Darcy f vs Fanning f_F?

This app uses the Darcy factor in ΔP = f (L/D)(½ρv²). f = 4 f_F relative to the Fanning factor common in some chemical-engineering texts.

Does ΔP / 100 include fittings?

No. The gradient is straight pipe only. Hero ΔP includes L + Σ L_eq.

Are steam and air densities fixed?

Yes — typical screening presets. For HP steam or compressed air, treat results as order-of-magnitude only.

Pressure Drop & Friction Loss Calculator

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

Darcy–Weisbach equation (closed-conduit friction) · Haaland (1983) explicit friction-factor approximation · Crane Technical Paper No. 410 (fitting L/D factors) · ASME B36.10M / B36.19M (pipe ID by NPS/schedule)

Δ P = f \cdot \frac{L _{total}}{D} \cdot \frac{1}{2} ρ v^{2}

h_{f} = \frac{Δ P}{ρ \cdot g}

\frac{1}{f} = - 1.8 lo g_{10} [(\frac{ε / D}{3.7})^{1.11} + \frac{6.9}{R e}]

R e = \frac{ρ \cdot v \cdot D}{μ}

Darcy-Weisbach Equation, Haaland Explicit Friction & Crane TP-410 Fitting Equivalents

Darcy–Weisbach ΔP = f (L_tot/D) (½ρv²)Haaland f explicit Colebrook approx.ε (new CS) 0.045 mmCrane L/D 30 / 8 / 340

Hero ΔP is total friction drop on L + Σ L_eq. Friction factor f uses the Haaland explicit approximation to Colebrook–White. ID comes from the B36.10M / B36.19M schedule row. Fitting L/D values are Crane TP-410 screening factors (90° LR elbow 30, gate 8, globe 340). Steam/air/crude/condensate use fixed screening ρ and μ — HP steam and compressed air are order-of-magnitude only. ΔP/100 is reported for straight pipe only (no fittings).

ΔP (Total Friction Pressure Drop) — Hero output — friction loss on L + Σ L_eq (bar or psi).
f (Darcy Friction Factor) — Haaland / laminar 64/Re (dimensionless).
L (Straight Pipe Length) — Physical run length (m or ft).
L_eq (Fitting Equivalent Length) — Σ (L/D)·D for elbows, gates, globes.
D (Inside Diameter (ID)) — Schedule bore from the pipe table (m).
v (Mean Velocity) — v = Q / A with A = π D²/4.
ε (Absolute Roughness) — Selectable surface roughness (mm).
Re (Reynolds Number) — Re = ρ v D / μ.

2. Allowances, Tolerances & Standards

Results are single-phase Newtonian screening. Confirm pump curves and project velocity limits separately.

Absolute Roughness ε0.015 / 0.045 / 0.15 / 0.30 mm

Presets for SS/PVC, new CS, corroded CS, and heavily corroded steel.

Crane L/D (this app)Elbow 30 · Gate 8 · Globe 340

Converted as L_eq = (L/D) × D and added to straight L before ΔP.

ΔP / 100 reportingStraight pipe only

Gradient excludes fittings. Imperial shows psi per 100 ft (scaled from the 100 m straight basis).

Flow RegimeRe < 2300 → f = 64/Re

Otherwise Haaland turbulent branch. Transition band is not specially smoothed.

Quick Reference Lookup Table

Water ~20 °C — NPS 4 Sch 40, 100 m straight, no fittings (Haaland, ε = 0.045 mm)
Q (m³/h)	v (m/s)	ΔP (bar)	ΔP (psi)
20	0.676	~0.045	~0.65
40	1.353	~0.168	~2.44
50	1.691	0.259	3.76
80	2.706	~0.66	~9.6
100	3.382	~1.03	~14.9
150	5.073	~2.33	~33.8

50 m³/h is independently verified near 0.259 bar (3.76 psi) with ρ ≈ 998 kg/m³. Live calculator uses the app water ρ(T) correlation (~999 kg/m³ at 20 °C) and recomputes f(Re). Other rows are v²-scaled screens.

