| name | pipe-sizing |
| description | Pipe sizing — velocity criteria, Darcy-Weisbach friction factor, economic pipe diameter, pressure drop, NPS schedules, liquid/gas/steam pipe sizing, ASME B31.3, API 14E erosional velocity. |
| metadata | {"priority":7,"promptSignals":{"phrases":["pipe sizing","pipe diameter selection","economic pipe diameter","pipe velocity","pressure drop pipe","NPS schedule","API 14E erosion"],"minScore":3}} |
Pipe Sizing — Complete Skill
Velocity Criteria (Rule-of-Thumb Starting Point)
| Fluid | Recommended Velocity [m/s] |
|---|
| Water (suction) | 0.5–1.5 |
| Water (discharge) | 1.0–3.0 |
| Cooling water | 1.5–3.0 |
| Process liquid | 1.0–3.0 |
| Viscous liquid | 0.5–1.5 |
| Saturated steam | 15–30 |
| Superheated steam | 30–60 |
| Process gas (low P) | 10–20 |
| Process gas (high P) | 5–15 |
| Compressed air | 8–15 |
| Slurries | 1.5–4.5 (above critical deposition) |
Pressure Drop Calculation (Darcy-Weisbach)
Frictional pressure drop:
ΔP_f = f × (L/D) × (ρ V²/2)
f = Darcy friction factor (from Moody chart or Colebrook-White)
L = pipe length [m]; D = internal diameter [m]
ρ = fluid density [kg/m³]; V = velocity [m/s]
Colebrook-White (implicit):
1/√f = -2 log₁₀(ε/(3.7D) + 2.51/(Re√f))
ε = absolute roughness [mm]:
- Commercial steel/welded: 0.046 mm
- Cast iron: 0.26 mm
- Galvanized steel: 0.15 mm
- Stainless (seamless): 0.015 mm
- HDPE/PVC: 0.0015 mm
Swamee-Jain (explicit approximation, ±3%):
f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re^0.9)]²
Reynolds number:
Re = ρ V D / μ = V D / ν
Minor losses:
ΔP_minor = K × ρV²/2
K values: gate valve (open) 0.1; globe valve 10; elbow 90° 0.9; tee (branch) 1.0
Equivalent length:
L_e = K × D / f (add to straight pipe length)
Economic Pipe Diameter
Annual cost method:
C_annual = C_capital/n + C_pump_energy
Optimal D minimizes total annual cost
Economic diameter approximation (liquids):
D_econ = 0.45 × Q^0.45 × ρ^0.13 × μ^0.025 / ΔP_allow^0.2 [m; Darby approximation]
Thumb rule (water, mild steel):
D_econ ≈ 3.9 × Q^0.45 [mm; Q in m³/hr]
Gas Pipe Sizing (Compressible Flow)
Low-pressure gas (ΔP < 10% P₁): use incompressible Darcy-Weisbach with ρ at mean P
High-pressure gas (ΔP > 10% P₁):
P₁² - P₂² = f × L/D × ρ₁ V₁² × P₁ (isothermal gas flow)
Or using volumetric flow rate Q at base conditions:
P₁² - P₂² = (C × f × L × Q_b² × G × T_b) / (D⁵ × P_b²)
G = gas specific gravity; T_b, P_b = base conditions (15°C, 101.325 kPa)
Choked flow check:
V < c × √(2γ/(γ+1)) → subcritical; if V approaches c → choke at outlet
Steam Pipe Sizing
Saturated steam:
Specific volume v_g from steam tables at P [bar]
ṁ = Q / v_g; V = ṁ × v_g / A
Typical ΔP: 0.1–0.3 bar/100m of equivalent pipe
Pressure drop (Unwin formula for steam):
ΔP = 18000 × f × L × W² / (D⁵ × ρ_avg) [Pa; W in kg/s, D in mm, L in m]
Steam trap sizing: condensate capacity = steam flow × X_quality_drop
API 14E Erosional Velocity (Oil & Gas)
Prevents erosion from sand/slugs at high velocity:
V_e = C / √ρ_mixture
C = empirical constant:
- Continuous service (solids present): C = 100 ft/s·(lb/ft³)^0.5 SI: C ≈ 122
- Intermittent/clean service: C = 150 → 200
Mixture density:
ρ_m = ρ_L × H_L + ρ_G × (1-H_L) [kg/m³]
H_L = liquid holdup fraction
Maximum erosional velocity: V_e = C/√ρ_m [m/s]
Design: V_actual ≤ 0.85 × V_e (allow margin)
NPS Pipe Schedules (ASME B36.10M / B36.19M)
NPS designations: nominal pipe size; actual OD ≠ NPS for small pipes
| NPS | OD [mm] | Sch 40 ID [mm] | Sch 80 ID [mm] | Sch 160 ID [mm] |
|---|
| 1" | 33.4 | 26.6 | 24.3 | 20.7 |
| 2" | 60.3 | 52.5 | 49.3 | 42.8 |
| 4" | 114.3 | 102.3 | 97.2 | 87.3 |
| 6" | 168.3 | 154.1 | 146.3 | 131.8 |
| 8" | 219.1 | 202.7 | 193.7 | 175.4 |
| 12" | 323.9 | 303.2 | 288.9 | 257.2 |
Schedule selection:
Sch 40 = standard; Sch 80 = extra strong; Sch 160 = high pressure; XXS = double extra strong
Wall thickness to pressure (ASME B31.3):
t = P × D_o / (2 × (S_E + P × Y)) + corrosion allowance
S = allowable stress; E = joint efficiency; Y = temperature coefficient
Flow Regime and Multiphase
Single phase: use Darcy-Weisbach
Two-phase: Lockhart-Martinelli or Beggs-Brill (horizontal/inclined); Orkiszewski (vertical)
Slug flow prevention: keep v_SL + v_SG within slug-free region on flow map
Minimum Pipe Size for Solids Transport
Slurry critical velocity (Durand):
V_c = F_L × √(2gD(ρ_s - ρ_f)/ρ_f)
F_L = factor from Durand chart (0.8–1.8 depending on d_particle/D)
Output
Provide: selected NPS and schedule, internal diameter D [mm], velocity V [m/s], Reynolds number Re, friction factor f, pressure drop ΔP [Pa/m and total], erosional velocity limit V_e [m/s] (if applicable), economic diameter comparison, applicable standard (ASME B31.3/B31.1/API 14E), and schedule selection basis (pressure rating at temperature T).
