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freixas
Keymaster

This topic relies on background information in The Compressibility of Air and Mass Flow, Speed, and Pressure.

Most of the information in this post comes from an article titled Air speed and blowing pressure in woodwind and brass instruments. I have summarized it and adapted it for melodicas.

# Air Speed

For working purposes, we can estimate that when we play the melodica, the volume flow rate from our lungs is around 0.1 to 1 liter per second. We might be able to produce a flow of 5 L/s for a very brief time. This estimate is the same as for any instrument since it depends on our lungs. In talking with a flute player, she remarked on how long I was able to play on a single breath, so perhaps the typical flow rates for melodicas lean more to the low end than the high.

As covered in the background articles listed above, the speed of the flow is dependent on the cross section of the passage. I measured some mouthpieces that I own:

• The tube mouthpiece has a rectangular entrance 12 mm x 2.8 mm for an area of 33.6 mm2.
• The same tube has a circular exit with a diameter of 10 mm for an area of about 78.54 mm2.
• My “trumpet” mouthpiece has a circular entrance with a diameter of 20 mm that quickly narrows to a diameter of 7.5 mm. The respective areas are 314.12 mm2 and 44 mm2.

We can convert flow rates to cross-sections to air speeds using these formulas: $$\begin{gather*} V &= Avt \\ v &= \frac {V}{At} \\v &=\frac{V}{A}\end{gather*}$$ $V$ is the volume in liters, $A$ is the cross-section in m2, $v$ is the velocity in m/s, and $t$ is the time (t=1 for a flow rate measured in L/s, when we want a velocity in m/s).

So for a flow of 01. to 1 L/s:

• Tube entrance: 2.95 to 29.5 m/s.
• Tube exit: 1.27 to 12.7 m/s.
• Trumpet entrance: 0.318 to 3.18 m/s.
• Trumpet narrows: 2.27 to 22.7 m/s.

The trumpet mouthpiece numbers are a bit deceptive. You would rarely, if ever, use the full area—your lips narrow the opening. If you limited your lips to a tiny area of 2 mm2, for example, the air speed could range from 50 m/s to 500 m/s, although it is very unlike you could achieve the latter number, as it exceeds the speed of sound.

While interesting, the speeds at the entrance aren’t relevant—the volume flow rate is. Speeds throughout the instrument vary depending on the area of the cross-section it flows through, and the variation is simultaneous. So when you blow at a tube’s entrance at 2.95 m/s, the air flows out the tube at 1.27 m/s.

# Pressure

I’ll copy this directly from the article I cited, since the author claims that these are measured pressures and are unlikely to vary from one wind instrument to another since they are based on the lungs, not the instruments:

“Measured blowing pressures usually range between 1 to 10 kilopascals (kPa) or 1% to 10% of atmospheric pressure”.

My interpretation of this is that the author is talking about relative pressure, the pressure difference from atmospheric pressure (which is about 101.325 kPa).

# Power

I’ll copy one more section, because I find it interesting:

“…the range of power provided by the player’s breath to the instrument: here that gives 0.1 to 10 watts. This overestimates the range in practice, however, because high notes, which require higher pressure on most instruments, are usually played with lower flow, so power over a watt is rare. Instruments have typical efficiencies of only 1% or so, so the output sound power is usually measured in milliwatts. However, one milliwatt at one meter distance gives about 80 decibels…”

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