Darcy–Weisbach Pressure Drop Calculator
Solve the classic pipe-loss relation ΔP = f · (L/D) · (ρv²)/2 for any of its six unknowns — pressure drop, friction factor, pipe length, diameter, fluid density, or velocity — with step-by-step math, a live pipe schematic, and companion head-loss metrics.
The friction factor is the engine of the loss
The Darcy friction factor f packs all the physics of the wall–fluid interaction into a single dimensionless number. In fully developed laminar flow it is purely a function of Reynolds number, f = 64/Re. In turbulent flow it depends on both Re and the relative roughness ε/D, and must be read from the Moody chart or solved implicitly with the Colebrook–White equation. Smooth pipe at high Re has f ≈ 0.008–0.012; commercial steel is typically 0.02–0.03; heavily corroded or scaled pipe can exceed 0.05. Every doubling of f doubles the pressure drop at the same flow.
Diameter dominates everything else
Because ΔP ∝ 1/D, diameter is the single most powerful variable in the equation. At the same volumetric flow, halving the diameter multiplies the pressure drop by 32 (2⁵) — a factor of 2 from the 1/D term itself and a further 16 from the velocity quadrupling as the same flow is forced through a quarter of the area. This is why modestly upsizing a pipe is the classic energy-saving move in pumping systems: a small increase in capital cost buys a large reduction in pumping power.
Velocity enters squared
ΔP scales with v², so the pressure drop is extremely sensitive to how fast the fluid is pushed. Doubling the flow rate through the same pipe quadruples the pressure drop and therefore quadruples the pumping power (since power = ΔP × Q, and Q itself doubled). This squared dependence is the reason designers aim for the lowest practical velocities — and why flow balancing in a large network is so difficult. The friction factor itself also drifts with Reynolds number, so the exponent is not exactly 2 in practice, but the v² term dominates.
Length enters linearly, roughness enters non-linearly
Pressure drop is directly proportional to pipe length — double the length and you double the loss. This linearity is what makes equivalent-length tables so useful: every fitting can be replaced by an equivalent straight length, and the whole system summed. Roughness is subtler: it only affects turbulent flow, and its influence saturates at high Re when the flow becomes fully rough and f depends only on ε/D. This is why a very rough pipe cannot be fixed by pumping slower — the friction factor stops falling once the roughness sublayer is fully exposed.
How to Use This Calculator
The Darcy–Weisbach equation links six quantities: the pressure drop ΔP, the friction factor f, the pipe length L, the internal diameter D, the fluid density ρ, and the average velocity v. Give the tool five of them and it will find the sixth.
1. Choose what to solve for
Pick any one of the six variables from the toggle. The calculator rearranges ΔP = f·(L/D)·(ρv²)/2 for whichever you choose and locks that field while you fill in the rest.
2. Enter the pipe geometry
Give the internal diameter D (not the nominal size) and the total straight-run length L. If you have fittings, convert them to equivalent lengths and add them to L for a first estimate.
3. Enter the fluid properties and flow rate
Set the density ρ from the presets (air, water, seawater, oil, mercury) or type your own. Then set the average velocity v — or derive it from volumetric flow using v = Q/(πD²/4).
4. Pick a realistic friction factor
The single most error-prone input. Use 0.005–0.01 for smooth pipe, 0.02–0.03 for commercial steel, 0.04–0.08 for rough or corroded pipe. In the Advanced panel, enter the fluid viscosity to check the Reynolds number and confirm whether the flow is laminar, transitional, or turbulent.
5. Read the result and the budget
The result card shows ΔP in Pa, kPa, bar, psi, and metres of fluid head. A colour-coded verdict classifies the flow regime, and the pressure budget bars put ΔP in context against the dynamic pressure and one atmosphere.
6. Check the schematic and the charts
The schematic shows the pressure gradient falling along the pipe, velocity vectors scaled to speed, and wall shear stress opposing the flow. The main chart plots ΔP against velocity for three friction factors; the Advanced chart plots ΔP against length for three diameters.
What This Tool Offers
Built around the Darcy–Weisbach relation ΔP = f·(L/D)·(ρv²)/2, the fundamental link between pipe friction, geometry, and flow energy.
Six-way solving
Solve for pressure drop, friction factor, length, diameter, density, or velocity. The calculator rearranges the Darcy–Weisbach equation automatically for whichever variable you choose.
Live pipe schematic
A scale drawing of the pipe with the pressure gradient falling along it, velocity vectors scaled to speed, wall-shear arrows opposing the flow, and dimension lines for L and D.
Pressure budget bars
See at a glance how the pressure drop compares with the dynamic pressure ½ρv² and with one atmosphere, so you can judge whether the loss is significant.
