FLD-09

Mach number

M = v / c. Subsonic, transonic, supersonic as M crosses 1.

Reading speed

FluidsMach

Governing equation

M=v/c

$v \in \left[1, 2000\right]$

where

v: Speed (m/s)
c: Sound speed (m/s)
M: Mach (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

M=v/c

$v \in \left[1, 2000\right]$

$v = 1$ $M = 0.003$

Along the curve

②

Domain of the variable — blue

v_{\min} = 1,\quad v_{\max} = 2000

$v \in \left[1, 2000\right]$

$v = 1$ $v = 1$

Along the curve

③

Response curve — green

M=v/c

$v \in \left[1, 2000\right]$

$v = 1$ $M = 0.003$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}M}{\mathrm{d}v}

$v \in \left[1, 2000\right]$

$v = 13.57$ $M^{\prime} = 0.003$

Along the curve

Lecture brief

Historical brief

Bernoulli, Navier–Stokes, Reynolds (1883) and Stokes drag made continuum flow a dimensionless craft. The sheets compute head, drag, Re and a pedagogical NS snapshot. This sheet (FLD-09 — Mach number) is the form associated with Mach. Working symbols: $v$ , $c$ $\rightarrow$ $M$ . c = √(γ R T) in an ideal gas. Compressibility corrections start near M ≈ 0.3.

Purpose

Purpose: compute

M

from

v

c

in Fluid physics via

M=v/c

M = v / c. Subsonic, transonic, supersonic as M crosses 1. Use it when a real fluid physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

v = 250.000\,\mathrm{m/s}

c = 340.000\,\mathrm{m/s}

, the governing relation

M=v/c

yields

M = 0.735\,\mathrm{—}

. A body, a Mach cone, a bow shock. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed v250 m/sSound speed c340 m/s

Outputs

Mach M0.735 —

Reading speed

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Narration of this film

A body, a Mach cone, a bow shock.

c = √(γ R T) in an ideal gas. Compressibility corrections start near M ≈ 0.3.

Reading speed

Watch on YouTube