The Flow of Hot Water from a Distant Hot-Water Tank

When turning on a hot-water faucet, there is an expected delay in the arrival of the hot water because the cold water in the pipe between the hot-water tank and the faucet must first run out. However, there is an additional delay caused by the cold pipe cooling the incoming hot water. This note analyzes this phenomenon, with specific emphasis on how the thermal coupling between the pipe and the fluid influences the additional delay.