Flow-regime verdict
Each result is classified from creeping / nearly static through typical process piping, water mains, HVAC, and up to erosion-risk velocity, with a note when the value sits outside normal design limits.
Multi-unit hints
Each field shows the value converted to related units — kPa, bar, psi, atm and metres of fluid head for ΔP; km/h, knots and ft/s for velocity; mm for diameter.
Reference tables
A pressure unit converter, a ΔP lookup grid across lengths and velocities, typical values by pipe system, and a full variable reference table.
Reference Tables & Conversions
A pressure unit converter, a ΔP lookup grid, typical Darcy–Weisbach values by system, and the full variable list.
Pressure unit converter
Pressure Drop ΔP Lookup
Computed from ΔP = f·(L/D)·(ρv²/2) with ρ = 1.225 kg/m³ (air), f = 0.02, D = 0.1 m. Values in Pa. Multiply by ρ/1.225 for other fluids, and by 1/f×0.02 for other friction factors.
| Length L (m) | v = 1 m/s | v = 5 m/s | v = 10 m/s | v = 20 m/s | v = 50 m/s | v = 100 m/s |
|---|
Typical Darcy–Weisbach Values by Pipe System
Representative order-of-magnitude values. ΔP is computed from the other columns using ΔP = f·(L/D)·(ρv²/2).
| System | ρ (kg/m³) | D (m) | L (m) | v (m/s) | f (–) | ΔP (Pa) |
|---|
Typical Friction Factors by Pipe Material
Darcy–Weisbach friction factor f for fully turbulent flow in clean, new pipe. Real values rise with age and fouling.
| Material | Relative roughness ε/D | Typical f (–) | Notes |
|---|---|---|---|
| Drawn tubing (copper, brass) | ~0.0000015 | 0.008–0.012 | Hydraulically smooth |
| PVC / plastic pipe | ~0.0000015 | 0.008–0.012 | Smooth, low loss |
| Commercial steel (new) | ~0.00045 | 0.018–0.025 | Standard pipework |
| Galvanised iron | ~0.0015 | 0.022–0.032 | Common in HVAC and water |
| Cast iron (new) | ~0.0025 | 0.025–0.035 | Water mains |
| Cast iron (aged, tuberculated) | ~0.02–0.05 | 0.045–0.08 | Heavy internal fouling |
| Concrete pipe | ~0.003 | 0.025–0.040 | Large water and sewer mains |
| Riveted steel | ~0.005–0.02 | 0.035–0.060 | Old industrial piping |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| ΔP | Pressure drop across the pipe | 1 – 10⁷ | Pa |
| f | Darcy–Weisbach friction factor | 0.005 – 0.10 | – |
| L | Pipe straight-run length | 0.1 – 10⁶ | m |
| D | Pipe internal diameter | 0.005 – 2 | m |
| ρ | Fluid density | 0.09 – 13 546 | kg/m³ |
| v | Average bulk velocity | 0.01 – 100 | m/s |
| Re | Reynolds number Re = ρvD/μ | 10² – 10⁷ | – |
| ε | Absolute wall roughness | 0.0000015 – 0.005 | m |
| hf | Head loss hf = ΔP/(ρg) | 0.01 – 1000 | m |
| K | Loss coefficient K = f·L/D | 0.1 – 10⁴ | – |
| τw | Wall shear stress f·ρv²/8 | 0.1 – 10³ | Pa |
What Does ΔP = f·(L/D)·(ρv²)/2 Measure?
The Darcy–Weisbach equation is the standard engineering formula for the pressure lost to friction as a fluid flows through a pipe. It says that the pressure drop is proportional to the dynamic pressure of the flow (½ρv²), to the friction factor of the pipe wall, and to the ratio of pipe length to diameter (L/D). The equation is dimensionally clean, valid across the full range from laminar to fully turbulent flow, and used in every branch of fluid engineering — from municipal water networks and HVAC systems to oil pipelines, chemical plants, and aircraft fuel lines.
Darcy–Weisbach Formula
The defining relationship is:
Rearranged to solve for the other five unknowns:
L = 2 · ΔP · D / (f · ρ · v²)
D = f · L · ρ · v² / (2 · ΔP)
ρ = 2 · ΔP · D / (f · L · v²)
v = √( 2 · ΔP · D / (f · L · ρ) )
Dividing through by ρg converts the equation to the head-loss form used by hydraulic engineers:
The group f·L/D is often called the loss coefficient K. Using it, the equation collapses to ΔP = K·(½ρv²) — the pressure drop is simply K times the dynamic pressure.
