Drinking Water Distribution & Treatment · Study · PE Civil: Water Resources and Environmental · FE → PE Prep
Drinking Water Distribution & Treatment
9% of exam
Demand and storage, distribution systems, sedimentation, coagulation/flocculation, filtration and membranes, disinfection (CT), softening, and adsorption.
9 concepts
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.
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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.
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Split distribution storage into operational/equalization, fire, and emergency components; size equalization by mass curve and set elevated-tank head for pressure.
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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 vt where drag balances submerged weight and falls at that constant speed. For small particles in the laminar (Stokes) regime (NRe<1), terminal velocity follows Stokes' law, rising with the square of diameter and with the density difference between particle and water.
vt=18μg(ρp−ρw)d2=18νg(SG−1)d2
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 vH while particles settle at vt. 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 v0
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 vt<v0, 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 vt≥v0
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 v0=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.
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 20,000gpd/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 0.5ft/min. Typical overflow rates for alum/ferric clarification run on the order of several hundred to about 1,000gpd/ft2
Exam strategy
Anchor every sedimentation problem on v0=Q/Asurface — for removal, only the plan area matters, so resist the urge to use depth or detention time in the removal criterion. If vt≥v0
Problem. A water plant treats Q=4.0MGD through a rectangular settling basin. Design for an overflow rate of 1,000gpd/ft2. Find the required surface area; for a 12ft depth, find the detention time; and check weir loading if the effluent weir is
Common pitfalls
•Sizing on detention time instead of overflow rate. Ideal (Type I) removal depends ONLY on v0=Q/Asurface — depth and detention time cancel out. Use plan area for removal; reserve detention for short-circuiting and sludge checks.
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.
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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.
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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.
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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.
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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.
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. Geometry makes
v0
equal to the flow divided by the plan (surface) area — the overflow rate — and entirely independent of depth. Any particle with
vt≥v0
is completely removed no matter where it enters; this is the central theorem of ideal sedimentation.
) plus the partial contributions of the slower particles.
r=v0vt(vt<v0);r=1(vt≥v0)
t=QV,v0=tH=AQ
.
WOR=LweirQ(gpd/ft),vH=AxQ
the particle is
100%
removed; otherwise removal is
vt/v0
. Keep units coherent: overflow rate is naturally a velocity (
ft/s
or
m/d
) but is usually reported as
gpd/ft2
, 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
NRe<1
before trusting Stokes' law, and finish by checking weir loading and horizontal velocity against the water-treatment caps.
Surface loading rate. The critical velocity: particles with vt≥v0 are fully removed. Depends only on plan area, not depth. Units ft/s, m/d, or gpd/ft2.
Stokes' law settling velocityvt=18μg(ρp−ρw)d2=18νg(SG−1)d2
Terminal velocity of a discrete particle for NRe<1. d = diameter, ν = kinematic viscosity, SG = particle specific gravity.
Reynolds number checkNRe=νvtd<1
Validity bound for Stokes' law. Above ∼1, use the general drag-coefficient form vt=4g(ρp−ρw)d/(3CDρw)
Removal ratio (partial)r=v0vt(vt<v0)
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≤1). Equals 1 when vt≥v0
Detention timet=QV=v0H
Hydraulic residence time. Bounds short-circuiting and sludge storage but does NOT set Type I removal.
Horizontal (approach) velocityvH=AxQ
Flow over basin cross-sectional (flow-normal) area. Kept <0.5ft/min in water treatment to avoid scouring settled sludge.
Weir overflow rateWOR=LweirQ
Flow per unit weir length (gpd/ft). Water-treatment limit ≤20,000gpd/ft to prevent floc liftover at the effluent.
Ideal-basin geometry relationvHv0=LH
Critical particle traverses depth H while moving length L; ties overflow rate, horizontal velocity, and basin proportions.
Convert a reported overflow rate to a velocity before comparing to a Stokes settling velocity.
200ft
long.
Solution. Surface area: A=Q/v0=(4.0×106gpd)/(1,000gpd/ft2)=4,000ft2.
Volume and detention: V=AH=4,000(12)=48,000ft3. With Q=4.0(1.547)=6.19cfs, t=V/Q=48,000/6.19=7,760s=2.15h — shorter than the NCEES typical hydraulic residence time of 4-8h for alum/ferric clarification, because the chosen 1,000gpd/ft2 is a high overflow rate.
Weir loading: WOR=Q/L=(4.0×106)/200=20,000gpd/ft — right at the water-treatment limit.
Sanity check: 48,000ft3=3.59×105gal; over 4MGD that is 0.090day=2.15h — agrees. Final: A=4,000ft2, t≈2.15h, WOR=20,000gpd/ft (at the cap — lengthen the weir to add margin).
Stokes settling velocity and Reynolds check
Problem. A discrete sand particle has diameter d=0.1mm (1×10−4m) and specific gravity 2.65. Water is at 20∘C (ν=1.003×10−6m2/s). Find its terminal settling velocity and confirm Stokes' law applies.
Problem. A basin passes Q=0.15m3/s over a plan area of 300m2. A particle settles at vt=0.30mm/s. What fraction of these particles is removed, and what is the cutoff diameter for 100% removal?
Comparing mismatched units. Overflow rate is usually gpd/ft2 but settling velocity is ft/s or m/d; convert (1gpd/ft2=1.547×10−6ft/s) before deciding removal.
•Using Stokes' law out of range. Verify NRe<1; for larger/faster particles drag is non-linear and you must use the drag-coefficient form, or Stokes overpredicts vt.
•Treating partial removal as all-or-nothing. Particles slower than v0 are still partly removed, r=vt/v0; ignoring them underestimates total efficiency.
•Skipping the weir-loading check. A correctly sized surface area can still fail if weir overflow rate exceeds ∼20,000gpd/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). v0=Q/Aplan governs removal; vH=Q/Ax 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.