HYD-04

Rectangular weir discharge

Q = (2/3) Cd L √(2g) H^{3/2} for a sharp-crested weir.

Reading speed

WeirsKindsvater–CarterISO 1438

Governing equation

Q=\dfrac{2}{3}C_d L\sqrt{2g}\,H^{3/2}

$H \in \left[0.02, 1.5\right]$

where

C_d: Discharge coefficient (—)
L: Crest length (m)
H: Head on crest (m)
Q: Discharge (m³/s)

The figure, part by part

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①

Governing law — red

Q=\dfrac{2}{3}C_d L\sqrt{2g}\,H^{3/2}

$H \in \left[0.02, 1.5\right]$

$H = 0.02$ $Q = 0.008$

Along the curve

②

Domain of the variable — blue

H_{\min} = 0.02,\quad H_{\max} = 1.5

$H \in \left[0.02, 1.5\right]$

$H = 0.02$ $H = 0.02$

Along the curve

③

Response curve — green

Q=\dfrac{2}{3}C_d L\sqrt{2g}\,H^{3/2}

$H \in \left[0.02, 1.5\right]$

$H = 0.02$ $Q = 0.008$

Along the curve

④

Rate of change — amber

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

$H \in \left[0.02, 1.5\right]$

$H = 0.029$ $Q^{\prime} = 0.702$

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-04 — Rectangular weir discharge) is the form associated with Kindsvater–Carter · ISO 1438. Working symbols: $C_d$ , $L$ , $H$ $\rightarrow$ $Q$ . Torricelli efflux integrated across a rectangular nappe gives the 3/2 power of head; Cd absorbs contraction and viscosity.

Purpose

Purpose: compute

Q

from

C_d

L

H

in Hydraulics via

Q=\dfrac{2}{3}C_d L\sqrt{2g}\,H^{3/2}

Q = (2/3) Cd L √(2g) H^{3/2} for a sharp-crested weir. 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 = 0.620\,\mathrm{—}

L = 1.500\,\mathrm{m}

H = 0.250\,\mathrm{m}

, the governing relation

Q=\dfrac{2}{3}C_d L\sqrt{2g}\,H^{3/2}

yields

Q = 0.343\,\mathrm{m^{3}/s}

. Fully ventilated nappe, neglected velocity of approach. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Discharge coefficient C_d0.62 —Crest length L1.5 mHead on crest H0.25 m

Outputs

Discharge Q0.343 m³/s

Reading speed

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Narration of this film

Fully ventilated nappe, neglected velocity of approach.

Torricelli efflux integrated across a rectangular nappe gives the 3/2 power of head; Cd absorbs contraction and viscosity.

Reading speed

Watch on YouTube