Potable Pipeline Engineering Suite

hf (ft) = 10.44 · L · Q^1.852 / (C^1.852 · d^4.8655) ΔP (psi) = 0.4333 · hf

Variables & units:

• Q — flow rate, gpm
• d — pipe inside diameter, inches
• C — Hazen-Williams roughness coefficient (dimensionless, empirical)
• L — pipeline length, feet

Assumptions & limitations: turbulent flow of potable water near 60 °F. C is empirical and material/age dependent — cement-mortar-lined ductile iron ≈ 140 new, PVC ≈ 150, unlined cast iron 60–100 with age. Outside its calibration range Hazen-Williams can deviate ±10–15% from Darcy-Weisbach; use Darcy-Weisbach where temperature or fluid differs.

Source: Williams & Hazen empirical formula; standard practice per AWWA M32 (Computer Modeling of Water Distribution Systems). The psi-per-foot form (constant 4.52) appears in NFPA 13.

V (fps) = 0.4085 · Q / d²

Variables & units: Q — flow rate, gpm; d — inside diameter, inches. Exact continuity identity (V = Q/A), not an empirical formula.

Flag tiers (Industry Approximation — Verify with PE; thresholds vary by agency):

• < 2 fps — informational: check turnover, water age, sedimentation
• 2–5 fps — typical municipal design range
• 5–8 fps — upper municipal limit range; review
• > 8 fps — exceeds typical municipal maximum

Source: common municipal design guidance derived from GLUMRB "Ten States Standards" practice and typical utility design manuals. The computed velocity is reported unmodified in all cases.

A (in²) = π · Do² / 4 T (lb) = 2 · P · A · sin(θ/2) We (lb/ft) = γs · Hc · Do / 12 Fs (lb/ft) = f · (2·We + Wp+w) L (ft) = SF · P · A · tan(θ/2) / Fs

Variables & units:

• Do — pipe outside diameter, inches (thrust acts on the OD cross-section)
• P — design or test pressure, psi
• θ — fitting deflection angle, degrees (horizontal bends, 0 < θ ≤ 90°)
• f — soil-to-pipe friction coefficient (0.25–0.40 typical; lower for polyethylene-encased pipe)
• Wp+w — pipe plus contained water weight, lb/ft
• γs, Hc — soil unit weight (lb/ft³) and depth of cover (ft) for the earth prism We
• SF — safety factor (1.5 typical per DIPRA practice)

DIPRA-aligned preliminary thrust-restraint estimate based on longitudinal friction resistance only. Does not include passive soil bearing resistance. Final restrained length must be verified against DIPRA/AWWA/manufacturer requirements.

Assumptions & limitations: horizontal bend in uniform soil above the water table; friction-only resistance is conservative relative to the full DIPRA method (which adds passive bearing, ½·Rs). Not applicable to vertical bends, dead ends, or reducers without modification.

Source: DIPRA, Thrust Restraint Design for Ductile Iron Pipe; AWWA Manual M41. Friction-only simplification: Industry Approximation — Verify with PE.

t (in) = P · Do / (2 · S) P (psi) = 2 · S · t / Do

Variables & units: P — internal pressure, psi; Do — outside diameter, inches; S — allowable hoop stress, psi; t — wall thickness, inches.

Assumptions & limitations: thin-wall assumption (accurate for t/Do ≤ ~0.10; conservative beyond). S must already include the design/safety factor and any temperature or joint derating — this tool applies no additional factor. Internal pressure only; external loads, vacuum, and bending are excluded.

Source: Barlow's formula as applied in AWWA Manual M11 (Steel Pipe — A Guide for Design and Installation). The AWWA C900/C905 pressure-class equation PC = 2·HDS/(DR−1) is the same relation in dimension-ratio form.

Wc (psi) = γs · H / 144 Δy/D (%) = 100 · (DL·Wc + WL) · K / (0.149·PS + 0.061·E′)

Why PS and the load terms are required: the Iowa formula balances load (numerator) against the combined stiffness of the pipe ring (0.149·PS) and the surrounding soil (0.061·E′). Without pipe stiffness and the earth/live loads the equation is indeterminate — they are not optional refinements.

Variables & units: PS — pipe stiffness at 5% deflection per ASTM D2412, psi; E′ — modulus of soil reaction, psi; K — bedding constant (0.083–0.110; 0.10 typical); DL — deflection lag factor (use 1.0 with prism load, up to 1.5 with Marston load); γs — soil unit weight, lb/ft³; H — cover, ft; WL — live load at pipe depth, psi.

E′ guidance (granular embedment)	psi
Dumped / uncompacted	50–200
Slight compaction (< 85% Proctor)	200–400
Moderate compaction (85–95%)	1000
High compaction (> 95%)	2000–3000

HS-20 live load (commonly tabulated)	psi
1 ft cover	12.50
2 ft cover	5.56
4 ft cover	2.78
8 ft cover	0.69

Assumptions & limitations: flexible pipe with granular embedment; prism earth load; long-term soil consolidation captured only through DL. Allowable deflection varies by material — 5% initial is common for PVC (AWWA M23); check the governing product standard. Verify E′ and live loads against project geotechnical data and AASHTO.

Source: Spangler (1941), modified by Watkins (1958); AWWA M23 (PVC Pipe), M45 (Fiberglass), M55 (PE); ASTM D2412; E′ values per Howard (USBR).

ΔP (psi) = ρ · a · ΔV / 144 ΔH (ft) = a · ΔV / g (g = 32.174 ft/s²) Total = operating pressure + ΔP

Variables & units: ρ — fluid mass density, slug/ft³ (water ≈ 1.94 at 60 °F); a — pressure wave speed, fps; ΔV — velocity change, fps (full stoppage assumed).

Typical wave speeds: ductile iron 3000–4400 fps; steel 3000–4000 fps; PVC 1100–1500 fps (function of pipe material, wall, and entrained air — compute from pipe properties or take from manufacturer data).

Assumptions & limitations: valid for closure faster than one wave round-trip (t < 2L/a). Ignores friction, wave reflections, and column separation; a matching downsurge of −ΔP occurs and can drive the line into vacuum. This is a screening value, not a substitute for a full transient (method-of-characteristics) model on critical systems.

Source: Joukowsky (1898); discussed in AWWA M11 and standard transient references (Wylie & Streeter, Fluid Transients in Systems).

Fb = γw · π · (Do/12)² / 4 Wp = γp · π/4 · [(Do/12)² − ((Do−2t)/12)²] Ws = [γs·(Hc−Hsub) + (γs−γw)·Hsub] · Do/12, Hsub = min(Hw, Hc) SF = (Wp + Ws) / Fb Ballast (concrete, air wt) = [SFreq·Fb − (Wp+Ws)] · γc / (γc − γw)

Variables & units: γw = 62.4 lb/ft³; γc = 150 lb/ft³ (normal-weight concrete); Do, t — inches; Hc, Hw — feet; γp, γs — lb/ft³. All forces per foot of pipe.

Assumptions & limitations: worst case — pipe empty and fully submerged (groundwater at or above the crown); simple soil prism of width Do (no trench shear or wedge effects); soil below the water table taken at buoyant unit weight (γs − 62.4). Ballast is reported as concrete air weight, already corrected for the ballast's own submergence. Required SF varies by agency — 1.1 to 1.5 is typical; confirm the governing standard.

Source: Archimedes principle + prism method as discussed in AWWA M11 (flotation) and ASCE buried-pipe practice. Industry Approximation — Verify with PE.