Gauge vs Absolute Pressure¶

Pressure is the most common source of unit errors in engineering. quantia handles gauge and absolute pressure the same way it handles temperature — via an affine unit that carries both a scale factor and an offset.

The problem¶

A gauge pressure reading of 0 psig does not mean "no pressure" — it means atmospheric pressure. The relationship is:

\[P_{absolute} = P_{gauge} \times scale + P_{atm}\]

where \(P_{atm}\) = 101 325 Pa (standard atmosphere, exact).

This is mathematically identical to the Celsius → Kelvin conversion:

\[T_K = T_{°C} \times 1 + 273.15\]

quantia uses the same AffineUnit mechanism for both.

The four pressure units¶

Symbol	Type	Offset	Use when
`psia`	absolute	0 Pa	reservoir pressure, PVT calculations
`psig`	gauge	101 325 Pa	wellhead, separator, surface readings
`bara`	absolute	0 Pa	SI-adjacent absolute
`barg`	gauge	101 325 Pa	European gauge readings

Converting between them¶

import quantia as qu

# 0 psig is always 1 atm absolute
qu.Q(0.0, 'psig').to('psia')    # UnitFloat(14.695..., 'psia')
qu.Q(0.0, 'psig').to('Pa')      # UnitFloat(101325.0, 'Pa')

# Typical wellhead pressure
qu.Q(500.0, 'psig').to('psia')  # UnitFloat(514.695..., 'psia')
qu.Q(500.0, 'psig').to('bara')  # UnitFloat(35.487...,   'bara')

# Reservoir pressure in various units
qu.Q(3500.0, 'psia').to('MPa')  # UnitFloat(24.13..., 'MPa')
qu.Q(3500.0, 'psia').to('barg') # UnitFloat(240.3..., 'barg')

Ambiguous `psi` and `bar`¶

Using plain psi or bar emits a UserWarning and is treated as absolute. Always use psia/psig or bara/barg explicitly:

qu.Q(100.0, 'psi')   # ⚠ UserWarning: treated as psia
# UserWarning: Ambiguous: 'psi' treated as 'psia' (absolute). Use 'psia' or 'psig' explicitly.
qu.Q(100.0, 'psia')  # ✓ no warning
qu.Q(100.0, 'psig')  # ✓ no warning

Legacy field unit: `kg/cm²`¶

Common in Latin America and older literature. quantia registers both spellings:

qu.Q(100.0, 'kg/cm2').to('psia')   # UnitFloat(1422.3..., 'psia')
qu.Q(100.0, 'kgf/cm2').to('bara')  # UnitFloat(98.07...,  'bara')

Gauge pressure in compound expressions¶

Gauge pressure cannot be used in compound expressions because the offset is non-linear when multiplied. quantia raises a DimensionError to prevent silent errors:

# This raises DimensionError — offset pressure × length is undefined
qu.Q(100.0, 'psig') * qu.Q(1.0, 'm')   # → DimensionError on .si_value()

# Correct approach: convert to absolute first
p_abs = qu.Q(100.0, 'psig').to('psia')
p_abs * qu.Q(1.0, 'm')                  # ✓ works

Uncertain pressure¶

ProbUnitFloat handles gauge pressure the same way:

with qu.config(seed=42, n_samples=3000):
    p_wh = qu.ProbUnitFloat.normal(500.0, 20.0, 'psig')

p_wh.to('psia').mean()   # ≈ UnitFloat(514.7, 'psia')
p_wh.to('bara').interval(0.90)