Formula · 3 min read

Pressure drop (Darcy–Weisbach)

Every meter of hose and every coupling eats pump head: 90 L/min through 25 mm hose loses ≈ 20 kPa over 3 m (f = 0.035). If the loop's total drop exceeds the CDU's available head, flow falls below the formula on paper — and the rack overheats on a Friday afternoon.

Formula

ΔP = f × (L / D) × (ρ × v² / 2)  ·  v = Q / A

Darcy–Weisbach with friction factor f (≈ 0.03-0.04 for smooth hose at these flows), ρ ≈ 1,020 kg/m³ for PG25, and v the flow velocity. Velocity is the killer — it enters squared, which is why stepping down one hose size hurts so much.

Worked example

90 L/min · 25 mm ID · 3 m · f 0.035 → v 3.06 m/s → ΔP ≈ 20.0 kPa (2.9 psi)

That is just one straight hose. Add the rack manifold, two UQD couplings, elbows and the CDU heat exchanger, and a loop can easily demand 100-150 kPa — which is exactly what CDU pump curves are sized against.

Try it

20.0 kPa ≈ 2.9 psi · velocity 3.06 m/s
⚠️ Velocity 3.1 m/s — above the ~3 m/s comfort zone; erosion and noise risk, step up the diameter

Common mistakes

  • Undersized hose. Halving diameter multiplies velocity fourfold and drop roughly sixteen-fold (v² and D both bite). 25 mm+ supply lines are normal at rack flows for a reason.
  • Ignoring fittings and the UQD. Each elbow adds an equivalent length; a quick disconnect is often the single highest-drop element in a sub-loop. Count them, don't wish them away.
  • Reading the pump curve wrong. A CDU's "available head" is at a flow rate; as loop drop rises, operating flow slides down the curve. Check the intersection, not the brochure peak.

Related

Coolant flow rate (what Q should be) · What is a CDU? · Commissioning (verifying real ΔP and flow)

Sources

Darcy–Weisbach with Darcy friction factor; PG25 density ≈ 1,020 kg/m³ at 25 °C. Friction factor from Moody/Colebrook smooth-pipe turbulence — engineering approximation for first-pass sizing, not a substitute for vendor loop data.