Introduction to Pressure Drop
Pressure drop (ΔP) is the reduction in fluid pressure that occurs as fluid moves through a pipe due to friction and elevation changes. Accurate pressure drop calculation is essential for sizing pumps, selecting pipe diameters, and ensuring adequate flow throughout a piping system.
There are two primary methods for calculating pressure drop in pipes:
- Darcy-Weisbach equation — applicable to all fluids and flow regimes
- Hazen-Williams formula — simpler, empirical method for water only
The Darcy-Weisbach Equation
The fundamental equation for pressure drop in a straight pipe is:
Where:
- ΔP = pressure drop (Pa)
- f = Darcy friction factor (dimensionless)
- L = pipe length (m)
- D = pipe inner diameter (m)
- ρ = fluid density (kg/m³)
- v = flow velocity (m/s)
The term ρv²/2 is the velocity pressure, and L/D is the pipe length-to-diameter ratio. The friction factor f accounts for pipe roughness and Reynolds number.
The Friction Factor
For laminar flow (Re < 2300), f = 64/Re — straightforward and exact.
For turbulent flow (Re > 4000), the friction factor is determined by the Colebrook-White equation:
This is implicit in f and requires iterative solution. The Moody chart provides graphical solutions.
Typical Friction Factors
| Pipe Material | Roughness ε (mm) | Typical f (Re=10⁵) |
|---|---|---|
| Drawn tubing (copper, brass) | 0.0015 | 0.016 |
| Commercial steel (new) | 0.045 | 0.019 |
| Galvanized iron | 0.15 | 0.023 |
| Cast iron | 0.26 | 0.025 |
| Concrete | 0.3-3.0 | 0.028-0.045 |
| Riveted steel | 1-10 | 0.035-0.06 |
Worked Example
Problem: Water at 20°C flows at 2 m/s through 100 m of 100 mm ID new commercial steel pipe. Calculate pressure drop.
-
Calculate Reynolds number:
- ρ = 1000 kg/m³, μ = 0.001 Pa·s
- Re = ρvD/μ = 1000 × 2 × 0.1 / 0.001 = 200,000 (turbulent)
-
Find friction factor (using Colebrook or Moody):
- ε/D = 0.00045, Re = 200,000 → f ≈ 0.019
-
Apply Darcy-Weisbach:
- ΔP = 0.019 × (100/0.1) × (1000 × 4/2) = 0.019 × 1000 × 2000 = 38,000 Pa = 38 kPa
Minor Losses from Fittings
Straight pipe friction is only part of total pressure loss. Fittings and valves add "minor losses" expressed as:
Typical K-factors (resistance coefficients):
| Fitting | K-factor |
|---|---|
| 90° elbow, standard | 0.9 |
| 45° elbow | 0.4 |
| Gate valve (open) | 0.17 |
| Globe valve (open) | 6.0 |
| Ball valve (open) | 0.05 |
| Tee through-flow | 0.9 |
| Tee branch | 1.8 |
| Sharp entrance | 0.5 |
| Sudden expansion (D₁/D₂) | (1 - (D₁/D₂)²)² |
Hazen-Williams for Water
For water systems at ambient temperature, many engineers use the simpler Hazen-Williams formula:
Where:
- Q = flow (m³/s)
- C = Hazen-Williams roughness coefficient
- D = diameter (m)
- S = hydraulic gradient (m/m, head loss per unit length)
Typical C-Factors
| Pipe Material | C-factor |
|---|---|
| PVC, HDPE (new) | 150 |
| Copper, brass | 140 |
| New steel (lined) | 120-130 |
| 20-year-old steel | 100 |
| Old cast iron | 80 |
| Riveted steel | 60-80 |
Best Practices
- Use conservative friction factors — add a safety margin of 10-20% for aging, fouling, and future corrosion
- Size for 1-3 m/s velocity in liquid lines to balance capital cost and operating cost
- Include all fittings in minor loss calculations — a long run with many elbows can exceed the straight-pipe loss
- Consider suction piping separately — keep suction velocities under 1.5 m/s and minimize fittings to protect NPSH
- Use the right equation — Darcy-Weisbach for general engineering; Hazen-Williams only for water distribution where specified
Summary
Pressure drop calculation is fundamental to piping system design. The Darcy-Weisbach equation with an appropriate friction factor provides the most accurate results for any fluid. Always include both straight-pipe losses and minor losses from fittings, and verify your results with online calculators or pipe flow software for complex systems.