Opening your learning space
Starting the app …
Opening your learning space
Starting the app …
Mach number compares a flow speed with the local speed of sound.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
Ma and γ dimensionless; v,a in m/s; Rs in J/(kg·K); T in K
| Symbol | Meaning | Unit |
|---|---|---|
| Local speed ratio to sound speed | dimensionless | |
| Flow speed relative to the medium | m/s | |
| Local speed of sound | m/s | |
| Heat-capacity ratio cp/cv | dimensionless | |
| Specific gas constant and absolute temperature | J/(kg·K), K |
Ma=\frac{v}{a},\qquad a=\sqrt{\gamma R_sT}Ma=v/a is the definition. a=√(γRsT) applies to a calorically perfect gas in local thermodynamic equilibrium. Mach number depends on local sound speed, so the same velocity at another temperature gives a different Ma. Ma<1 is subsonic and Ma>1 supersonic; transonic effects do not begin at one universal sharp boundary for an entire flow field.
Ma=v/a is the definition. a=√(γRsT) applies to a calorically perfect gas in local thermodynamic equilibrium. Mach number depends on local sound speed, so the same velocity at another temperature gives a different Ma. Ma<1 is subsonic and Ma>1 supersonic; transonic effects do not begin at one universal sharp boundary for an entire flow field.
Mach number compares a flow speed with the local speed of sound.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Mach number” and check its unit and magnitude.
Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Ma and γ dimensionless; v,a in m/s; Rs in J/(kg·K); T in K.
Formula cluster
Mach number compares a flow speed with the local speed of sound.
Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic.
Classify compressibility and flow regimes in nozzles, aircraft and gas systems.
Here is how to work through a typical Mach number (Ma = v/a) task step by step:
Task
Work through the numerical example for “Mach number” and check its unit and magnitude.
Solution path
Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic.
Mach is a ratio of two speeds and is therefore dimensionless. Ma=0.8 means the object or fluid locally moves at 80 percent of sound speed. Without a value for a, it does not determine a speed in m/s. Mach uses local sound speed; the ideal-gas expression depends on the stated gas model. Application: Classify compressibility and flow regimes in nozzles, aircraft and gas systems. The numerical example Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic anchors the idea in a concrete measurement case.
In an ideal gas, small pressure disturbances propagate according to compressibility and density. For a calorically perfect gas, a=√(γRsT); higher absolute temperature raises a. Real-gas states or strong thermal nonequilibrium may require a more detailed property model. Mach uses local sound speed; the ideal-gas expression depends on the stated gas model. The corresponding units are Ma and γ dimensionless; v,a in m/s; Rs in J/(kg·K); T in K. Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic. This checks that the reference quantities are compatible.
Ma=1 is the local sound speed. A real flow may be subsonic in one region and supersonic in another; “transonic” often describes a region containing both and possibly shocks. Local Mach number and geometry are more informative than one global value. Mach uses local sound speed; the ideal-gas expression depends on the stated gas model. Scope: Ma=v/a is the definition. a=√(γRsT) applies to a calorically perfect gas in local thermodynamic equilibrium. Mach number depends on local sound speed, so the same velocity at another temperature gives a different Ma. Ma<1 is subsonic and Ma>1 supersonic; transonic effects do not begin at one universal sharp boundary for an entire flow field. A practical application is Classify compressibility and flow regimes in nozzles, aircraft and gas systems.
Write the quantity and unit from the variable list next to every value: Ma and γ dimensionless; v,a in m/s; Rs in J/(kg·K); T in K. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example Air with local a≈340 m/s at 20 °C flows at 170 m/s: Ma=170/340=0.50, half the sound speed and subsonic. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Mach uses local sound speed; the ideal-gas expression depends on the stated gas model.
The background states this starting condition: Ma=v/a is the definition. a=√(γRsT) applies to a calorically perfect gas in local thermodynamic equilibrium. Mach number depends. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Mach uses local sound speed; the ideal-gas expression depends on the stated gas model.
Quanta exam set
Curated exam set for "Mach number":
Question (front)
Which formula describes Mach number?
Answer in your set
Question (front)
How do you rearrange Mach number for Base equation for the target quantity?
Answer in your set
Question (front)
Which common mistake happens with Mach number?
Answer in your set
+ 8 more cards: units, variables, derivation, example, exam task
The formula set contains 11 cards. After importing, review them and start practicing; your ratings determine later review intervals.
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
Create a curated FSRS exam set for Ma = v/a: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential