By Wu Peng, Senior Process Instrumentation Engineer · Last reviewed July 22, 2026
To calculate the pressure drop in a pipe, use the Darcy-Weisbach equation: Δp = f (L/D) (ρv²/2). Multiply the friction factor by the pipe length divided by the inside diameter, then by the dynamic pressure of the flow. That one pressure drop formula covers any Newtonian liquid, any pipe material and any flow rate. The real work is finding the friction factor, and this guide walks every step with numbers you can check.
Pressure drop is pumping energy you pay for. A 2-inch steel line moving 12 m³/h of water loses about 5 kPa for every 10 m of run, and every elbow and valve adds more. Below: the formula, the friction factor without a Moody chart, worked examples in both kPa and psi, fitting losses, and the sizing rules engineers screen against. If you want the answer without the algebra, our pipe pressure drop calculator runs the same method and shows its work.
Contents
- Pressure drop basics
- The pressure drop formula
- Finding the friction factor
- Worked example
- Imperial worked example
- Laminar flow
- Fittings and valves
- Rules of thumb
- Measuring pressure drop
- FAQ
Pressure drop basics
Pressure drop is the pressure lost between two points in a line because the fluid rubs against the pipe wall and against itself. Put a gauge at the pump discharge, another 50 m downstream, and the difference is the friction loss of everything in between. Five variables set the number.
| Variable | Effect on pressure drop |
|---|---|
| Flow rate (velocity) | Strongest day-to-day driver. Loss rises with the square of velocity; doubling the flow in the worked example below multiplies the drop by 3.75. |
| Inside diameter | Strongest design lever. At fixed flow, loss scales with roughly the fifth power of bore. One size up (DN50 to DN65) cuts the example loss by 59 percent. |
| Pipe length | Linear. Twice the run, twice the loss. |
| Fluid properties | Density scales the loss directly; viscosity sets the flow regime and, through it, the friction factor. |
| Wall roughness | Rougher wall, higher friction factor. Matters in turbulent flow only. |
Elevation change adds a separate static term (ρgh). This guide covers the friction part; both belong in a line calculation.
The pressure drop formula
The standard equation for pressure drop in a pipe is the Darcy-Weisbach equation:
Δp = f × (L / D) × (ρ × v² / 2)
| Symbol | Meaning and SI unit |
|---|---|
| Δp | Pressure drop, Pa |
| f | Darcy friction factor, dimensionless (4 times the Fanning factor; do not mix the two) |
| L | Pipe length, m |
| D | Inside diameter, m (not the nominal size) |
| ρ | Fluid density, kg/m³ |
| v | Mean velocity, m/s |
The last bracket, ρv²/2, is the dynamic pressure of the flow, so the formula reads naturally: every diameter of travel costs the flow f times its dynamic pressure. The same equation comes in head form, h = f (L/D)(v²/2g), which returns meters of fluid column; multiply by ρg to get back to pascals. Our pressure units guide covers the conversions.
Darcy-Weisbach handles liquids directly. Gases can be treated as incompressible with inlet density as long as the calculated drop stays below about 10 percent of the inlet absolute pressure, a Crane TP-410 practice. Beyond that, split the line into segments or move to a compressible method.
Finding the friction factor
The friction factor depends on the Reynolds number and on the relative roughness of the wall. Compute the Reynolds number first:
Re = ρ × v × D / μ
where μ is the dynamic viscosity in Pa·s. Below about 2,300 the flow is laminar and the factor is exact: f = 64/Re. Above about 4,000 it is turbulent, and f comes from the Colebrook-White equation, which is implicit and traditionally read off a Moody chart. The Swamee-Jain approximation skips both:
f = 0.25 / [log10(ε/(3.7D) + 5.74/Re0.9)]²
It tracks Colebrook-White within about one percent across normal industrial ranges, well inside the uncertainty of any roughness estimate. Between 2,300 and 4,000 the regime is unstable; size on the turbulent result to stay safe.
| Pipe material | Absolute roughness ε (mm) |
|---|---|
| Commercial steel | 0.045 |
| Stainless steel | 0.015 |
| Cast iron | 0.26 |
| PVC and PE | 0.0015 to 0.007 |
| Concrete | 0.3 to 3.0 |
Published values for new pipe. Corrosion, scale and biofilm raise roughness over the years in service.
Worked example
Water at 20 °C (density 998 kg/m³, viscosity 1.002 × 10−3 Pa·s) flows at 12 m³/h through 50 m of 2-inch schedule 40 steel pipe, inside diameter 52.5 mm, roughness 0.045 mm.
Step 1. Velocity. Flow area A = πD²/4 = 2.165 × 10−3 m², and 12 m³/h is 0.00333 m³/s. So v = Q/A = 1.54 m/s, comfortably inside the usual 1 to 3 m/s range for water. Our pipe velocity calculator does this step on its own.
Step 2. Reynolds number. Re = 998 × 1.54 × 0.0525 / 0.001002 = about 80,500. Turbulent.
Step 3. Friction factor. Relative roughness ε/D = 0.045/52.5 = 0.00086. Swamee-Jain returns f = 0.0223.
Step 4. Pressure drop. Δp = 0.0223 × (50/0.0525) × (998 × 1.54²/2) = 0.0223 × 952 × 1,183 Pa = 25.1 kPa with these rounded figures; carried at full precision the answer is 25.2 kPa (0.25 bar), or 5.0 kPa per 10 m. In head terms the pump supplies 2.6 m of water column just to cover friction.
These are the default numbers in our pressure drop calculator, so you can rerun the case and change one variable at a time. Doubling the flow to 24 m³/h lifts the loss to 94 kPa, 3.75 times as much.
