[freixas]

Is air compressible? And why should we care? Air is compressible., but when analyzing the air flow through a melodica, it turns out to be very useful to be able to treat it as incompressible.

What do I mean by compressible? In fluid dynamics, gases and liquids are called fluids. In formulas, the greek letter rho (ρ)  is used to represent the density of a fluid, which is its mass divided by its volume:$$\rho = \frac{m}{V}$$

Flowing air (as in a melodica), can be treated as compressible or incompressible depending on its velocity. At low speeds (below Mach 0.3) and in an open system (where the air that flows in has one or more exits), the errors generated by treating air as incompressible are small.  Mach 1 is the speed of sound. Since the speed of sound in dry air at 20° C is 343 m/s, we can treat the air flowing through a melodica as incompressible if its velocity is 102.9 m/s (370 km/h) or less. The slower the flow, the smaller the error.

How fast does air move in a melodica? A sneeze produces about the fastest airflow from lungs and measures about 4.5 m/s. We can expect most airflow to be much less than that. This is far below 343 m/s.

To summarize: air is compressible, but when we analyze the air flow, we can treat it as incompressible in most cases because any error we get will be small.

It’s easy to confuse compressibility with pressure. Compressing or decompressing a fluid means that the same mass occupies a smaller or bigger volume. Pressure is the force a fluid exerts per unit area:$$P=\frac{F}{A}$$

Pressure comes from the kinetic energy of the molecules in a fluid, which move in random directions. If you enclose a cubic meter of air in a solid container and heat it, you will increase the kinetic energy of the molecules and raise the pressure of the fluid, but you will not change its fluid density—it will still have the same mass.

• This topic was modified 3 years, 7 months ago by freixas.

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