At what minimum speed (in mph) would an automobile have to travel for compressibility effects to be important? Assume the local air temperature is 60F.
This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
The key idea is that compressibility effects tend to be important when the flow Mach number exceeds 0.3 (this is not a magical number it is a rule of thumb). For an automobile, this means that the speed must be at least
U = 0.3\,a\,,
where a is the local speed of sound.
At 60°F the local temperature in Kelvin is
T = \frac{60-32}{1.8} + 273.15 \approx 289\,K\,.
For calorically perfect air,
a=\sqrt{\gamma RT}=\sqrt{1.4\times287\times289}\,.
Calculating,
287\times289\approx82943\quad,\quad 1.4\times82943\approx116120\,,
so
a\approx\sqrt{116120}\approx340\,m/s\,.
Thus the threshold speed is
U = 0.3\times340\approx102\,m/s\,.
Converting to miles per hour using 1\,m/s\approx2.23694\,mph,
U\approx102\times2.23694\approx228\,mph\,.
Therefore, an automobile would have to travel at a minimum speed of approximately 228 mph for compressibility effects to be important. That’s Bugatti/Koenigsegg/McLaren territory. SSC Tuatara. Yangwang U9.
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their significance below. If they are marked as relevant, I encourage you to take a look at them:
Textbook sections:
- Chapter 5 Engineering Models: Incompressible Flow (RELEVANT)
- Chapter 1.3: Acoustics and Compressible Flow (RELEVANT)
- Chapter 8 Engineering Models: Incompressible Flow (RELEVANT)
- Chapter 7 Engineering Models: Incompressible Flow (RELEVANT)
- Chapter 1.6: Shock waves (RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.