Consider a cylindrical pipe with uniform cross area. If water is flowing in the downward direction then .
By equation of continuity, AV=av where A and a represent cross section areas and V and v represent velocity at A and a respectively.
Since A=a ,Equation of continuity will be
But as the water is coming in the downward direction velocity at two different points can't be equal.
Then how is this possible???
If you consider a pipe with level difference, you may need to use Bernoulli's principle
p + \rho g h + \rho v^2/2 = const,
where p is pressure at the given cross-section, \rho is the density of a fluid, h is the height of the cross-section and v is the speed of the stream throw the cross-section. It is needed because potential energy of a fluid is changed. If a fluid falls free, it cannot feel all the cross-section of the pipe according to the equation of continuity mentioned in question (and actual area of stream will be changed according to speed) or the stream will break into drops.