Convert between feet/metres of head and psi/bar/kPa using Head = 2.31·psi/SG, with specific-gravity correction
Understand head vs pressure, where the 2.31 ft/psi factor comes from, and why specific gravity changes the answer
Both directions are the same equation rearranged:
Where 2.31 comes from: a column of water 1 ft tall puts 0.433 psi on its base (62.4 lb/ft³ ÷ 144 in²/ft²). Inverting, 1 psi needs 1 ÷ 0.433 = 2.31 ft of water — so 2.31 ft H₂O = 1 psi at SG = 1.
Non-psi/non-ft inputs are first converted on an SG-independent basis: 1 bar = 14.5038 psi, 1 psi = 6.89476 kPa, 1 m = 3.28084 ft.
Pressure at the bottom of a column is density × height (P = ρ·g·h). A denser fluid makes more pressure per foot, so for the same pressure it needs less head — head scales as 1/SG.
A centrifugal pump develops a fixed head regardless of fluid, but the pressure rise in psi rises and falls with the SG of whatever it is pumping — which is exactly why the SG term belongs in the conversion.
Use Head (ft) = 2.31 × Pressure (psi) ÷ specific gravity. For water (SG = 1), 100 psi equals 2.31 × 100 = 231 ft of head. To go the other way, Pressure (psi) = Head (ft) × SG ÷ 2.31, so 150 ft of water is 150 × 1 ÷ 2.31 = 64.9 psi.
Pressure at the bottom of a column equals fluid density times height (P = ρ·g·h), so a denser fluid makes more pressure per foot of column. Head scales as 1/SG: 100 psi gives 231 ft of water (SG 1) but 271.8 ft of diesel (SG 0.85) because the lighter fluid needs a taller column to make the same pressure. Centrifugal pumps add head, not pressure, so the developed psi changes with the fluid being pumped.
2.31 is the number of feet of water that exerts 1 psi at the base of the column at SG = 1. It comes from 144 in²/ft² ÷ 62.4 lb/ft³ = 2.3094 ft per psi. The reciprocal, 0.433, is the psi developed per foot of water column. Dividing by specific gravity adapts both constants to any other fluid.