Drinking Water Distribution & Treatment

A. Drinking water distribution systems

Distribution Systems: Fire Flow and Pressure

How looped mains, minimum pressures, and fire-flow demand combine: the max-day-plus-fire governing case and the Hazen-Williams hydraulics that decide whether residual pressure holds.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

C. Present, short-term, and long-term demands

Water Demands and Population Projection

Turn per-capita use into average, max-day, and peak-hour demands, and project population by arithmetic, geometric, and declining-growth models to set present vs. design-year flows.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

D. Storage

Storage Sizing: Equalization, Fire and Emergency

Split distribution storage into operational/equalization, fire, and emergency components; size equalization by mass curve and set elevated-tank head for pressure.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

E. Sedimentation

Sedimentation and Overflow Rate

The ideal-basin theory of discrete (Type I) settling: why overflow rate alone decides removal, how settling velocity compares to it, and how weir loading and detention time bound the design.

Sedimentation is the quiet workhorse between coagulation and filtration: let the floc fall out under gravity so the filters are not buried. The single most counterintuitive — and most tested — result in all of water treatment lives here: in an ideal basin, removal of a discrete particle depends only on the overflow rate (surface loading), not on the basin's depth or detention time. Examinees who size a clarifier by detention time alone, or who never check weir loading, leave points on the table. This material is the NCEES PE Civil Reference Handbook §6.9.6 Settling and Sedimentation, built on the Hazen-Camp ideal-basin model.

Discrete (Type I) settling

Type I settling is the gravitational fall of discrete, non-flocculating particles in dilute suspension — grit, dense sand, and well-formed inert particles that neither change size nor interfere with one another. Each particle quickly reaches a terminal velocity

v_t

where drag balances submerged weight and falls at that constant speed. For small particles in the laminar (Stokes) regime (

N_{Re} < 1

), terminal velocity follows Stokes' law, rising with the square of diameter and with the density difference between particle and water.

v_t = \dfrac{g\,(\rho_p - \rho_w)\,d^{2}}{18\,\mu} = \dfrac{g\,(SG - 1)\,d^{2}}{18\,\nu}

The ideal basin and the critical overflow rate

Model a rectangular basin with four zones — inlet, settling, sludge, and outlet — in which water moves horizontally at velocity

v_H

while particles settle at

v_t

. A particle entering at the very top of the settling zone traces a straight path; the slowest particle that still reaches the sludge zone before the outlet defines the critical settling velocity

v_0

. Geometry makes

v_0

equal to the flow divided by the plan (surface) area — the overflow rate — and entirely independent of depth. Any particle with

v_t \ge v_0

is completely removed no matter where it enters; this is the central theorem of ideal sedimentation.

v_0 = \dfrac{Q}{A_{surface}} \quad (\text{overflow rate} = \text{critical settling velocity})

Removal efficiency of an ideal basin

Particles slower than the critical velocity are not lost entirely — those entering low enough in the inlet still reach the sludge zone. For a particle with

v_t < v_0

, the fraction removed equals the ratio of its settling velocity to the critical velocity, because removal depends linearly on where in the depth it enters. Total removal across a suspension sums the fully-removed fraction (all particles with

v_t \ge v_0

) plus the partial contributions of the slower particles.

r = \dfrac{v_t}{v_0}\quad (v_t < v_0); \qquad r = 1\quad (v_t \ge v_0)

Detention time and depth — and why they do not set removal

Detention time is the basin volume divided by flow,

t = V/Q

, and depth relates the two through

v_0 = H/t

. These bound the design — too short a detention invites short-circuiting and resuspension, and Type II flocculent settling (where floc grows as it falls) does benefit from depth and time — but for ideal Type I removal they do not appear in the criterion. Depth buys settling time and settling distance in equal measure, so they cancel: a shallow, wide basin and a deep, narrow one of the same plan area remove the same discrete particle. Real basins still need adequate depth for sludge storage and to damp inlet turbulence.

