Inertance
Encyclopedia
Inertance is a measure of the pressure gradient in a fluid required to cause a change in flow-rate with time. The unit of inertance is Pa m−3 s2 and the usual symbol is I.
For a circular tube the inertance is given by:
where
The pressure gradient is related to the change in flow-rate by the equation:
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 gradient to accelerate the fluid.
The equation assumes constant density, that all parts of the fluid undergo the same acceleration and that the flow is fully developed (turbulent) "plug flow". This precludes sharp bends, water hammer and so on.
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:
where
is the frequency in Hz.
For a circular tube the inertance is given by:
where
- ρ is the densityDensityThe mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
(in units of kg / m3) of the fluid - ℓ is the length (in units of meters) of the tube
- A is the cross sectional area (in units of m2) of the tube
The pressure gradient is related to the change in flow-rate by the equation:
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 gradient to accelerate the fluid.
The equation assumes constant density, that all parts of the fluid undergo the same acceleration and that the flow is fully developed (turbulent) "plug flow". This precludes sharp bends, water hammer and so on.
In respiratory physiology
Respiratory physiology
Respiratory physiology is the branch of human physiology focusing upon respiration.Topics include:-Volumes:* lung volumes* vital capacity* functional residual capacity* dead space* spirometry* body plethysmography* peak flow meter-Mechanics:...
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
Reactance
Reactance is the opposition of a circuit element to a change of electric current or voltage, due to that element's capacitance or inductance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current...
through the relation:
where
is the frequency in Hz.