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Friends, consider a pipe of uniform cross section held vertical and water flows through it top to bottom. Now if we apply equation of continouty here we find that velocity at enter or at top must be equal to velocity at exit (or bottom) because of constant cross section. O.K?

But due to gravitational acceleration velocity at bottom (exit) should be greater than that of top by an addition of (2gh)^2 (if h is differnce between enter and exit).

i.e V(bottom) = V(top) + (2gh)^2

so is continouty equation invalid here? or if I am wrong somewhere please correct me!