How the pressure drop is calculated
Friction between the fluid and the pipe wall costs pressure. The Darcy-Weisbach equation describes this loss for any fluid and pipe:
Δp = (f · L ÷ D + ΣK) · ρ · v² ÷ 2
Re = ρ · v · D ÷ μ
1 ÷ √f = −2 log10(k ÷ (3.7 D) + 2.51 ÷ (Re √f))
- f
- Darcy friction factor; 64/Re for laminar flow (Re below 2,300), Colebrook-White for turbulent flow
- L, D
- pipe length and inner diameter
- ΣK
- sum of loss coefficients for bends, valves and tees
- v
- mean velocity, flow divided by cross-section
- k
- absolute wall roughness
- μ
- dynamic viscosity
Worked example
50 m³/h of water at 20 °C flows through 100 m of DN100 steel pipe with 102.3 mm inside diameter. The velocity is 1.69 m/s and the Reynolds number about 172,000, so the flow is turbulent. Colebrook-White gives a friction factor of 0.0188, and the pressure drop is 0.262 bar, or 2.67 m of head.
Typical wall roughness
| Material | Roughness k (mm) |
|---|---|
| PVC, PE, PP, copper (new) | 0.0015 – 0.007 |
| Stainless steel | 0.015 |
| Steel, commercial (new) | 0.045 |
| Galvanised steel | 0.15 |
| Cast iron | 0.26 |
| Steel, corroded | 0.5 – 2 |
| Concrete | 0.3 – 3 |
Old pipes with deposits can be much rougher than new ones. For existing lines, a conservative roughness gives a safer result.
Bends, valves and fittings
Each fitting adds a loss of K · ρv²/2. Add the K-values of all fittings in the line and enter the sum. Typical values: 90° long-radius elbow 0.3, standard elbow 0.75, open gate valve 0.2, open globe valve 6 to 10, swing check valve 2, tee through branch 1.3, pipe entry from a tank 0.5, exit into a tank 1.0.