HYD-23

Orifice discharge

Q = Cd A √(2 g h). A hole in a tank, vena contracta inside Cd.

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OrificesOrifice Cd

Governing equation

Q=C_d A\sqrt{2gh}

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

where

C_d: Discharge coefficient (—)
A: Orifice area (cm^2)
h: Head (m)
Q: Discharge (L/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}

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

$h = 0.1$ $Q = 1.709$

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}

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

$h = 0.1$ $Q = 1.709$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}h}

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

$h = 0.225$ $Q^{\prime} = 5.951$

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-23 — Orifice discharge) is the form associated with Orifice Cd. Working symbols: $C_d$ , $A$ , $h$ $\rightarrow$ $Q$ . Bernoulli from free surface to the jet. Cd = Cc Cv ≈ 0.61 for a sharp orifice.

Purpose

Purpose: compute

Q

from

C_d

A

h

in Hydraulics via

Q=C_d A\sqrt{2gh}

Q = Cd A √(2 g h). A hole in a tank, vena contracta inside Cd. 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{—}

A = 20.000\,\mathrm{cm^2}

h = 2.500\,\mathrm{m}

, the governing relation

Q=C_d A\sqrt{2gh}

yields

Q = 8.54\,\mathrm{L/s}

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

Calculator

Inputs

Discharge coefficient C_d0.61 —Orifice area A20 cm^2Head h2.5 m

Outputs

Discharge Q8.54 L/s

Reading speed

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Narration of this film

A tank, an orifice, a jet.

Bernoulli from free surface to the jet. Cd = Cc Cv ≈ 0.61 for a sharp orifice.

Reading speed

Watch on YouTube