Engineering Calculators
● Darcy-Weisbach / Colebrook-White Guide

Pipe Pressure Drop & Pump Sizing: Darcy-Weisbach and the Friction Factor

A plain-language guide to sizing a coolant pump: how Darcy-Weisbach turns flow, pipe size and roughness into a pressure drop, where the friction factor comes from (laminar vs turbulent, Swamee-Jain), how fitting minor losses add up, and how pressure drop becomes pump head and power.

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Why a cooler needs a pump, and a pump needs a pressure drop

You can size a heatsink or a heat exchanger perfectly, but nothing moves the coolant through it for free. Every metre of pipe, every bend and every valve resists the flow, and the pump has to make up that resistance as a pressure rise. Sizing the pump therefore comes down to one number: the total pressure drop of the loop at the flow rate you need. Get that, and the pump head and power fall straight out of it.

Darcy-Weisbach: the master equation

The pressure drop along a straight pipe is given by the Darcy-Weisbach equation, ΔP = f·(L/D)·(ρ·v²/2). Three of those terms are just geometry and flow: the pipe's length-to-diameter ratio L/D, and the dynamic pressure ρ·v²/2 (how much "push" the moving fluid carries, which rises with the square of velocity). The fourth, the Darcy friction factor f, is where all the physics hides — it captures how much the pipe wall drags on the flow, and it depends on whether the flow is smooth (laminar) or chaotic (turbulent).

Where the friction factor comes from

The dividing line is the Reynolds number, Re = v·D/ν, which weighs the fluid's inertia against its viscosity. Below about Re = 2300 the flow is laminar and orderly, and the friction factor is exactly f = 64/Re — no roughness dependence at all, because the fluid glides in smooth layers that never touch the wall's texture. Above about Re = 4000 the flow is turbulent, the wall roughness starts to matter, and the friction factor is read from the Moody chart — or, for a design tool, from the Swamee-Jain equation, an explicit formula that reproduces the chart without the iteration the original Colebrook equation needs. In between (2300–4000) the flow is genuinely unpredictable, so this calculator just interpolates across the gap.

Minor losses, pump head vs power, and a coolant-loop checklist

Why fittings can dominate a short run, the difference between pump head and pump power, and how to turn all of this into a pump specification.

"Minor" losses that aren't always minor

Every elbow, tee, valve and pipe entrance adds a local loss, tallied as ΔP = ΣK·(ρ·v²/2), where each fitting contributes a loss coefficient K (a 90° elbow ≈ 0.9, a fully-open globe valve ≈ 10, a sharp entrance ≈ 0.5). They're called "minor" losses by tradition, but on a short, fitting-heavy run — exactly what a compact liquid-cooling loop tends to be — they can easily outweigh the straight-pipe friction. The published K values vary a lot between sources and connection types, so treat them as representative and use a manufacturer's figure for anything dominant (a control valve, say).

Head and power are not the same thing

Two different numbers come out of the pressure drop. The pump head, H = ΔP/(ρ·g), is a height of fluid — it's what you match against a pump's published head-vs-flow curve to check the pump can actually deliver your flow. The pump power is energy per second: the hydraulic power ΔP·Q is the useful part, and dividing by the pump's efficiency (small coolant pumps are often only 30–60% efficient) gives the shaft/electrical power the pump actually draws. A pump can have plenty of head yet still need surprising electrical power once its efficiency is accounted for.

Coolant-loop checklist

  1. Fix the flow rate from the heat you need to move and the allowable coolant temperature rise (the Heat Exchanger and Heatsink calculators set this).
  2. Keep pipe velocity in the ~1–3 m/s band: below that, air and sediment don't clear; above it, pressure drop and erosion climb fast.
  3. Add up every fitting's K — on a compact loop the fittings often dominate, so don't skip them.
  4. Compute the total pressure drop at your design flow, convert to head, and check it against the pump's curve at that flow, not just its dead-head maximum.
  5. Size the electrical supply from the shaft power (hydraulic ÷ efficiency), and leave margin — a fouled cold plate or a partially-closed valve raises the system resistance over time.

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