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2013-12-21T11:35:11Z

Construction: correcting a mistake (see talk page)

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'''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:

:<math>I = {\rho \cdot \ell \over A} \,</math>

where
:<math> \rho </math> is the [[density]] (with dimensionality of mass per volume) of the fluid
:<math> \ell </math> is the length of the tube
:<math> A </math> is the cross-sectional area of the tube

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

:<math> \Delta p = I \cdot {\dot Q} = I \cdot {\mathrm d Q \over {\mathrm d t}}</math>

where
:<math> p </math> is the [[pressure]] of the fluid
:<math> Q </math> 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]] through the relation:

:<math> X = j \omega I</math>

where
:<math>\omega = 2 \pi f</math>
:<math>f</math> is the frequency in Hz.

==References==
*{{cite book | author= Massey, B.S. | title= Mechanics of Fluids | year = 1989 | publisher=Chapman & Hall | id= ISBN 0-412-34280-4 }}

[[Category:Fluid mechanics]]

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en>D.Lazard: /* Construction */ correcting a mistake (see talk page)