HYD-03

Chézy uniform velocity

V = C √(R S) for uniform open-channel flow.

Reading speed

Open channelChézy 1771

Governing equation

V = C\sqrt{R S}

$R \in \left[0.1, 8\right]$

where

C: Chézy C (m^{1/2}/s)
R: Hydraulic radius (m)
S: Slope (—)
V: Velocity (m/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.

00:0 / 00:08

①

Governing law — red

V = C\sqrt{R S}

$R \in \left[0.1, 8\right]$

$R = 0.1$ $V = 0.5$

Along the curve

②

Domain of the variable — blue

R_{\min} = 0.1,\quad R_{\max} = 8

$R \in \left[0.1, 8\right]$

$R = 0.1$ $R = 0.1$

Along the curve

③

Response curve — green

V = C\sqrt{R S}

$R \in \left[0.1, 8\right]$

$R = 0.1$ $V = 0.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V}{\mathrm{d}R}

$R \in \left[0.1, 8\right]$

$R = 0.15$ $V^{\prime} = 2.073$

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-03 — Chézy uniform velocity) is the form associated with Chézy 1771. Working symbols: $C$ , $R$ , $S$ $\rightarrow$ $V$ . Chézy balanced gravity and wall resistance on a prismatic reach and found V proportional to √(R S).

Purpose

Purpose: compute

V

from

C

R

S

in Hydraulics via

V = C\sqrt{R S}

V = C √(R S) for uniform open-channel flow. 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 = 50.000\,\mathrm{m^1/2/s}

R = 1.200\,\mathrm{m}

S = 0.001\,\mathrm{—}

, the governing relation

V = C\sqrt{R S}

yields

V = 1.732\,\mathrm{m/s}

. Enter Chézy C (m^{1/2}/s) and hydraulic radius. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Chézy C C50 m^{1/2}/sHydraulic radius R1.2 mSlope S0.001 —

Outputs

Velocity V1.732 m/s

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Enter Chézy C (m^{1/2}/s) and hydraulic radius.

Chézy balanced gravity and wall resistance on a prismatic reach and found V proportional to √(R S).

Reading speed

Watch on YouTube