3. Material & Code Limitations

Keep liquid headers near 1.5–3.0 m/s when practical. Steam/air densities in this tool are fixed screening values.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
Liquid headers (CS)	Typical v ≈ 1.5–3.0 m/s	Economic ΔP often ≤ ~0.1–0.2 bar / 100 m	Default case (~1.35 m/s at 40 m³/h in NPS 4 Sch 40) sits in the usual band.
Pump suction	Often 0.6–1.5 m/s	Protect NPSHa	Prefer larger ID and fewer fittings on suction lines.
Steam / air (this app)	Fixed ρ / μ presets	Order-of-magnitude only	HP steam and compressed air need project properties — not the LP presets.
Non-Newtonian fluids	Out of scope	N/A	Slurries and polymers need specialized rheology models.

Code Applicability & Safety Boundaries

Calculator scope: single-phase Darcy–Weisbach ΔP with Haaland f and Crane L/D elbows/gates/globes.
Does not size pumps, control valves, or two-phase / flashing flow.
Globe valves (L/D = 340) can dominate — remove or resize before blaming pipe ID.

4. Step-by-Step Worked Example

Field VerificationShow

Step-by-Step Worked Example: Match the Calculator Default

Reproduce the app default: water @ 20 °C, Q = 40 m³/h, NPS 4 Sch 40, L = 100 m, ε = 0.045 mm, four 90° LR elbows, two gate valves.

Fluid:Water @ 20 °C (app ρ ≈ 999 kg/m³, μ ≈ 0.001 Pa·s)Flow Q:40 m³/hPipe:NPS 4 Sch 40 (ID = 102.26 mm)Straight length L:100 mFittings:4 × elbow (L/D=30) + 2 × gate (L/D=8)Roughness ε:0.045 mm (new commercial steel)

Velocity from ID

v = Q / (π D^{2} /4)

D = 0.10226 m → A = 0.008213 m². Q = 40/3600 = 0.01111 m³/s → v = 1.353 m/s.

Result:v = 1.353 m/s

Within typical liquid header guidance.

Reynolds number

R e = ρ v D / μ

Re ≈ 999 × 1.353 × 0.10226 / 0.001 ≈ 1.38 × 10⁵ (turbulent).

Result:Re ≈ 1.38×10⁵

Haaland turbulent branch applies.

Haaland friction factor

1/ f = - 1.8 lo g_{10} [(ε / D /3.7)^{1.11} + 6.9/ R e]

ε/D ≈ 0.000440 → f ≈ 0.01903.

Result:f ≈ 0.01903

Matches the calculator friction factor for the default case.

Equivalent length with fittings

L_{t o t} = L + \sum (L / D) \cdot D

Σ L/D = 4×30 + 2×8 = 136 → Σ L_eq = 136 × 0.10226 ≈ 13.91 m. L_tot ≈ 113.9 m.

Result:L_tot ≈ 113.9 m

Fittings add ~14% equivalent length.

Total ΔP (hero)

Δ P = f (L_{t o t} / D) (1/2 ρ v^{2})

ΔP ≈ 0.194 bar (≈ 2.81 psi). Straight-only gradient ≈ 0.170 bar / 100 m.

Result:ΔP ≈ 0.194 bar · ΔP/100 m ≈ 0.170 bar

Hero includes fittings; ΔP/100 badge is straight pipe only.

Conclusion: Default app case: v ≈ 1.35 m/s, f ≈ 0.0190, L_tot ≈ 113.9 m, ΔP ≈ 0.194 bar (2.81 psi). Raise NPS or cut globe valves if ΔP is excessive.

5. Frequently Asked Questions & Technical References

Show

Colebrook–White is implicit in √f. Haaland is an explicit approximation typically within ~1.5% of Colebrook — adequate versus roughness uncertainty.