SME
Aerodynamics
Intro to compressibility
Use this for “At 11 km the air is 216.65 K. An airliner flies at 230 m/s. Find its Mach number.”
Diagram
M = 0.7795 < 1: each front runs ahead of the point, so no cone forms and the air ahead hears it coming.
This is an example. Type your own values to start a new problem.
a (m/s)
=
γ
×
R
×
T (K)
M
=
V (m/s)
a (m/s)
Formulas
a
=
√
1.4 × 287 ×
T
295
=
√
1.4 × 287 × 216.65
M
=
V
a
0.7795
=
230
295
Assumptions
•
Air is a perfect gas with γ = 1.4 and R = 287 J/(kg·K).
•
The speed of sound a depends on temperature only, not on pressure.
•
Mach number M is the speed in units of the local speed of sound.
Step-by-step
WE KNOW
T = 216.65 K, V = 230 m/s
FIND
speed of sound (a), Mach number (M)
Step 1 · Find speed of sound (a)
Use a = √(1.4 × 287 × T)
γ times R times the temperature, then the square root.
a
=
√
1.4 × 287 × 216.65
a
=
√
401.8 × 216.65
a
=
√
87
,049.97
a
=
295.0423
m/s
Step 2 · Find Mach number (M)
Use M = V ÷ a
Divide the speed by the speed of sound.
M
=
230
295.0423
M
=
0.7795
Check
Put the numbers back in. Both sides should match.
295.0423
=
√
1.4 × 287 × 216.65
✓
0.7795
=
230
295.0423
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Prandtl–Glauert correction of Cₚ
Use this for “At low speed, a point on a wing has a pressure coefficient Cₚ = −0.4. What is Cₚ at that point when the wing flies at M = 0.6?”
Subsonic, transonic, supersonic or hypersonic
Use this for “An airliner cruises at M 0.85. Is its flow subsonic, transonic, supersonic or hypersonic?”