Inertance

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This article is about the fluid flow property. For the related mechanical property, see Inertance (mechanical networks).

Inertance is a measure of the pressure difference in a fluid required to cause a change in flow-rate with time. The base SI units of inertance are kg m−4 or Pa m−3 s2 and the usual symbol is I.

The inertance of a tube is given by:

where

is the density (with dimensionality of mass per volume) of the fluid
is the length of the tube
is the cross-sectional area of the tube

The pressure difference is related to the change in flow-rate by the equation:

where

is the pressure of the fluid
is the volumetric flow-rate (with dimensionality of volume per time)

This equation assumes constant density, that the acceleration is uniform, and that the flow is fully developed "plug flow". This precludes sharp bends, water hammer, and so on.

To some, it may appear counterintuitive that an increase in cross-sectional area of a tube reduces the inertance of the tube. However, for the same mass flow-rate, a lower cross-sectional area implies a higher fluid velocity and therefore a higher pressure difference to accelerate the fluid.

In respiratory physiology, inertance (of air) is measured in cmH2O L−1 s2.

1 cmH2O L−1 s2 ≈ 98100 Pa m−3 s2.

Using small-signal analysis, an inertance can be represented as a fluid reactance (c.f. electrical reactance)) through the relation:

where

is the frequency in Hz.

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