t = \dfrac{V}{Q}, \qquad v_0 = \dfrac{H}{t} = \dfrac{Q}{A}

Weir loading and horizontal velocity

Two secondary checks keep an ideal basin from misbehaving. Weir (overflow) loading is the flow per unit length of effluent weir; if it is too high the upward approach velocity near the weir lifts settled floc back into the effluent, so water-treatment practice caps it near

20{,}000\,\text{gpd/ft}

. Horizontal velocity is the flow divided by the basin cross-section; too high a value scours the sludge blanket, so water-treatment horizontal velocity is held under about

0.5\,\text{ft/min}

. Typical overflow rates for alum/ferric clarification run on the order of several hundred to about

1{,}000\,\text{gpd/ft}^2

.

WOR = \dfrac{Q}{L_{weir}}\ (\text{gpd/ft}), \qquad v_H = \dfrac{Q}{A_{x}}

Exam strategy

Anchor every sedimentation problem on

v_0 = Q/A_{surface}

— for removal, only the plan area matters, so resist the urge to use depth or detention time in the removal criterion. If

v_t \ge v_0

the particle is

100\%

removed; otherwise removal is

v_t/v_0

. Keep units coherent: overflow rate is naturally a velocity (

\text{ft/s}

or

\text{m/d}

) but is usually reported as

\text{gpd/ft}^2

, so convert before comparing to a Stokes velocity. Use detention time and depth only for the secondary checks (short-circuiting, sludge storage) and for Type II flocculent settling, where depth genuinely helps. Always verify

N_{Re} < 1

before trusting Stokes' law, and finish by checking weir loading and horizontal velocity against the water-treatment caps.

Key equations

Overflow rate (critical settling velocity)

v_0 = \dfrac{Q}{A_{surface}}

Surface loading rate. The critical velocity: particles with $v_t \ge v_0$ are fully removed. Depends only on plan area, not depth. Units ft/s, m/d, or gpd/ft $^2$ .

Stokes' law settling velocity

v_t = \dfrac{g\,(\rho_p - \rho_w)\,d^{2}}{18\,\mu} = \dfrac{g\,(SG-1)\,d^{2}}{18\,\nu}

Terminal velocity of a discrete particle for $N_{Re}<1$ . $d$ = diameter, $\nu$ = kinematic viscosity, $SG$ = particle specific gravity.

Reynolds number check

N_{Re} = \dfrac{v_t\,d}{\nu} < 1

Validity bound for Stokes' law. Above $\sim 1$ , use the general drag-coefficient form $v_t=\sqrt{4g(\rho_p-\rho_w)d/(3C_D\rho_w)}$ .

Removal ratio (partial)

r = \dfrac{v_t}{v_0}\quad (v_t < v_0)

Fraction of a slower particle removed in an ideal basin; equals $h/H$ in the geometric model ( $h$ = limiting entry/fall height, $H$ = basin depth, so $r \le 1$ ). Equals $1$ when $v_t \ge v_0$ .

Detention time

t = \dfrac{V}{Q} = \dfrac{H}{v_0}

Hydraulic residence time. Bounds short-circuiting and sludge storage but does NOT set Type I removal.

Horizontal (approach) velocity

v_H = \dfrac{Q}{A_{x}}

Flow over basin cross-sectional (flow-normal) area. Kept $< 0.5\,\text{ft/min}$ in water treatment to avoid scouring settled sludge.

Weir overflow rate

WOR = \dfrac{Q}{L_{weir}}

Flow per unit weir length (gpd/ft). Water-treatment limit $\le 20{,}000\,\text{gpd/ft}$ to prevent floc liftover at the effluent.

Ideal-basin geometry relation

\dfrac{v_0}{v_H} = \dfrac{H}{L}

Critical particle traverses depth $H$ while moving length $L$ ; ties overflow rate, horizontal velocity, and basin proportions.

