An efficient water supply management system can be one of the applications of the Internet of Things (IoT). Water is a basic physiological need, and smart management of water plays a significant role in a smart city. This paper focuses on a mathematical model and IoT framework that aid in developing a smart city. A framework is developed for water supply management. The efficiency of the water supply can be measured by monitoring leakage conditions, overflow of water, automatic meter reading and online bill payments, and water consumption status of households, community, state, and eventually the whole country as well as the automatic water supply line cut-off. The system where the IoT is being deployed consists of embedded hardware in which sensors and microcontrollers provide messages and gain feedback from each other with the help of the internet, and this process can not only be monitored but also can be controlled from a remote location. The developed framework addresses all these aspects and mathematical equations are used and formulated while developing the IoT application. The mathematical equations are concentrated on consumption level (CL), leakage reporting (LR), and bill amount (BA) based on consumption. These become the point of contact for deploying IoT and eventually a framework is developed. This framework can be useful not only in water supply management but also in the management of road traffic, pollution, garbage, home automation and so on. In a nutshell, this paper illustrates the usage of the IoT framework in water supply management which contributes to developing the smart city.