HYD-32

Francis contracted weir

Q = 1.84 (L − 0.1 n H) H^{3/2} (SI). End contractions n = 0, 1 or 2.

Reading speed

WeirsFrancis

Governing equation

Q=1.84\,(L-0.1 n H)H^{3/2}

$H \in \left[0.04, 1.2\right]$

where

L: Crest length (m)
H: Head (m)
n: Free ends n (—)
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=1.84\,(L-0.1 n H)H^{3/2}

$H \in \left[0.04, 1.2\right]$

$H = 0.04$ $Q = 0.022$

Along the curve

②

Domain of the variable — blue

H_{\min} = 0.04,\quad H_{\max} = 1.2

$H \in \left[0.04, 1.2\right]$

$H = 0.04$ $H = 0.04$

Along the curve

③

Response curve — green

Q=1.84\,(L-0.1 n H)H^{3/2}

$H \in \left[0.04, 1.2\right]$

$H = 0.04$ $Q = 0.022$

Along the curve

④

Rate of change — amber

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

$H \in \left[0.04, 1.2\right]$

$H = 0.047$ $Q^{\prime} = 0.89$

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-32 — Francis contracted weir) is the form associated with Francis. Working symbols: $L$ , $H$ , $n$ $\rightarrow$ $Q$ . Francis shortened the effective crest by 0.1 H per unsuppressed end. Full-width (n = 0) recovers a simple weir.

Purpose

Purpose: compute

Q

from

L

H

n

in Hydraulics via

Q=1.84\,(L-0.1 n H)H^{3/2}

Q = 1.84 (L − 0.1 n H) H^{3/2} (SI). End contractions n = 0, 1 or 2. Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 1.500\,\mathrm{m}

H = 0.300\,\mathrm{m}

n = 2.000\,\mathrm{—}

, the governing relation

Q=1.84\,(L-0.1 n H)H^{3/2}

yields

Q = 0.4354\,\mathrm{m^{3}/s}

. A contracted nappe, a shortened L, a discharge. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Crest length L1.5 mHead H0.3 mFree ends n n2 —

Outputs

Discharge Q0.4354 m³/s

Reading speed

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Narration of this film

A contracted nappe, a shortened L, a discharge.

Francis shortened the effective crest by 0.1 H per unsuppressed end. Full-width (n = 0) recovers a simple weir.

Reading speed

Watch on YouTube