Apump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe. what is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? treat the fluid as ideal and incompressible.

The important point here is that volumetric flow rate in the pump and the pipe is the same.

Q = AV, where Q = Volumetric flow  rate, A = Cross sectional area, V = velocity

Q (pump) = (π*15^2)/4*2 = 353.43 cm^3/s
Q (pipe) = (π*(3/10)^2)/4*V = 0.071V

Q (pump) = Q (pipe)
0.071V = 353.43 => V = 5000 cm/s

Therefore, the flow  of water in the pipe is 5000 cm/s.