FLD-10

Froude number

Fr = v / √(g L). Inertia versus gravity on a free surface.

Reading speed

FluidsFroude

Governing equation

Fr=\dfrac{v}{\sqrt{gL}}

$v \in \left[0.05, 20\right]$

where

v: Speed (m/s)
L: Length (m)
Fr: Froude (—)

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

Fr=\dfrac{v}{\sqrt{gL}}

$v \in \left[0.05, 20\right]$

$v = 0.05$ $Fr = 0.013$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.05,\quad v_{\max} = 20

$v \in \left[0.05, 20\right]$

$v = 0.05$ $v = 0.05$

Along the curve

③

Response curve — green

Fr=\dfrac{v}{\sqrt{gL}}

$v \in \left[0.05, 20\right]$

$v = 0.05$ $Fr = 0.013$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Fr}{\mathrm{d}v}

$v \in \left[0.05, 20\right]$

$v = 0.175$ $Fr^{\prime} = 0.261$

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-10 — Froude number) is the form associated with Froude. Working symbols: $v$ , $L$ $\rightarrow$ $Fr$ . Critical flow at Fr = 1. Hydraulic jumps live where Fr crosses unity.

Purpose

Purpose: compute

Fr

from

v

L

in Fluid physics via

Fr=\dfrac{v}{\sqrt{gL}}

Fr = v / √(g L). Inertia versus gravity on a free surface. 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 = 2.000\,\mathrm{m/s}

L = 1.500\,\mathrm{m}

, the governing relation

Fr=\dfrac{v}{\sqrt{gL}}

yields

Fr = 0.521\,\mathrm{—}

. A channel, a hump, a jump. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Speed v2 m/sLength L1.5 m

Outputs

Froude Fr0.521 —

Reading speed

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Narration of this film

A channel, a hump, a jump.

Critical flow at Fr = 1. Hydraulic jumps live where Fr crosses unity.

Reading speed

Watch on YouTube