Final answer:
The continuity equation governs fluid flow and dictates that for a constant flow velocity, if the radius of a pipe or jug decreases, the volume of water must increase to maintain the same flow rate.
Step-by-step explanation:
According to the principles of fluid dynamics and the continuity equation, for an incompressible fluid like water, the product of the cross-sectional area (A) of a pipe or tube and the velocity (V) of the fluid flow must remain constant along the pipe. Therefore, if the radius of the jug or tube decreases, the cross-sectional area decreases. For the velocity to remain constant under these conditions, the volume of water in the jug must increase to maintain the same flow rate, as the equation of continuity states that A₁V₁ = A₂V₂, where subscript 1 denotes the initial state and subscript 2 denotes the final state.
If the radius decreases, creating a smaller cross-sectional area, A₂, with the same flow velocity V, the volume flow rate (Q), which equals A·V, would become less unless the amount of water (therefore volume) increases to compensate for the reduced area.