HYD-08

Torricelli orifice

Q = Cd A √(2 g H) through a small orifice.

Reading speed

OrificesTorricelliISO 5167

Governing equation

Q=C_d A\sqrt{2gH}

$H \in \left[0.1, 20\right]$

where

C_d: Coefficient (—)
D: Orifice diameter (m)
H: Head (m)
Q: Discharge (m³/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

Q=C_d A\sqrt{2gH}

$H \in \left[0.1, 20\right]$

$H = 0.1$ $Q = 0.002$

Along the curve

②

Domain of the variable — blue

H_{\min} = 0.1,\quad H_{\max} = 20

$H \in \left[0.1, 20\right]$

$H = 0.1$ $H = 0.1$

Along the curve

③

Response curve — green

Q=C_d A\sqrt{2gH}

$H \in \left[0.1, 20\right]$

$H = 0.1$ $Q = 0.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}H}

$H \in \left[0.1, 20\right]$

$H = 0.225$ $Q^{\prime} = 0.006$

Along the curve

Lecture brief

Historical brief

Open-channel and pipe flow were written by Chezy, Manning, Darcy and Weisbach in the nineteenth century, then Bakhmeteff and Bélanger on the hydraulic jump. The sheets compute conveyance, head loss and gradually varied profiles. This sheet (HYD-08 — Torricelli orifice) is the form associated with Torricelli · ISO 5167. Working symbols: $C_d$ , $D$ , $H$ $\rightarrow$ $Q$ . Torricelli identified orifice speed with free-fall from the free surface; Cd folds vena-contracta and viscous loss.

Purpose

Purpose: compute

Q

from

C_d

D

H

in Hydraulics via

Q=C_d A\sqrt{2gH}

Q = Cd A √(2 g H) through a small orifice. Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C_d = 0.610\,\mathrm{—}

D = 0.050\,\mathrm{m}

H = 3.000\,\mathrm{m}

, the governing relation

Q=C_d A\sqrt{2gH}

yields

Q = 0.00919\,\mathrm{m^{3}/s}

. Small circular orifice, constant head. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Coefficient C_d0.61 —Orifice diameter D0.05 mHead H3 m

Outputs

Discharge Q0.00919 m³/s

Reading speed

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Narration of this film

Small circular orifice, constant head.

Torricelli identified orifice speed with free-fall from the free surface; Cd folds vena-contracta and viscous loss.

Reading speed

Watch on YouTube