# Mach Number Formula

In fluid dynamics, the Mach number (M) named after Ernst Mach is a dimensionless quantity which describes the ratio of the flow of velocity past a boundary to the local speed or sound; wherein c is the speed of the sound in the medium.It shows how fast the object can move if it is moving equally or faster than the speed of the sound.

The Mach number formula is expressed by,

Mach number = Object Speed / Speed of Sound

This term is commonly applied in aeronautics when two objects move at high speed for e.g., wind channels and nozzles. The speeds of sound are termed on the basis the mach numbers.

If the Mach number < 1, the speed is said to be subsonic.

When the Mach number ∼ 1, the speed is transonic.

If the Mach number >1, the speed is supersonic

If the Mach number >>>, the speed is hypersonic.

Example 1

The speed of the aircraft is 800 ft/sec, determine the Mach number.

Solution:

Given:

speed = 800 ft/sec,

speed of sound = 980 ft/s.

Mach number formula is given by,

Mach number = Speed of Object / Speed of sound

Mach number = 800 / 980

Therefore, Mach number = 0.816

Hence, the speed is subsonic.

Example 2

If the Mach number is 1.15, determine the speed of the object.

Solution:

Given:

Mach number M = 1.15,

speed of sound = 980 ft/s

Mach number formula is given by,

Mach number = Speed of Object / Speed of sound

Speed of object = Mach number × Speed of sound

= 1.15 × 980 ft/sec

Therefore, Speed of object = 1127

Hence, the speed is supersonic.