5 ms·

Mach value is lower for lower pressure, about 250 m/s for hyperloop proposal

krasin 13y ago
Wolfram Alpha disagrees. It says: Mach(20 C, 1 atm): 343.051 m/s Mach(20 C, 0.1 atm): 343.182 m/s Not much higher, but definitely not lower. http://www.wolframalpha.com/input/?i=speed+of+sound+in+dry+air+at+20+C+and+0.1+atmosphere+pressure http://www.wolframalpha.com/input/?i=speed+of+sound+in+dry+a... Unfortunately, it refuses to show Mach(20 C, 0.001 atm), since the lowest supported pressure is 0.098 atm.
- krasin 13y ago
  There's still a chance that Wolfram Alpha is incorrect; I am unable to prove or disprove that, because I don't know aerodynamics.
  - lutusp 13y ago
    The problem is that atmospheric Mach numbers don't follow from first principles, and the Wolfram Alpha values emanate from an empirically derived approximation. An analytical relationship between the speed of sound and air pressure arising from first principles would require a solution to the Navier-Stokes equations, for which solution a million dollar prize lies unclaimed: http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations Quote: "The Navier–Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have not yet proven that, in three dimensions, solutions always exist (existence), or that if they do exist, then they do not contain any singularity (smoothness). These are called the Navier–Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize for a solution or a counter-example." > There's still a chance that Wolfram Alpha is incorrect ... At the moment there is no "correct". It's all based on field observations, numerical modeling, and estimation.
- VladRussian2 13y ago
  You are right, my bad with the low pressure speed of sound . Anyway the high transonic flow isn't a piece of cake as well.
- DonPedro 13y ago
  I'll go out on a limb here and wager that SpaceX engineers know the Mach value for various permutations of temperature and air density. But I might be wrong...

Wolfram Alpha disagrees. It says: Mach(20 C, 1 atm): 343.051 m/s Mach(20 C, 0.1 atm): 343.182 m/s Not much higher, but definitely not lower. http://www.wolframalpha.com/input/?i=speed+of+sound+in+dry+air+at+20+C+and+0.1+atmosphere+pressure http://www.wolframalpha.com/input/?i=speed+of+sound+in+dry+a... Unfortunately, it refuses to show Mach(20 C, 0.001 atm), since the lowest supported pressure is 0.098 atm.

krasin 13y ago
There's still a chance that Wolfram Alpha is incorrect; I am unable to prove or disprove that, because I don't know aerodynamics.
- lutusp 13y ago
  The problem is that atmospheric Mach numbers don't follow from first principles, and the Wolfram Alpha values emanate from an empirically derived approximation. An analytical relationship between the speed of sound and air pressure arising from first principles would require a solution to the Navier-Stokes equations, for which solution a million dollar prize lies unclaimed: http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations Quote: "The Navier–Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have not yet proven that, in three dimensions, solutions always exist (existence), or that if they do exist, then they do not contain any singularity (smoothness). These are called the Navier–Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize for a solution or a counter-example." > There's still a chance that Wolfram Alpha is incorrect ... At the moment there is no "correct". It's all based on field observations, numerical modeling, and estimation.
VladRussian2 13y ago
You are right, my bad with the low pressure speed of sound . Anyway the high transonic flow isn't a piece of cake as well.
DonPedro 13y ago
I'll go out on a limb here and wager that SpaceX engineers know the Mach value for various permutations of temperature and air density. But I might be wrong...