FLD-16

Bulk modulus

K = − Δp / (ΔV/V). How hard a fluid is to compress.

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FluidsBulk modulus

Governing equation

K=-\dfrac{\Delta p}{\Delta V/V}

$\Delta p \in \left[0.1, 200\right]$

where

\Delta p: Pressure rise (MPa)
\Delta V/V: Volumetric strain (—)
K: Bulk modulus (GPa)

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

K=-\dfrac{\Delta p}{\Delta V/V}

$\Delta p \in \left[0.1, 200\right]$

$\Delta p = 0.1$ $K = 0.022$

Along the curve

②

Domain of the variable — blue

\Delta p_{\min} = 0.1,\quad \Delta p_{\max} = 200

$\Delta p \in \left[0.1, 200\right]$

$\Delta p = 0.1$ $\Delta p = 0.1$

Along the curve

③

Response curve — green

K=-\dfrac{\Delta p}{\Delta V/V}

$\Delta p \in \left[0.1, 200\right]$

$\Delta p = 0.1$ $K = 0.022$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}\Delta p}

$\Delta p \in \left[0.1, 200\right]$

$\Delta p = 1.357$ $K^{\prime} = 0.222$

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-16 — Bulk modulus) is the form associated with Bulk modulus. Working symbols: $\Delta p$ , $\Delta V/V$ $\rightarrow$ $K$ . Water is near 2.2 GPa. The definition is the isothermal or adiabatic derivative −v(∂p/∂v).

Purpose

Purpose: compute

K

from

\Delta p

\Delta V/V

in Fluid physics via

K=-\dfrac{\Delta p}{\Delta V/V}

K = − Δp / (ΔV/V). How hard a fluid is to compress. 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

\Delta p = 10.000\,\mathrm{MPa}

\Delta V/V = 0.004\,\mathrm{—}

, the governing relation

K=-\dfrac{\Delta p}{\Delta V/V}

yields

K = 2.22\,\mathrm{GPa}

. A piston, a tiny volume shrink, a large Δp. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Pressure rise \Delta p10 MPaVolumetric strain \Delta V/V0.0045 —

Outputs

Bulk modulus K2.22 GPa

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Narration of this film

A piston, a tiny volume shrink, a large Δp.

Water is near 2.2 GPa. The definition is the isothermal or adiabatic derivative −v(∂p/∂v).

Reading speed

Watch on YouTube