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Why is pressure lower where an ideal fluid moves faster through a narrow pipe?

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differential manometer, Torricellian barometer, and siphon — fluid mechanics Figure 1: Schematic representations of (A) a differential manometer, (B) a Torricellian barometer, and (C) a siphon.

In fluid mechanics, the relationship between pressure and velocity in an ideal fluid is governed by Bernoulli’s theorem. This principle states that for an inviscid, steady flow, the total mechanical energy—comprising pressure, gravitational potential energy, and kinetic energy—remains constant along a streamline.12

When an ideal fluid flows horizontally through a pipe of varying cross-section, the fluid must speed up in constricted areas to maintain a constant mass flow rate. Because the total energy is conserved, an increase in the fluid's kinetic energy (velocity) must be balanced by a corresponding decrease in the energy associated with fluid pressure.12

It is helpful to view this relationship as a cause-and-effect sequence: the pressure drop at a constriction creates the necessary pressure gradient to accelerate the fluid as it enters the narrower section. This phenomenon, where pressure is lowest where velocity is highest, is known as the Venturi effect.2