Step 1: Central administration: The Vijayanagara Empire (founded 1336) was headed by a king with substantial centralized authority, assisted by ministers; the empire was divided into provinces (nayankara/rajya) administered by military chiefs called 'nayakas,' who collected revenue and maintained troops in return for their assignments.
Step 2: The Nayaka system: Nayakas held considerable local autonomy in practice, controlling land revenue and local militias, somewhat similar in structure to the later Mughal jagir/mansab arrangement, which sometimes created tension between central and local power.
Step 3: Water management: importance: Since the Vijayanagara region receives relatively low and seasonal rainfall, effective water management was essential to sustain its large urban population and agriculture.
Step 4: Water systems built: The rulers and elite built an extensive network of tanks (reservoirs), canals, and wells; notable structures include the Kamalapuram tank (which supplied water to the royal centre via a channel) and the Hiriya canal, drawing water from the Tungabhadra river to irrigate agricultural tracts around the capital.
Final Answer: Vijayanagara combined centralized kingship with a semi-autonomous nayaka provincial system, and sustained its dry-zone capital through an advanced network of tanks and canals (like the Kamalapuram tank and Hiriya canal) drawing on the Tungabhadra.