What is the difference / relationship between inertia and inertance in
a fluid dynamics context (eg, fluid inertia and not acoustic
inertance)?

Can one properly say that fluid inertia is equal to the length of a
segment of a tube carrying a liquid divided by the cross sectional
area of the tube (possibly expressed as "I=L/A"?

Inertance is a measure of the inertia of a fluid.

The following reference derives the formula for fluid inertance
(called "inductance" in the reference) as being (rho)l/(pi)R^2 where
rho is the fluid's density, l is the length of the tube, and (pi)R^2
is the tube's cross-sectional area.  Your formula was very close, but
it omits the fluid's density.  In addition, L is commonly used as the
symbol for a fluid's inertance rather than for the length of the tube.

"Duality" by Steven A. Jones, Louisiana Tech University
http://www2.latech.edu/~sajones/Senior%20Design%20Web%20Pages/Homework%2010%20on%20Duality.htm

The substitution of (rho)l(pi)R^2 for the fluid's mass m is explained
in the following reference:

"The Simple Harmonic Oscillator" Physics 36 / Music 36 Duke University
(Spring 2005) http://www.phy.duke.edu/~dtl/36h4_sho.html

Other potentially useful references are:

"Hydraulic Ram" by Neville Hogan, Integrated Modeling of Physical
System Dynamics (1994)
http://ocw.mit.edu/NR/rdonlyres/Mechanical-Engineering/2-141Fall-2002/5242E7CD-1E31-44AE-A13D-DAB1EF25EC7A/0/hydraulic_ram.pdf

"Tutorial 1-Creating Models of Engineering Systems" by D. J. Dunn,
Instrumentation and Control http://www.freestudy.co.uk/control/t1.pdf

Sincerely,

Wonko

Search Terms: fluid inertia inertance

Thanks.  Wonko found information that I hadn't even after a fairly thorough search .

"Can one properly say that fluid inertia is equal to the length of a
segment of a tube carrying a liquid divided by the cross sectional
area of the tube (possibly expressed as "I=L/A"?"

I would answer "no" to this question.  Inertia describes the
resistance of a body to changing its state of motion.  The inertia of
an object is proportional to its mass--you have to apply a larger
force to change the velocity of a concrete truck than to change that
of a matchbox car.  So, I would say that the inertia of the fluid in a
tube is proportional to its mass, or rho*L*A (that's density times
length times cross-sectional area).

"What is the difference / relationship between inertia and inertance in
a fluid dynamics context?"

Inertance, as you have defined it, is analogous to inertia, but
instead of describing how much FORCE is required to bring about a
given change in VELOCITY in a given time, it describes how much
PRESSURE is required to bring about a given change in RATE OF FLOW in
a given time.

Your formula, "I=L/A", is appropriate for the case where you measure
rate of flow by the MASS of fluid that passes through the tube per
unit time.  Wonko's formula, "I=rho*L/A", is the one to use if you
measure rate of flow by the VOLUME of fluid that passes through the
tube per unit time.

So if you want to use your 'inertance' to determine, say, how much
pressure will be required to change the flow rate through your tube
from 1 kg/sec to 3 kg/sec in 5 seconds, you should use I=L/A.  If you
want to use it to determine the pressure required to change the flow
rate from .001 m^3/sec to .003 m^3/sec, you need to know the density
of the fluid, and you should use I=rho*L/A.