Linear System (Water distribution in a city)

In every city there seems to be a water distribution system that governs the flow of water through out the city. In this distribution system, water flows at a steady rate. This implies that the rate of flow of water into the system equals the rate of flow of water out of the system. The conservation principle of this system will be the conservation of momentum. Modeling this system derives a differential equation that can be used to determine the amount of water in the city with respect to time. Next, a governing equation that will determine approximately the amount of water in the city at any time in years can be derived. On the other hand, a network of water distribution in the city can be designed. With a network, several equations can be computed with the unknowns being the amount of water flowing through a specific node (company, household, water station). Here, the various equations with its unknowns can be computed into the linear system equation Ax = b (Matrix form) and be computed.