Pipe Flow Pressure Drop Calculator

Formula

• Velocity: V = Q / A with A = π D² / 4 (Q in m³/s, D in m).
• Reynolds: Re = ρ V D / μ. Laminar Re ≤ 2000 → f = 64/Re. Turbulent → Swamee–Jain f = [−2 log₁₀(ε/D/3.7 + 5.74/Re^0.9)]⁻².
• Darcy friction head: h_f = f (L/D) V² / (2g). Minor: h_m = K V² / (2g). Elevation: h_elev = Δz (rise positive).
• Total: h = h_f + h_m + h_elev. Pressure drop: ΔP = ρ g h.
• Hydraulic power loss (dissipation only): P = ρ g Q (h_f + h_m). Elevation is potential energy, not included in power loss.
• Hazen–Williams (water): h_f (m) = 10.67 L Q^1.852 / (C^1.852 D^4.8704) with Q in m³/s and D in m. Minor and elevation still add with the same V.

How it works

Estimate friction, minor, and elevation head for a straight pipe run. Darcy–Weisbach uses Swamee–Jain friction for laminar/turbulent Newtonian liquids; Hazen–Williams covers water-like irrigation lines. Metric and Imperial, material and fluid presets, ΣK fittings, and elevation change. Feed total head into the pump power calculator.

Pick Metric or Imperial, then Darcy–Weisbach or Hazen–Williams. Choose a material preset to fill roughness (and suggested C). In Darcy mode pick a fluid preset for density and viscosity. Optional elbow / tee / gate counts refresh Total K using typical values (0.9 / 1.8 / 0.2). Elevation rise is positive. CALCULATE fills pressure drop, head stack, velocity, Re, f, and power loss and updates the sketch. Editing a field or switching units/method clears Results. RESET restores defaults for the active unit system and returns method to Darcy.

Friction, minor losses, and elevation

h_total = h_f + h_m + Δz. ΔP = ρ g h_total.

Default Darcy keep-alive (K = 0, Δz = 0): ≈ 339 kPa and 34.6 m friction head.

Darcy–Weisbach vs Hazen–Williams

Laminar Re ≤ 2000 · transitional 2000–4000 · turbulent ≥ 4000.

Typical ε: copper/PVC 0.0015 mm, commercial steel 0.045 mm, galvanized 0.15 mm.

Fittings K and velocity limits

Worked example

Metric Darcy default: 50 mm ID, 100 m galvanized pipe (ε = 0.15 mm), 25 m³/h water at 998 kg/m³ and 1 cP, no fittings, level run.

1. A = π (0.05)² / 4 = 0.0019635 m²
2. V = (25/3600) / A = 3.537 m/s
3. Re = 998 × 3.537 × 0.05 / 0.001 ≈ 176 500 (turbulent)
4. ε/D = 0.003 → Swamee–Jain f ≈ 0.02712
5. h_f = 0.02712 × (100/0.05) × 3.537² / (2 × 9.81) ≈ 34.58 m
6. ΔP = 998 × 9.81 × 34.58 / 1000 ≈ 338.5 kPa

Result: Pressure drop ≈ 339 kPa, head loss 34.6 m, hydraulic power loss ≈ 2.35 kW. With ΣK = 3.6 and +10 m elevation the same geometry returns ≈ 459 kPa and 46.9 m total head.

When to use

• Estimating friction and total head for pump TDH
• Comparing material roughness or Hazen–Williams C on the same line
• Screening velocity and Reynolds number in liquid pipe design
• Adding typical fitting K and elevation to a straight-run balance

Limitations

• Single straight run only — not a multi-branch network or Excel element table
• Incompressible single-phase Newtonian liquid; no compressible gas or slurry
• Turbulent Darcy uses Swamee–Jain, not iterative Colebrook
• Hazen–Williams is for water / water-like liquids, not oils
• Fitting K values are typical handbook figures, not manufacturer Cv data
• No reverse-solve for minimum diameter or flow from a max ΔP (phase 2)
• No plastic SDR/CTS schedule catalog or 2K/3K fitting methods

FAQ

Darcy vs Fanning friction factor?

This calculator uses the Darcy (Moody) friction factor f_D in ΔP = f (L/D) ρ V² / 2. The Fanning factor is f_F = f_D / 4. Do not mix them in the same formula.

When should I use Hazen–Williams instead of Darcy?

Use Hazen–Williams for water and irrigation screening when you have a C coefficient and want the common municipal formula. Use Darcy whenever density and viscosity matter (oils, process fluids) or you need a laminar / transitional check.

Typical roughness and C values?

Drawn copper and PVC ≈ 0.0015 mm; commercial new steel ≈ 0.045 mm; galvanized ≈ 0.15 mm; new cast iron ≈ 0.26 mm. Hazen–Williams C is often ≈ 150 for plastics, 130 for new steel, 120 for galvanized, and lower for aged iron.

How do fittings enter the calculation?

Minor head is h_m = K V² / (2g). Enter Total K, or use the quick counts (90° elbow ≈ 0.9, tee branch ≈ 1.8, open gate ≈ 0.2) to refresh K. Elevation rise adds static head on top of friction and minor losses.

How do I use this with the pump power calculator?

Run CALCULATE here, take total head loss (friction + minor + elevation), add any discharge pressure head your process needs, then enter that TDH with your flow on the pump power calculator to get hydraulic, shaft, and electrical power.

Does hydraulic power loss include elevation?

No. Power loss is dissipation from friction and fittings only: P = ρ g Q (hf + hm). Elevation change still appears in total head and ΔP for pump TDH, but it is potential energy, not a frictional loss.