HYD-22

Rectangular weir Q = C L H^{3/2}

Q = C L H^{3/2}. Sharp-crested weir; C absorbs Cd √(2g) and end contractions.

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WeirsKindsvater–Carter

Governing equation

Q=C L H^{3/2}

$H \in \left[0.03, 1.5\right]$

where

C: Weir coefficient (m^{1/2}/s)
L: Crest length (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 L H^{3/2}

$H \in \left[0.03, 1.5\right]$

$H = 0.03$ $Q = 0.011$

Along the curve

②

Domain of the variable — blue

H_{\min} = 0.03,\quad H_{\max} = 1.5

$H \in \left[0.03, 1.5\right]$

$H = 0.03$ $H = 0.03$

Along the curve

③

Response curve — green

Q=C L H^{3/2}

$H \in \left[0.03, 1.5\right]$

$H = 0.03$ $Q = 0.011$

Along the curve

④

Rate of change — amber

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

$H \in \left[0.03, 1.5\right]$

$H = 0.039$ $Q^{\prime} = 0.655$

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-22 — Rectangular weir Q = C L H^{3/2}) is the form associated with Kindsvater–Carter. Working symbols: $C$ , $L$ , $H$ $\rightarrow$ $Q$ . Torricelli on an elemental strip, integrated in H. Rehbock and Kindsvater–Carter give C(H, P).

Purpose

Purpose: compute

Q

from

C

L

H

in Hydraulics via

Q=C L H^{3/2}

Q = C L H^{3/2}. Sharp-crested weir; C absorbs Cd √(2g) and end contractions. 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 = 1.840\,\mathrm{m^1/2/s}

L = 1.200\,\mathrm{m}

H = 0.250\,\mathrm{m}

, the governing relation

Q=C L H^{3/2}

yields

Q = 0.2760\,\mathrm{m^{3}/s}

. A weir plate, a nappe, a head H. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Weir coefficient C1.84 m^{1/2}/sCrest length L1.2 mHead H0.25 m

Outputs

Discharge Q0.2760 m³/s

Reading speed

Watch on YouTube

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Narration of this film

A weir plate, a nappe, a head H.

Torricelli on an elemental strip, integrated in H. Rehbock and Kindsvater–Carter give C(H, P).

Reading speed

Watch on YouTube