Head vs Pressure: Why Pumps Are Rated in Feet Instead of PSI

Key Formula / Key Facts Box

Overview — What It Is and Why It Matters

In pump specifications the term “head” is a measure of energy per unit weight of fluid, expressed as a vertical height (feet or meters). Pressure, by contrast, is energy per unit volume (psi or pascal). Because a pump adds energy by raising the fluid’s potential, describing that energy as a height of liquid is the most direct representation.

Using head instead of pressure makes performance curves independent of fluid density. The same head value applies to water, oil, or low‑viscosity solvents; only the conversion to pressure changes with ρ. Mis‑interpreting the head‑to‑pressure relationship can lead to undersized piping, excessive motor loading, or seal failure.

The Method — Derivation and Variants

The relationship originates from the definition of static pressure in a column of fluid:

ΔP = ρ g H

Rearranging yields the governing formula shown above.

US‑customary derivation (water):

ρ_water = 62.4 lb/ft³
g = 32.174 ft/s²
1 psi = 144 lb/ft²

ΔP (psi) = (62.4 lb/ft³ × 32.174 ft/s² × H ft) / 144 lb/ft² ≈ 0.433 H.

SI derivation (water):

ρ_water = 1000 kg/m³
g = 9.80665 m/s²

ΔP (Pa) = ρ g H → 1 m head = 9.80665 kPa (≈ 9.81 kPa).

Variants appear when the fluid is not water, when compressible gases are involved, or when velocity and friction heads are added. The total dynamic head (TDH) used for pump selection is:

TDH = H_static + H_friction + H_velocity

Each term may be expressed in feet (or meters) and summed before conversion to pressure.

Worked Example

Example 1 – US customary (water)

A cooling‑water loop requires 500 gpm flow, a static lift of 30 ft, pipe friction loss of 10 ft, and a velocity head of 2 ft. Determine the required pump head, the corresponding pressure rise, and the motor shaft power assuming 70 % pump efficiency.

1. TDH = 30 ft + 10 ft + 2 ft = 42 ft.
2. Pressure rise: ΔP = 0.433 psi/ft × 42 ft = 18.2 psi.
3. Convert flow to ft³/s: 500 gpm ÷ 7.4805 = 66.9 ft³/min = 1.115 ft³/s.
4. Hydraulic power = ΔP × Q = 18.2 psi × 144 in²/ft² × 1.115 ft³/s ≈ 2,926 lb·ft/s.
5. Convert to horsepower: 2,926 lb·ft/s ÷ 550 = 5.3 hp.
6. Motor shaft power = 5.3 hp ÷ 0.70 ≈ 7.6 hp (≈ 5.7 kW).

The pump should be selected with a rating of at least 42 ft head at 500 gpm.

Example 2 – SI (light oil, ρ = 850 kg/m³)

A process requires 0.03 m³/s of oil to overcome 8 m static head, 3 m friction loss, and 0.5 m velocity head. Find the required head, pressure rise, and brake power for a pump operating at 75 % efficiency.

1. TDH = 8 m + 3 m + 0.5 m = 11.5 m.
2. Pressure rise: ΔP = ρ g H = 850 kg/m³ × 9.80665 m/s² × 11.5 m ≈ 96,200 Pa ≈ 96.2 kPa.
3. Hydraulic power = ΔP × Q = 96,200 Pa × 0.03 m³/s ≈ 2,886 W.
4. Brake power = 2,886 W ÷ 0.75 ≈ 3,848 W ≈ 3.85 kW.

The selected pump must deliver ≥ 11.5 m head at 0.03 m³/s.

Calculator

For quick head‑to‑pressure conversions and TDH calculations, use the online tool: Total Dynamic Head Calculator.

Reference Values & Typical Ranges

• Water: 1 ft head = 0.433 psi; 1 m head = 9.81 kPa.
• Typical industrial centrifugal pumps: 20 ft – 450 ft head (6 m – 137 m).
• Positive‑displacement pumps can be rated up to 700 ft head for high‑pressure services.
• Viscous liquids use the same head values; pressure conversion uses the specific ρ of the liquid.
• Compressible gases: head is rarely used; pressure rating is preferred.

Sources: ANSI/HI 1.1‑2014, API 610, ISO 9906:2012.

Application Guidance

When selecting a pump, start with the required TDH expressed in feet (or meters). Use the manufacturer’s head‑vs‑flow curve to locate the operating point that satisfies the desired flow rate.

Convert head to pressure only when:

• Checking pipe wall stress or burst ratings.
• Comparing against pressure‑rated components such as seals, relief valves, or pressure vessels.
• Complying with ASME pressure‑code requirements.

Field‑adjustment tips:

• Altitude: Effective g decreases slightly; multiply head by (g_local/g_standard).
• Temperature: Fluid density changes; recalculate the conversion factor ΔP = ρ g H.
• Multi‑stage pumps: Total head is the sum of stage heads; verify NPSH_R for each stage.

Common Mistakes, Limits & Safety Notes

1. Unit mix‑up. Applying the 0.433 psi/ft factor (water) to oil or glycol under‑predicts pressure by up to 30 %.
2. Ignoring velocity head. At high velocities (> 5 ft/s) the v²/2g term can add > 1 ft head, leading to pump oversizing.
3. Using head for gases. Gas density varies with pressure; head does not represent true energy addition—use pressure rise directly.
4. Neglecting NPSH. A high head rating does not guarantee cavitation‑free suction; always confirm NPSH_A > NPSH_R.
5. Assuming 100 % efficiency. Real pumps operate 60–80 % efficient; motor power must be derated accordingly.
6. Overlooking temperature effects. Water density drops ~0.3 % per 10 °C rise, altering the psi‑per‑ft factor.
7. Exceeding seal or casing pressure limits. Convert head to pressure and compare with the lowest rated component (often seals rated ~150 psi).