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

where denotes position along the flow, and denotes time in seconds. Volume velocity is thus in physical units of volume per second (m /s).

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

for .

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

would express the conservation of volume velocity from one tube segment to the next.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University