables of a problem to limelight which might not achieve the breakthrough instead by any other way of the available solution in mathematics. Ultimately, in this study, the flow-correction has got to be a different dimension by the mode of application of mathematics. With the final form of the differential solution, the head-loss estimation has been adjusted for the loops in a distribution network in order to get the given flows passing through the pipe-loops made into the subsequent corrected values. Future scope of this study is enormous; the following up of this study’s initiative proceeding for the numerous subjective fields of concern & lastly not the least indeed, the further research on the outcomes determined in this study by such application of the mathematical passage to go to finding out its further implication.
Head-loss, Pipe-flow, Darcy-Weisbach Equation, Leibnitz’s differential form, Flow-correction, Distribution network, Water supply
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