FLD-17

Speed of sound

c = √(K/ρ). Newton–Laplace speed in a compressible fluid.

Reading speed

FluidsNewton–Laplace

Governing equation

c=\sqrt{K/\rho}

where

K: Bulk modulus (GPa)
\rho: Density (kg/m³)
c: Sound speed (m/s)

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-17 — Speed of sound) is the form associated with Newton–Laplace. Working symbols: $K$ , $\rho$ $\rightarrow$ $c$ . Use the adiabatic bulk modulus. In air c = √(γ R T) ≈ 343 m/s at 20 °C.

Purpose

Purpose: compute

c

from

K

\rho

in Fluid physics via

c=\sqrt{K/\rho}

c = √(K/ρ). Newton–Laplace speed in a compressible fluid. 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

K = 2.200\,\mathrm{GPa}

\rho = 1000.000\,\mathrm{kg/m^{3}}

, the governing relation

c=\sqrt{K/\rho}

yields

c = 1483.2\,\mathrm{m/s}

. A pulse, a fluid column, a travel time. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Bulk modulus K2.2 GPaDensity \rho1000 kg/m³

Outputs

Sound speed c1483.2 m/s

Reading speed

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Narration of this film

A pulse, a fluid column, a travel time.

Use the adiabatic bulk modulus. In air c = √(γ R T) ≈ 343 m/s at 20 °C.

Reading speed

Watch on YouTube