ENV-43

Cippoletti weir

Trapezoidal weir discharge.

Reading speed

GoverningCippoletti weir

Governing equation

Q=1.86 L H^{3/2}

$H \in \left[0.05, 0.8\right]$

where

L: L (m)
H: H (m)
Q: Cippoletti weir (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=1.86 L H^{3/2}

$H \in \left[0.05, 0.8\right]$

$H = 0.05$ $Q = 0.025$

Along the curve

②

Domain of the variable — blue

H_{\min} = 0.05,\quad H_{\max} = 0.8

$H \in \left[0.05, 0.8\right]$

$H = 0.05$ $H = 0.05$

Along the curve

③

Response curve — green

Q=1.86 L H^{3/2}

$H \in \left[0.05, 0.8\right]$

$H = 0.05$ $Q = 0.025$

Along the curve

④

Rate of change — amber

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

$H \in \left[0.05, 0.8\right]$

$H = 0.055$ $Q^{\prime} = 0.783$

Along the curve

Lecture brief

Historical brief

Streeter–Phelps (1925) oxygen sag, settling theory and Guldberg–Waage kinetics made water and air quality a rate problem. The lab computes sag, overflow and a snapshot of reactor mass balance. This sheet (ENV-43 — Cippoletti weir) is the form associated with Cippoletti weir. Working symbols: $L$ , $H$ $\rightarrow$ $Q$ . Trapezoidal weir discharge. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

Q

from

L

H

in Environmental via

Q=1.86 L H^{3/2}

Trapezoidal weir discharge. Use it when a real environmental question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 1.200\,\mathrm{m}

H = 0.250\,\mathrm{m}

, the governing relation

Q=1.86 L H^{3/2}

yields

Q = 0.279\,\mathrm{m^{3}/s}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

L L1.2 mH H0.25 m

Outputs

Cippoletti weir Q0.279 m³/s

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Trapezoidal weir discharge. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube