Continuity equation
Also called Equation of continuity, Continuity of flow
The continuity equation states that an incompressible fluid filling a pipe carries the same product of cross sectional area and speed everywhere along it. A narrower section therefore forces the fluid to move faster.
The AP Physics 1 sheet prints it as , and essential knowledge 8.4.A.2 says what it encodes: conservation of mass flow rate in incompressible fluids. Matter cannot pile up inside a full pipe, so whatever enters a section each second must leave it each second.
Students reliably invert the consequence, expecting a squeeze to slow the fluid down the way a crowd slows in a doorway. It does the opposite. Solve for the second speed:
Smaller area, larger speed. And the area of a circular pipe goes as the square of the radius, so halving the radius quarters the area and quadruples the speed. Factor-of-change reasoning has its own AP science practice, 2.D, so expect a question to want the ratio rather than a number.
Two conditions are doing quiet work. The fluid has to be incompressible, or density could change instead of speed, and the pipe has to be completely filled, which the AP exam conventions grant unless a question says otherwise.
Pair it with Bernoulli's equation: continuity gives you the speed at the second point, and Bernoulli then gives you the pressure there.