Mechanical · fluids

Pipe Flow & Pressure Drop

Darcy–Weisbach, the Moody diagram, and what it costs to push a fluid through a pipe.
Darcy–Weisbach · Swamee–Jain
turbulent

Set-up

define the run
20.0 L/s
100 mm
50 m

The Moody diagram

drag the marker along the curve · or use the flow slider
laminar (f = 64/Re) other roughness curves your pipe's curve log–log axes: friction factor f vs Reynolds number Re
Results
Flow detail
Cross-section

Velocity profile & wall gradient

updates live with flow, pipe and fluid
Relationships

What drives the pressure drop

amber markers track your current run
Pipe library

Standard sizes & roughness

roughness values are typical references, not certificates
Field notes

How the numbers fit together

Using this tool

How to estimate pressure drop in a pipe

Pushing fluid through a pipe costs energy, lost to friction along the walls. The Darcy–Weisbach equation ties that loss to four things: how fast the fluid moves, how long and wide the pipe is, and how rough its walls are. The friction factor comes off the Moody diagram above — the iconic log–log chart relating friction to the Reynolds number and relative roughness. Drag the operating point to see how your pipe sits on it.

Worked example

Water at 20 °C through 100 mm commercial steel pipe at 20 L/s gives a velocity of about 2.55 m/s and a Reynolds number near 250,000 — firmly turbulent.

The friction factor lands around 0.018, and over 50 m of pipe that's roughly 30 kPa of pressure drop. Step up one pipe size and that figure falls sharply — pressure drop scales with diameter to the fifth power.

Laminar or turbulent — does it matter?

A lot. Below a Reynolds number of ~2,300 flow is laminar and friction follows the clean f = 64/Re law. Above ~4,000 it's turbulent and roughness starts to matter. Most pumped liquid systems are turbulent.

Why is the turbulent velocity profile flatter than the laminar one?

Turbulent eddies constantly mix momentum across the pipe, dragging the slow fluid near the wall and the fast fluid at the centre toward each other — the result is a blunter, more uniform core with almost all the speed change crammed into a thin layer near the wall, unlike laminar flow's smooth parabola.

Why is diameter such a big deal?

Because pressure drop scales with 1/D⁵. A small increase in bore dramatically cuts the loss — often the cheapest fix for an under-performing line is simply a larger pipe.

Does this include fittings and valves?

No — this is straight-pipe (major) loss only. Elbows, valves, tees, and entrance/exit effects add "minor losses" that can be significant in a real system and need to be added separately.

What velocity should I aim for?

For water, very roughly 1–2.5 m/s is a common comfortable band — slow enough to limit erosion and noise, fast enough to avoid settling. The tool flags when you're outside typical ranges.

Results are for reference only. Check these numbers against other sources before relying on them for a real system design.