HYD-37

Open-channel continuity Q = AV

Q = A V. The definition of mean velocity in a prismatic reach.

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Open channelContinuity

Governing equation

Q=AV

$V \in \left[0.05, 6\right]$

where

A: Area (m²)
V: Mean velocity (m/s)
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=AV

$V \in \left[0.05, 6\right]$

$V = 0.05$ $Q = 0.175$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.05,\quad V_{\max} = 6

$V \in \left[0.05, 6\right]$

$V = 0.05$ $V = 0.05$

Along the curve

③

Response curve — green

Q=AV

$V \in \left[0.05, 6\right]$

$V = 0.05$ $Q = 0.175$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}V}

$V \in \left[0.05, 6\right]$

$V = 0.087$ $Q^{\prime} = 3.5$

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-37 — Open-channel continuity Q = AV) is the form associated with Continuity. Working symbols: $A$ , $V$ $\rightarrow$ $Q$ . Mass conservation for an incompressible liquid. Pair with Manning or Chezy to close the uniform-flow problem.

Purpose

Purpose: compute

Q

from

A

V

in Hydraulics via

Q=AV

Q = A V. The definition of mean velocity in a prismatic reach. Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 3.500\,\mathrm{m^{2}}

V = 1.200\,\mathrm{m/s}

, the governing relation

Q=AV

yields

Q = 4.200\,\mathrm{m^{3}/s}

. A cross-section, a mean V, a discharge. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Area A3.5 m²Mean velocity V1.2 m/s

Outputs

Discharge Q4.200 m³/s

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Narration of this film

A cross-section, a mean V, a discharge.

Mass conservation for an incompressible liquid. Pair with Manning or Chezy to close the uniform-flow problem.

Reading speed

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