Explanation:
In order to solve this question you need to be familiar with two physical formulas:
(1) The continuity equation
(2) The volumetric rate of flow eqaution
According to the continuity equation:
Intial rate of flow = final rate of flow
In this case, the inital rate of flow refers to when the water entered the pipe, and the final rate of flow refers to when the water exited the pipe.
According to the volumetric flow rate formula:
The volumetric rate of flow = velocity X area
We know that the amount of water didn't change along the pipe, however the area did. At each point, the pipe's cross-section is the area through which the water flows. In order to maintain the equation, if the area is smaller then the velocity must be greater. Since the cross-section of B is smaller than of A, the velocity in side B must be proportionately greater than the velocity in side A.