Pipeline Pressure Drop Calculator

Pressure drop in a pipeline is the loss of static pressure required to push a fluid through a length of pipe at a given flow rate. This calculator estimates the frictional pressure drop for a straight, round pipe using the Darcy–Weisbach equation with a standard friction-factor model (laminar: 64/Re; turbulent: Haaland approximation). It is commonly used for sizing pipe diameters, checking whether a pump/compressor has enough margin, and comparing design options.

What this calculator does (and what it does not)

Included: wall-friction losses for fully developed, single-phase, Newtonian flow in a straight circular pipe. The key output is the pressure drop ΔP across the entered length.

Not included by default: minor losses from fittings/valves/entrances/exits, elevation (static head) changes, compressibility effects for gases at large pressure changes, two-phase flow, non-Newtonian rheology, or heat/temperature-driven property variation. See Assumptions & limitations for details.

Inputs explained

• Pipe diameter, D (m): the internal diameter that the fluid flows through. Using an outside diameter will underpredict ΔP.
• Pipe length, L (m): straight-run length over which you want the frictional drop.
• Absolute roughness, ε (m): a surface roughness parameter used for turbulent friction factor (relative roughness ε/D). If unknown, you can start with typical values (see table below) and refine using vendor/standard data.
• Volumetric flow rate, Q (m³/s): volumetric throughput at the flowing conditions.
• Dynamic viscosity, μ (Pa·s): viscosity at the flowing temperature (water at ~20 °C is about 0.001 Pa·s).
• Fluid density, ρ (kg/m³): density at the flowing temperature/pressure (water ~998–1000 kg/m³ near room temperature).

Equations used

The calculator follows the standard Darcy–Weisbach workflow:

1. Compute cross-sectional area: A = πD²/4
2. Compute average velocity: v = Q/A
3. Compute Reynolds number: Re = (ρvD)/μ
4. Compute Darcy friction factor f:
   • Laminar (typically Re < 2000): f = 64/Re
   • Turbulent: Haaland explicit approximation (close to Moody chart across common engineering ranges)
5. Compute pressure drop: ΔP = f (L/D) (ρv²/2)

Darcy–Weisbach in MathML:

Haaland approximation (one common form) for turbulent flow:

1/√f = −1.8 log₁₀[( (ε/3.7D)^1.11 ) + (6.9/Re )]

Note: Some references write the Haaland equation with the terms inside the log arranged slightly differently; the intent is the same—an explicit approximation to the implicit Colebrook–White relation.

Typical absolute roughness values (order-of-magnitude)

How to interpret the results

• ΔP (pressure drop): the frictional pressure loss across the pipe length L. If your page displays kPa, remember: 1 kPa = 1000 Pa.
• Head loss equivalent (optional concept): you can convert pressure drop to head loss (meters of fluid) using h_f = ΔP/(ρg), where g ≈ 9.81 m/s². This is useful for pump sizing.
• Sensitivity: for a fixed diameter, ΔP grows roughly with v² (and thus roughly with Q²) in turbulent flow, so small increases in flow can cause large increases in required pressure.

Worked example (turbulent water flow)

Given: Water at ~20 °C flowing in a commercial steel pipe.

• D = 0.10 m
• L = 100 m
• ε = 0.000045 m
• Q = 0.010 m³/s
• μ = 0.001 Pa·s
• ρ = 1000 kg/m³

1. Area: A = πD²/4 = π(0.10)²/4 ≈ 0.00785 m²
2. Velocity: v = Q/A = 0.010 / 0.00785 ≈ 1.27 m/s
3. Reynolds: Re = ρvD/μ = (1000)(1.27)(0.10)/0.001 ≈ 1.27×10⁵ (turbulent)
4. Relative roughness: ε/D = 0.000045/0.10 = 4.5×10⁻⁴
5. Friction factor (Haaland): f ≈ 0.017–0.02 (typical magnitude at this Re and roughness)
6. Dynamic pressure term: ρv²/2 ≈ 1000(1.27²)/2 ≈ 808 Pa
7. Pressure drop: ΔP = f(L/D)(ρv²/2) ≈ 0.018(100/0.10)(808) ≈ 14,500 Pa ≈ 14.5 kPa

Interpretation: over 100 m, you need roughly 14–15 kPa of additional upstream pressure (ignoring fittings/elevation) to maintain 0.010 m³/s. If the line includes multiple valves/bends, the true required pressure will be higher once minor losses are added.

Design comparisons: diameter vs. pressure drop

The table below illustrates the typical tradeoff: larger diameter reduces velocity and pressure drop rapidly (especially in turbulent flow), at the cost of larger pipe size.

Assumptions & limitations

• Minor losses excluded: losses from bends, tees, valves, entrances/exits, reducers/expanders are not included. In short systems or highly fitted piping, minor losses can be comparable to (or larger than) straight-run friction.
• Elevation/static head not included: if the outlet is higher than the inlet, add ρgΔz (or convert to head).
• Single-phase, Newtonian fluid: slurries, non-Newtonian fluids, and two-phase flows need different models.
• Property variation not modeled: μ and ρ are treated as constants. Large temperature changes or strong compressibility invalidate this assumption.
• Gas compressibility: for gases, if pressure drop is a significant fraction of absolute pressure, use a compressible gas-flow model (e.g., isothermal/adiabatic with appropriate friction treatment).
• Flow regime boundaries are approximate: the laminar/turbulent transition can depend on disturbances and entrance effects; “Re < 2000 laminar” is a guideline.
• Geometry: assumes a straight, circular pipe and fully developed flow. Non-circular ducts require hydraulic diameter and may need different correlations.

References (common engineering sources)

• Darcy–Weisbach equation (standard fluid mechanics texts)
• Colebrook–White equation and Moody diagram (turbulent friction factor)
• Haaland, S. E. (1983). “Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow.”