Liquid flows through a 4.0 cm diameter pipe at 1.0 m/s. there is a 2.0 cm diameter restriction on the line. what is the velocity in this restriction?

To determine the velocity in the restriction, we need to remember the law of conservation of mass where mass in should be equal to the mass out since mass cannot be created or destroyed. For this system, mass flow rate in is equal to mass flow rate out. We do as follows:

Mass flow rate in = Mass flow rate out
density (volumetric flow rate in) = density (volumetric flow rate out)

Since the liquid in and out are the same, then density would be cancelled.
(volumetric flow rate in) = (volumetric flow rate out)
Area in x velocity in = Area out x velocity out
velocity out = area in x velocity in / area out
velocity out = π (4/2)^2 (1.0) / π (2/2)^2
velocity out = 4 m/s