If a fluid is incompressible and flows through a pipe that narrows, what happens to its speed?

In fluid dynamics, when dealing with an incompressible fluid flowing through a pipe that narrows, the principle of continuity is at play. According to this principle, the mass flow rate must remain constant from one cross-section of the pipe to another. This means that the product of the cross-sectional area of the pipe and the fluid's velocity must be constant.

When the pipe narrows, the cross-sectional area decreases. Since the mass flow rate must remain the same, the fluid must compensate for this decrease in area by increasing its velocity. Therefore, the speed of the fluid increases as it flows through the narrower section of the pipe. This relationship is fundamental to fluid mechanics and is governed by the continuity equation, which states that A1V1 = A2V2, where A is the area and V is the velocity.

In this scenario, the correct understanding of how incompressibility and pipe geometry influence fluid speed highlights why the speed increases as the fluid is forced through a narrower passage.