Pressure Drop Calculator (Darcy-Weisbach)

Darcy-Weisbach Equation Explained

The Darcy-Weisbach equation is the most accurate general method for pressure drop in pipes:

DeltaP = f x (L / D) x (rho x v^2 / 2)

Where DeltaP = pressure drop (Pa), f = Darcy friction factor, L = pipe length (m), D = inner diameter (m), rho = fluid density (kg/m3), v = average velocity (m/s).

Example: water (1000 kg/m3) at 2 m/s in a 100 mm pipe, 100 m long, f = 0.02: DeltaP = 0.02 x (100/0.1) x (1000 x 4 / 2) = 40,000 Pa = 40 kPa. Doubling velocity quadruples the drop because v appears squared.

Typical Friction Factors

| Pipe Condition | Darcy Friction Factor (f) |

|---|---|

| Smooth drawn tubing (copper, plastic) | 0.01 - 0.02 |

| New commercial steel | 0.015 - 0.025 |

| Slightly corroded steel | 0.02 - 0.04 |

| Heavily fouled / old pipe | 0.04 - 0.08 |

For laminar flow (Re < 2300), f = 64/Re exactly. For turbulent flow, f depends on Reynolds number and relative roughness — use the Moody chart or Colebrook equation. A 0.02 default is a reasonable first estimate for clean industrial water lines.

Worked Example: Sizing a Pump for Line Loss

A 100 m long, 100 mm ID water line carries 2 m/s (56.5 m3/h). With f = 0.02:

DeltaP = 0.02 x (100/0.1) x (1000 x 2^2 / 2) = 40 kPa

Convert to head: h = DeltaP / (rho x g) = 40,000 / (1000 x 9.81) = 4.1 m. This head loss must be added to static head when sizing the pump. A 200 m line doubles the drop to 80 kPa (8.1 m); a 50 mm line at the same velocity quadruples it to 160 kPa.