FLD-24

Archimedes buoyancy

F = ρ g V. The buoyant force equals the weight of displaced fluid.

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FluidsArchimedes

Governing equation

F_b=\rho g V

$V \in \left[0.1, 2000\right]$

where

\rho: Fluid density (kg/m³)
V: Displaced volume (L)
F_b: Buoyancy (N)

The figure, part by part

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①

Governing law — red

F_b=\rho g V

$V \in \left[0.1, 2000\right]$

$V = 0.1$ $F_b = 0.981$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.1,\quad V_{\max} = 2000

$V \in \left[0.1, 2000\right]$

$V = 0.1$ $V = 0.1$

Along the curve

③

Response curve — green

F_b=\rho g V

$V \in \left[0.1, 2000\right]$

$V = 0.1$ $F_b = 0.981$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}F_b}{\mathrm{d}V}

$V \in \left[0.1, 2000\right]$

$V = 12.68$ $F_b^{\prime} = 9.81$

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-24 — Archimedes buoyancy) is the form associated with Archimedes. Working symbols: $\rho$ , $V$ $\rightarrow$ $F_b$ . Surface integral of hydrostatic pressure. A floating body displaces its own weight.

Purpose

Purpose: compute

F_b

from

\rho

V

in Fluid physics via

F_b=\rho g V

F = ρ g V. The buoyant force equals the weight of displaced 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

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

V = 40.000\,\mathrm{L}

, the governing relation

F_b=\rho g V

yields

F_b = 392.4\,\mathrm{N}

. A submerged block, an upward arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Fluid density \rho1000 kg/m³Displaced volume V40 L

Outputs

Buoyancy F_b392.4 N

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Narration of this film

A submerged block, an upward arrow.

Surface integral of hydrostatic pressure. A floating body displaces its own weight.

Reading speed

Watch on YouTube