Flow-rate conversion

1\,\text{gpd/ft}^2 = 1.547\times10^{-6}\,\text{ft/s} = 4.72\times10^{-7}\,\text{m/s} = 0.0407\,\text{m/d}

Convert a reported overflow rate to a velocity before comparing to a Stokes settling velocity.

Worked examples

Sizing a clarifier on overflow rate

Problem. A water plant treats $Q = 4.0\,\text{MGD}$ through a rectangular settling basin. Design for an overflow rate of $1{,}000\,\text{gpd/ft}^2$ . Find the required surface area; for a $12\,\text{ft}$ depth, find the detention time; and check weir loading if the effluent weir is $200\,\text{ft}$ long.

Solution. Surface area:

A = Q/v_0 = (4.0\times10^{6}\,\text{gpd})/(1{,}000\,\text{gpd/ft}^2) = 4{,}000\,\text{ft}^2

. Volume and detention:

V = A\,H = 4{,}000(12) = 48{,}000\,\text{ft}^3

. With

Q = 4.0(1.547) = 6.19\,\text{cfs}

,

t = V/Q = 48{,}000/6.19 = 7{,}760\,\text{s} = 2.15\,\text{h}

— shorter than the NCEES typical hydraulic residence time of

4

-

8\,\text{h}

for alum/ferric clarification, because the chosen

1{,}000\,\text{gpd/ft}^2

is a high overflow rate. Weir loading:

WOR = Q/L = (4.0\times10^{6})/200 = 20{,}000\,\text{gpd/ft}

— right at the water-treatment limit. Sanity check:

48{,}000\,\text{ft}^3 = 3.59\times10^{5}\,\text{gal}

; over

4\,\text{MGD}

that is

0.090\,\text{day} = 2.15\,\text{h}

— agrees. Final:

A = 4{,}000\,\text{ft}^2

,

t \approx 2.15\,\text{h}

,

WOR = 20{,}000\,\text{gpd/ft}

(at the cap — lengthen the weir to add margin).

Stokes settling velocity and Reynolds check

Problem. A discrete sand particle has diameter $d = 0.1\,\text{mm}$ ( $1\times10^{-4}\,\text{m}$ ) and specific gravity $2.65$ . Water is at $20^\circ\text{C}$ ( $\nu = 1.003\times10^{-6}\,\text{m}^2/\text{s}$ ). Find its terminal settling velocity and confirm Stokes' law applies.

Solution. Stokes velocity:

v_t = \dfrac{g(SG-1)d^2}{18\nu} = \dfrac{9.81(2.65-1)(1\times10^{-4})^2}{18(1.003\times10^{-6})}

. Numerator:

9.81(1.65)(1\times10^{-8}) = 1.619\times10^{-7}

. Denominator:

1.805\times10^{-5}

.

v_t = 8.97\times10^{-3}\,\text{m/s} = 8.97\,\text{mm/s} = 775\,\text{m/d}

. Reynolds check:

N_{Re} = v_t d/\nu = (8.97\times10^{-3})(1\times10^{-4})/(1.003\times10^{-6}) = 0.89 < 1

— Stokes valid. Sanity check:

775\,\text{m/d}

is far above any practical overflow rate (tens of m/d), so this dense particle is removed with huge margin. Final:

v_t \approx 8.97\,\text{mm/s}

(

N_{Re} = 0.89

, Stokes confirmed).

Removal efficiency of a slow particle

Problem. A basin passes $Q = 0.15\,\text{m}^3/\text{s}$ over a plan area of $300\,\text{m}^2$ . A particle settles at $v_t = 0.30\,\text{mm/s}$ . What fraction of these particles is removed, and what is the cutoff diameter for $100\%$ removal?

