Volume Velocity of a Gas
The volume velocity of a gas flow is defined as particle
velocity
times the cross-sectional area
of the flow, or




When a flow is confined within an enclosed channel, as it is in an
acoustic tube, volume velocity is conserved when the tube
changes cross-sectional area, assuming the density remains
constant. This follows directly from conservation of mass in a flow:
The total mass passing a given point
along the flow is given by
the mass density
times the integral of the volume volume
velocity at that point, or

As a simple example, consider a constant flow through two cylindrical
acoustic tube sections having cross-sectional areas and
,
respectively. If the particle velocity in cylinder 1 is
, then
the particle velocity in cylinder 2 may be found by solving


It is common in the field of acoustics to denote volume velocity by an
upper-case . Thus, for the two-cylinder acoustic tube example above,
we would define
and
, so that

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Pressure is Confined Kinetic Energy
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Particle Velocity of a Gas