Pipe Pressure Drop Calculator — Darcy-Weisbach (Dairy Piping)
Calculate pressure drop in dairy plant pipelines using the Darcy-Weisbach equation. Size pumps correctly and verify existing pipe layouts.
What is Pressure Drop in Dairy Pipelines?
Pressure drop (ΔP) is the loss of pressure as fluid flows through a pipe due to friction between the fluid and pipe wall. It directly determines:
- Pump head requirements: Under-sized pump = no flow
- CIP velocity: Minimum 1.5 m/s needed for effective cleaning — check ΔP across circuit
- PHE and valve sizing: Each fitting adds resistance
Darcy-Weisbach Equation
ΔP (Pa) = f × (L/D) × (ρ × v²/2)
Head Loss (m) = f × (L/D) × (v²/2g)
Where:
- f = Darcy friction factor (use 0.02–0.03 for turbulent dairy flow in SS pipes)
- L = pipe length (m)
- D = pipe internal diameter (m)
- ρ = fluid density (kg/m³) — milk ≈ 1030 kg/m³
- v = flow velocity (m/s)
- g = 9.81 m/s²
Friction Factor (f) for Dairy SS Pipes
For turbulent flow (Re > 4000), typical for dairy pipelines:
- Sanitary SS pipe (smooth): f ≈ 0.015–0.020
- Mild steel or slightly rough: f ≈ 0.020–0.030
Recommended Flow Velocities in Dairy
| Line Type | Recommended Velocity |
|---|---|
| Suction (pump inlet) | 0.5–1.0 m/s |
| Discharge (pump outlet) | 1.5–3.0 m/s |
| CIP circuits | 1.5–2.5 m/s |
| Long transfer lines | 1.0–2.0 m/s |
| Gravity drain lines | 0.5–1.0 m/s |
Fittings Equivalent Lengths (for adding to pipe length L)
| Fitting | Equivalent Length (× pipe diameter) |
|---|---|
| 90° elbow (SS sanitary) | 30 × D |
| 45° elbow | 16 × D |
| T-junction (through) | 20 × D |
| T-junction (branch) | 60 × D |
| Butterfly valve (open) | 6 × D |
| Ball valve (full open) | 3 × D |
Multiply fitting multiplier by pipe diameter to get equivalent pipe length in metres, then add to actual pipe length.
Example
50 mm ID pipe, 30 m long, milk at 2 m/s, f = 0.020:
ΔP = 0.020 × (30/0.05) × (1030 × 2²/2) = 0.020 × 600 × 2060 = 24,720 Pa ≈ 0.25 bar
Head = 24,720 / (1030 × 9.81) = 2.45 m
Add this to the static head to find total pump head required.