ENV-40

Hazen–Williams head

Empirical pipe friction.

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GoverningHazen–Williams head

Governing equation

h=10.67 L Q^{1.852}/(C^{1.852} d^{4.87})

$Q \in \left[0.005, 0.4\right]$

where

L: L (m)
Q: Q (m³/s)
C: C (—)
d: d (m)
h: Hazen–Williams head (m)

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

h=10.67 L Q^{1.852}/(C^{1.852} d^{4.87})

$Q \in \left[0.005, 0.4\right]$

$Q = 0.005$ $h = 0.035$

Along the curve

②

Domain of the variable — blue

Q_{\min} = 0.005,\quad Q_{\max} = 0.4

$Q \in \left[0.005, 0.4\right]$

$Q = 0.005$ $Q = 0.005$

Along the curve

③

Response curve — green

h=10.67 L Q^{1.852}/(C^{1.852} d^{4.87})

$Q \in \left[0.005, 0.4\right]$

$Q = 0.005$ $h = 0.035$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}h}{\mathrm{d}Q}

$Q \in \left[0.005, 0.4\right]$

$Q = 0.007$ $h^{\prime} = 18.36$

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-40 — Hazen–Williams head) is the form associated with Hazen–Williams head. Working symbols: $L$ , $Q$ , $C$ , $d$ $\rightarrow$ $h$ . Empirical pipe friction. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

h

from

L

Q

C

d

in Environmental via

h=10.67 L Q^{1.852}/(C^{1.852} d^{4.87})

Empirical pipe friction. 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 = 500.000\,\mathrm{m}

Q = 0.050\,\mathrm{m^{3}/s}

C = 120.000\,\mathrm{—}

d = 0.250\,\mathrm{m}

, the governing relation

h=10.67 L Q^{1.852}/(C^{1.852} d^{4.87})

yields

h = 2.506\,\mathrm{m}

. 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 L500 mQ Q0.05 m³/sC C120 —d d0.25 m

Outputs

Hazen–Williams head h2.506 m

Reading speed

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Narration of this film

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

Empirical pipe friction. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube