Question

you need to extend a 2.50 inch diameter pipe, but you only have 1.00 inch diameter pipe on hand.you make a fitting to connect these pipes end to end. if the water is flowing at 6.00cm/s in the wide pipe, how fast will it be flowing through the narrow one?

Answer 1

According to what is called the continuity equation, the product of
(density)(cross sectional area)(velocity)
is a constant in steady-state flow.

For a liquid such as water, you can assume that the density is constant.

Therefore A*V = constant
Since Area is proprtional to diameter ^2,

D^2*V = constant

Now do the numbers.