Friction pressure drop scales with 1/d⁵ — a modest increase in diameter slashes losses.
From Darcy–Weisbach at fixed flow. Going from 25 mm to 32 mm pipe cuts friction loss by ~70%. Bigger pipe is usually cheaper than a bigger pump.
Only when friction is what is costing you. If the loss is mostly static lift, or a part-closed valve, or an undersized pump, going up a size changes almost nothing — you pay for the copper and the flow barely moves.
At 22 mm the rule says 0.381 kPa and the exact answer is 0.381 kPa — within half a percent. It holds to within 10% up to 33.6 mm, then drifts.
The fifth power assumes the friction factor stays put, and it does not — it falls as the bore grows and the flow turns over. Anchored at 22 mm the rule is close next door and drifts about 20% by the time you reach 54, always in the same direction: it promises more improvement than a bigger pipe actually delivers.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Pipe Flow & Pressure Drop Calculator →Friction pressure drop scales with 1/d⁵ — a modest increase in diameter slashes losses. From Darcy–Weisbach at fixed flow.