Mach Number Calculator
Calculate Mach number and determine compressible flow regimes
Calculate Mach Number
Speed of the moving object
Temperature affects the speed of sound: c = 331.3 × √(1 + T/273.15)
Mach Number Results
Formula: M = v/c
Input values: v = 0.0 m/s, c = 343.2 m/s
Flow Analysis
Example: Commercial Aircraft at Cruise
Problem
Aircraft: Boeing 747 cruising at 31,000 ft
Flight speed: 490 knots ≈ 252 m/s
Temperature at altitude: -46°C
Find: Mach number at cruise conditions
Solution
Step 1: Calculate speed of sound at -46°C
c = 331.3 × √(1 + (-46)/273.15) = 301.8 m/s
Step 2: Apply Mach number formula
M = v/c = 252/301.8 = 0.835
Result: Mach 0.835 (High Subsonic)
This is typical for commercial aircraft cruise conditions.
Flow Regimes
Speed of Sound vs Temperature
Applications
Aerospace
Aircraft design, flight performance
Space Technology
Rocket propulsion, re-entry vehicles
Gas Dynamics
Compressible flow analysis
Physics Tips
Mach number is dimensionless (no units)
Speed of sound increases with temperature
M = 1 defines the "sound barrier"
Compressibility effects become significant at M > 0.3
Understanding Mach Number
What is Mach Number?
The Mach number is a dimensionless quantity that represents the ratio of the speed of an object to the speed of sound in the surrounding medium. Named after physicist Ernst Mach, it's crucial for understanding compressible flow behavior and determining when compressibility effects become significant in fluid mechanics.
Physical Significance
- •Determines flow compressibility characteristics
- •Classifies flow regimes and shock wave formation
- •Critical for aerospace and high-speed applications
- •Independent of object size - only depends on speed ratio
Mach Number Formula
M = v/c
- M: Mach number (dimensionless)
- v: Object velocity (m/s)
- c: Speed of sound in the medium (m/s)
Speed of Sound Formula
c = 331.3 × √(1 + T/273.15)
Where T is temperature in Celsius
Historical Milestones
- • 1947: Chuck Yeager breaks sound barrier (Bell X-1)
- • 1976: Concorde enters supersonic service
- • 1976: SR-71 reaches Mach 3.3 (speed record)
- • 2004: NASA X-43A reaches Mach 9.6
Note: At high Mach numbers (M > 5), additional phenomena like chemical reactions and plasma formation become important.