Imperial worked example
Same method in US units, on the case behind a classic hydraulics cross-check: 60 GPM of water through 100 ft of 2-inch schedule 40 pipe, inside diameter 2.067 in.
Velocity works out to 5.7 ft/s, the Reynolds number to about 91,400, and the friction factor to 0.0220. The equation returns 2.83 psi per 100 ft. Plumbing and fire-protection references quote 2.7 to 3 psi for this exact case, so the method lands where decades of published tables say it should.
If you work across unit systems, keep the calculation in SI and convert at the end. Our flow rate units guide and pressure unit tables cover the conversions.
Laminar flow
Viscous fluids change the rules. Push gear oil (density 850 kg/m³, viscosity 100 cP, which is 0.1 Pa·s) at 1 m³/h through 10 m of DN25 pipe with a 26.6 mm bore: velocity is 0.50 m/s and the Reynolds number is only 113. That is laminar, so f = 64/Re = 0.566, and the drop is 22.6 kPa. Nearly the loss of the 50 m water example, from one fifth of the length.
Two laminar habits are worth keeping. Roughness does not matter, because 64/Re contains no roughness term. And the drop scales linearly with flow and with viscosity instead of with velocity squared, so a cold start at double the viscosity doubles the pressure drop. Size heat-traced oil lines on the winter viscosity, not the nameplate value.
Fittings and valves
Straight-run friction is rarely the whole story. Each fitting adds a loss proportional to the dynamic pressure, counted with a resistance coefficient K:
Δp (fittings) = ΣK × (ρ × v² / 2)
| Fitting | Typical K value |
|---|---|
| Standard 90-degree elbow | 0.9 |
| Long-radius elbow | 0.3 |
| Tee, through run | 0.6 |
| Tee, branch flow | 1.8 |
| Gate valve, fully open | 0.2 |
| Swing check valve | about 2 |
| Globe valve, fully open | about 10 |
Typical published values for screwed fittings (Crane TP-410 and standard handbooks). Flanged and large-bore fittings run lower; confirm vendor data for anything critical.
Add two standard elbows and an open gate valve to the worked example: ΣK = 2.0 and the dynamic pressure is 1,183 Pa, so the fittings add 2.4 kPa, nearly 10 percent on top of the 25 kPa straight run. A part-open globe or control valve is a different matter: it can drop more pressure than the rest of the line combined, which is exactly its job.
Rules of thumb
Before any calculation, most engineers screen a line size against sizing conventions:
| Service | Common design envelope |
|---|---|
| Water and liquid process lines | 1 to 4 psi per 100 ft (about 2 to 9 kPa per 10 m), velocity 1 to 3 m/s |
| Pump suction lines | Low end of the range; keep velocity down to protect the pump inlet |
| Compressed air mains | 0.3 to 0.5 psi per 100 ft |
Published sizing practice from engineering handbooks and compressed air industry guidance. Screening values, not limits.
The worked example sits at 5 kPa per 10 m, inside the envelope. Treat these numbers as first-pass screening: they say whether a line size is plausible, and the Darcy-Weisbach calculation says whether it is right. Run both before you lock in a bore.
Measuring pressure drop
Calculation predicts; measurement confirms. The standard instrument is a differential pressure transmitter piped across the section you care about. Across a strainer or filter, the reading is a health signal: rising DP means the element is loading up. Across a known length of straight pipe, it is a flow check, because the measured drop and the formula together give you velocity without cutting the line. That link between the two quantities is the subject of our guide to flow rate and pressure.
Flow meters spend pressure too, and the difference between element types is large. An orifice plate gives up most of its differential as permanent loss, a venturi tube recovers most of it in the diffuser, and an averaging pitot tube adds the least of the family. On long lines the meter belongs in the same pressure drop budget as the pipe friction; the differential pressure flow meter range covers the trade-offs.
Application example
Fuel handling, Zambia. For a customer metering diesel fuel, the proposal was an averaging pitot tube flow meter: it inserts a probe instead of restricting the bore, so its permanent pressure loss is the lowest of the differential pressure elements. Pressure loss, not the price list, drove the shortlist.
Whether the laminar or the turbulent formula applies is set by the Reynolds number; you can compute it directly from flow rate or velocity with our Reynolds number calculator.
FAQ
How to calculate pipe pressure drop?
Work four steps: get velocity from flow rate and pipe area, get the Reynolds number from velocity, bore, density and viscosity, find the friction factor (64/Re when laminar, Swamee-Jain or a Moody chart when turbulent), then apply Δp = f (L/D)(ρv²/2). Add fitting losses with the K-factor method.
What is the equation for pressure drop?
The Darcy-Weisbach equation, Δp = f (L/D)(ρv²/2), where f is the friction factor, L/D the length in diameters, and ρv²/2 the dynamic pressure. It applies to any Newtonian fluid in any pipe; in head form it reads h = f (L/D)(v²/2g).
How much pressure drop per 100 ft of pipe?
It depends on flow, bore and fluid. As a benchmark, 60 GPM of water in 2-inch schedule 40 pipe loses 2.83 psi per 100 ft. Liquid lines are commonly sized to run between about 1 and 4 psi per 100 ft at design flow.
What is the rule of thumb for pressure drop in pipe?
Keep liquid lines around 1 to 4 psi per 100 ft (2 to 9 kPa per 10 m) at 1 to 3 m/s, and compressed air mains near 0.3 to 0.5 psi per 100 ft. Rules of thumb screen a line size; a Darcy-Weisbach calculation confirms it.
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Written and technically reviewed by Wu Peng and the Instranova engineering team.