Darcy–Weisbach Variables
| Symbol | Meaning | Notes |
|---|---|---|
| ΔP | Pressure drop | Pa; the friction loss over the pipe run |
| f | Darcy friction factor | Dimensionless; 4× the Fanning friction factor |
| L | Pipe length | m; straight-run, or straight + equivalent lengths |
| D | Internal diameter | m; the true inside diameter, not nominal size |
| ρ | Fluid density | kg/m³; assume constant along the pipe |
| v | Average bulk velocity | m/s; equal to Q / (πD²/4) |
| μ | Dynamic viscosity | Pa·s; needed only to compute the Reynolds number |
How Each Variable Affects the Result
The equation is a product, so it is linear in f, L, and ρ: doubling any of these doubles the pressure drop. Velocity enters squared, so doubling the flow velocity quadruples the loss — and, at constant pipe size, doubles the volumetric flow, so the pumping power rises by a factor of eight. Diameter enters through 1/D directly and through v² indirectly when the flow rate is fixed, giving an effective 1/D⁵ dependence at constant Q. That is why the diameter is the single most powerful design lever in any piping system.
The friction factor f is the most nuanced term. In laminar flow it falls as 1/Re, so a slower, more viscous flow has a higher f — the opposite of the turbulent trend. In turbulent flow it rises with relative roughness ε/D and falls with Re, and at high Re it saturates at a value that depends only on roughness. The transition between laminar and turbulent (Re ≈ 2300–4000) is the region where simple correlations break down and the friction factor can jump abruptly.
Length is the dullest but most honest variable: pressure drop is directly proportional to L, so adding pipe is always costly. This is why designers work hard to shorten runs, use generous bend radii to reduce equivalent lengths, and place pumps and tanks as close to the load as the layout allows.
Darcy–Weisbach Calculation Examples
ΔP = 0.02 × (100/0.05) × (998 × 4)/2 = 0.02 × 2000 × 1996 = 79,840 Pa
ΔP = 0.018 × (30/0.3) × (1.2 × 100)/2 = 0.018 × 100 × 60 = 108.0 Pa
f = 2 × 79,840 × 0.05 / (100 × 998 × 4) = 7,984 / 399,200 = 0.02000
hf = ΔP / (ρg) = 79,840 / (998 × 9.80665) = 8.154 m of water
Frequently Asked Questions
They are the same physical idea scaled by a factor of 4. The Darcy–Weisbach factor (sometimes written fD) is what this calculator uses: ΔP = fD·(L/D)·(ρv²/2). The older Fanning factor fF is defined with a factor of 2 instead of 4 in the denominator, so fD = 4·fF. A Fanning factor of 0.005 corresponds to a Darcy factor of 0.020. Mixing the two conventions is one of the most common errors in pipe-loss calculations — if your answer is off by a factor of four, check which one your source is using. This calculator uses the Darcy convention throughout.
For laminar flow (Re < 2300) the exact answer is f = 64/Re — no chart needed. For turbulent flow, the Haaland equation is a good explicit approximation: 1/√f ≈ −1.8·log₁₀[ (ε/D / 3.7)¹·¹¹ + 6.9/Re ]. It is accurate to about 1% against the Colebrook–White equation, which is the standard but must be solved iteratively. For very rough pipe at high Re, f ≈ 0.25 / [log₁₀(ε/(3.7D))]², the fully-rough limit. In day-to-day work, a value of 0.02 for commercial steel and 0.01 for smooth plastic is often close enough for a first estimate.
Because the friction loss is the mechanical work done by the wall shear stress against the flow, and wall shear stress itself scales with the dynamic pressure ½ρv². The dynamic pressure is the kinetic energy per unit volume of the moving fluid, and it scales with v² for the same reason that kinetic energy does — it is the energy the fluid carries that must be dissipated into heat by friction. The L/D factor simply says the loss accumulates linearly along the pipe, and f is the efficiency of that dissipation. Put together: pressure drop = (friction efficiency) × (geometric accumulation) × (energy density), which is the whole equation in words.
Major losses are the friction losses in straight pipe — what the Darcy–Weisbach equation computes. Minor losses are the additional losses from fittings, bends, valves, entrances, exits, and other disturbances; despite the name, in short, compact systems they can easily dominate. Minor losses are usually written as ΔPminor = K·(½ρv²), where K is a fitting-specific loss coefficient (0.9 for a 90° elbow, 10 for a fully open gate valve, 0.5 for a sharp entrance, 1.0 for a sharp exit). To include them in this calculator, convert each fitting to an equivalent length Le = K·D/f and add it to L.
