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}

where

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

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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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