Consider a pipe that changes cross-section along its length, filled with an incompressible fluid in steady motion. Since the fluid does not accumulate anywhere nor appear from nothing, at every instant the same mass entering one cross-section must leave from the other. If the pipe narrows, the fluid has no choice but to flow faster to let the same amount of matter pass in the same time.
Principle — Continuity equation
For an incompressible fluid in steady motion, the product of the cross-sectional area and the velocity is conserved along the pipe:
The quantity , measured in cubic metres per second, is called the volumetric flow rate and represents the volume of fluid crossing a cross-section per unit time. The continuity equation thus states that, in an incompressible fluid, the flow rate is the same at every cross-section of the pipe: where the cross-section shrinks, the velocity increases in inverse proportion, and vice versa.
The narrowing pipe
When the pipe narrows, the fluid speeds up. This is the everyday observation of plumbing: pinching the end of a garden hose makes the jet come out faster, and a narrow tap sprays with greater speed than a wide one for the same flow rate.
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Topics: Fluidostatica e fluidodinamica
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