Several common reasons. First, the actual pipe is rarely the nominal size — internal diameter shrinks with wall thickness, scale, and deposits, and 1/D⁵ amplifies small errors. Second, fittings and valves are usually neglected — in a short, bendy run they can double the loss. Third, elevation change adds hydrostatic pressure that is not a friction loss at all. Fourth, the friction factor used may not match the actual Reynolds number. Fifth, the real flow may not be steady — surges, water hammer, and two-phase flow all behave differently. And finally, the pump curve gives the total head the pump delivers, which must cover friction plus elevation plus any residual pressure at the outlet — not just the friction loss computed here.
Roughness is folded into the friction factor f, not entered separately in the Darcy–Weisbach equation itself. To get f from roughness you need the relative roughness ε/D and the Reynolds number, then either read the Moody chart or use the Colebrook–White or Haaland equation. Absolute roughness ε for common materials runs from about 0.0015 mm for drawn tubing to 0.045 mm for commercial steel, 0.15 mm for galvanised iron, 0.26 mm for cast iron, and 1–5 mm for heavily tuberculated pipe. In the Advanced panel of this calculator you can enter the fluid viscosity to compute the Reynolds number and confirm which regime you are in.
The calculator works in SI internally — Pa, m, kg/m³, m/s, and a dimensionless f. The hints under each field show the value in common alternative units (kPa, bar, psi, atm for pressure; feet for length and diameter; km/h, knots, ft/s for velocity), and the pressure unit converter at the bottom of the page converts freely between all the common pressure units. If you have friction factor in the Fanning convention, multiply by 4 before entering it. If you have flow rate in m³/h, convert to velocity first with v = Q/(3600·πD²/4).
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| delta_P | Pressure drop | Pa |
| f | Darcy friction factor | |
| L | Pipe length | m |
| D | Pipe diameter | m |
| rho | Fluid density | kg/m3 |
| v | Average velocity | m/s |
What it means
The Darcy‑Weisbach equation is the standard method for calculating the pressure drop due to friction in a pipe with steady, incompressible flow. It is expressed as ΔP = f (L/D) (ρ v² / 2), where f is the Darcy friction factor (dimensionless), L is pipe length, D is internal diameter, ρ is fluid density, and v is average velocity. The friction factor depends on the Reynolds number and the relative roughness of the pipe, and it is obtained from the Moody chart or empirical correlations like the Colebrook equation. This equation is essential for designing piping systems, selecting pump sizes, and estimating energy losses. It accounts for head loss due to viscous shear. The equation is also used in conjunction with minor loss coefficients for fittings and valves. Understanding the Darcy‑Weisbach equation is crucial for civil, mechanical, and chemical engineers who work with fluid transport. It is also the basis for more complex network analysis using the Hardy Cross method.
Worked example
Darcy-Weisbach Pressure Drop – Two Examples
Real‑World| Parameter | Value |
|---|---|
| f | 0.02 |
| L | 100 m |
| D | 0.1 m |
| ρ | 1000 kg/m³ |
| v | 2 m/s |
| Parameter | Value |
|---|---|
| f | 0.025 |
| L | 50 m |
| D | 0.05 m |
| v | 1.5 m/s |
Common mistakes
- Friction factor f: For laminar flow, f = 64/Re; for turbulent, use the Colebrook equation or Moody chart. Do not assume a constant f.
- Length L and diameter D: Use the same units (e.g., m).
- Velocity v: Average velocity, not maximum.
- Pressure drop units: The result is in Pa (N/m²) if all SI units are used.
- Minor losses: This formula accounts only for pipe friction; add fittings, valves, and entrance/exit losses separately.
Applications
The Darcy‑Weisbach equation, ΔP = f·(L/D)·(ρv²/2), calculates the pressure drop due to friction in pipe flow. It is the most widely used formula for head loss in liquid and gas pipelines. The friction factor f depends on Reynolds number and pipe roughness, and can be determined from the Moody chart or explicit correlations. Engineers use this equation to size pumps, to design pipe networks, and to predict energy consumption in fluid transport systems. It is applied in water supply, oil and gas transportation, and chemical plant piping. By estimating the pressure drop, professionals can select appropriate pipe diameters, determine pump power requirements, and ensure that the system operates within acceptable pressure limits. Accurate prediction prevents over‑sizing of equipment and reduces operational costs.
- Design of water distribution and sewage networks
- Sizing of pipelines for oil, gas, and chemicals
- Pump selection and power requirement calculations
- Analysis of existing piping systems for capacity and energy efficiency
- Hydraulic design of fire protection systems
Related calculators · Process Design
Recently updated formulas
Suggest an improvement
Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.