Solution. Overflow rate:

v_0 = Q/A = 0.15/300 = 5.0\times10^{-4}\,\text{m/s} = 0.50\,\text{mm/s}

(

= 43.2\,\text{m/d}

). Since

v_t = 0.30\,\text{mm/s} < v_0 = 0.50\,\text{mm/s}

, removal is partial:

r = v_t/v_0 = 0.30/0.50 = 0.60

, i.e.

60\%

. Cutoff: particles with

v_t \ge 0.50\,\text{mm/s}

are

100\%

removed; that is the smallest particle whose Stokes velocity reaches the overflow rate. Sanity check: a particle settling at

60\%

of the critical velocity is removed

60\%

of the time — the linear ideal-basin result, independent of depth. Final:

r = 60\%

; full removal requires

v_t \ge 0.50\,\text{mm/s}

.

Common pitfalls

•Sizing on detention time instead of overflow rate. Ideal (Type I) removal depends ONLY on $v_0 = Q/A_{surface}$ — depth and detention time cancel out. Use plan area for removal; reserve detention for short-circuiting and sludge checks.
•Comparing mismatched units. Overflow rate is usually $\text{gpd/ft}^2$ but settling velocity is $\text{ft/s}$ or $\text{m/d}$ ; convert ( $1\,\text{gpd/ft}^2 = 1.547\times10^{-6}\,\text{ft/s}$ ) before deciding removal.
•Using Stokes' law out of range. Verify $N_{Re}<1$ ; for larger/faster particles drag is non-linear and you must use the drag-coefficient form, or Stokes overpredicts $v_t$ .
•Treating partial removal as all-or-nothing. Particles slower than $v_0$ are still partly removed, $r=v_t/v_0$ ; ignoring them underestimates total efficiency.
•Skipping the weir-loading check. A correctly sized surface area can still fail if weir overflow rate exceeds $\sim 20{,}000\,\text{gpd/ft}$ and lifts floc into the effluent — lengthen the weir, do not shrink the basin.
•Confusing overflow rate (per plan area) with horizontal velocity (per cross-section). $v_0=Q/A_{plan}$ governs removal; $v_H=Q/A_x$ governs scour — different areas, different checks.
•Applying Type I theory to flocculent or hindered suspensions. Type II floc grows as it settles (depth helps) and Type III/IV settle as a blanket; the depth-independent result is a Type I idealization only.

References

NCEES PE Civil Reference Handbook — §6.9.6 Settling and Sedimentation (Type I Discrete Settling, Overflow Rate)
Recommended Standards for Water Works (Ten States Standards), 2018 — Weir-loading and horizontal-velocity limits for sedimentation basins
Davis & Cornwell, Introduction to Environmental Engineering — Ideal (Hazen-Camp) basin theory and removal-ratio derivation

F. Coagulation and flocculation

Coagulation and Flocculation (Jar Test, Gt)

Destabilize colloids with metal coagulants, balance alkalinity demand, and size rapid-mix and flocculation basins by the velocity gradient G and the dimensionless product Gt.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

G. Membrane processes and media filtration

Media and Membrane Filtration

Size rapid sand and dual-media filters by loading rate, estimate clean-bed head loss, and read the MF/UF/NF/RO spectrum through flux, recovery and rejection.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

H. Disinfection, including disinfection byproducts

Disinfection: CT, Log Removal and DBPs

Apply the CT concept with the t10 baffling factor, convert CT into log-inactivation credit, work breakpoint chlorination, and balance disinfection against THM/HAA formation.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

I. Hardness and softening

Hardness and Lime-Soda Softening

Express hardness as CaCO3, split it into carbonate and noncarbonate fractions with a meq/L bar chart, and dose lime and soda ash by stoichiometry.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders

J. Other treatment

Other Treatment: Ion Exchange, GAC, Ozone, UV and Air Stripping

Work GAC adsorption isotherms and EBCT, ion-exchange capacity and regeneration, ozone/AOP, UV dose, and air stripping via Henry's law and the stripping factor.

Unlocks with an access pass — one-time payment, no auto-renew. View passes

Pass holders