Final answer:
The term for the increase in water depth in a horizontal drain when receiving flow from a vertical stack is called 'backwater rise'.
Step-by-step explanation:
The term that describes the increase in water depth in a horizontal drain at the base of a stack caused by the reduced velocity of water flowing in the horizontal pipe when receiving flow from a vertical stack is known as backwater rise. This phenomenon occurs when the downward flow from a vertical stack is discharged into a horizontal pipe, causing a temporary increase in water level until equilibrium is restored through the outflow of water. This effect is particularly relevant in plumbing and civil engineering where the design of drainage systems must account for such variations to prevent potential backflow and ensure efficient water movement.