This study is especially regarding the flow hydraulics in the network of water supply pipes. Water pressure requirement is the guiding principle of this study of water supply distribution network. Continuity of flow is the simultaneous happening required to be implemented into it along with that. Besides, the other flow-variables such as velocity, length of flow, pipe bed slopes etc. remain in their own degree of presence, directly or indirectly. So far, design of the pipe network is done by the Darcy-Weisbach & Hazen-Williams equation, following the famous Hardy-Cross method – these are conventional. In this study, formulations required for the network design have been developed in a new way of new invisionary mathematical exploration. Innovative applications of flow-mechanics, including ‘differential’ presence, have been applied to determine the flow equation of subjection. And, lastly, it has been shown how to obtain utilization of the derived equations by giving a simple but