FLD-08

Torricelli efflux

v = √(2 g h). Ideal speed from an orifice under a head h.

Reading speed

FluidsTorricelli

Governing equation

v=\sqrt{2gh}

$h \in \left[0.05, 40\right]$

where

h: Head (m)
v: Efflux speed (m/s)

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

v=\sqrt{2gh}

$h \in \left[0.05, 40\right]$

$h = 0.05$ $v = 0.99$

Along the curve

②

Domain of the variable — blue

h_{\min} = 0.05,\quad h_{\max} = 40

$h \in \left[0.05, 40\right]$

$h = 0.05$ $h = 0.05$

Along the curve

③

Response curve — green

v=\sqrt{2gh}

$h \in \left[0.05, 40\right]$

$h = 0.05$ $v = 0.99$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}h}

$h \in \left[0.05, 40\right]$

$h = 0.301$ $v^{\prime} = 4.581$

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-08 — Torricelli efflux) is the form associated with Torricelli. Working symbols: $h$ $\rightarrow$ $v$ . Bernoulli between the free surface and the vena contracta. A coefficient Cd < 1 in the lab.

Purpose

Purpose: compute

v

from

h

in Fluid physics via

v=\sqrt{2gh}

v = √(2 g h). Ideal speed from an orifice under a head h. 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

h = 4.000\,\mathrm{m}

, the governing relation

v=\sqrt{2gh}

yields

v = 8.859\,\mathrm{m/s}

. A tank, a jet, a falling range. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Head h4 m

Outputs

Efflux speed v8.859 m/s

Reading speed

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Narration of this film

A tank, a jet, a falling range.

Bernoulli between the free surface and the vena contracta. A coefficient Cd < 1 in the lab.

Reading speed

Watch on YouTube