pascal-seconds (Pa-s) to centipoises (cP) conversion

What is the Pascal-Second?

The pascal-second is the SI derived unit of dynamic (shear) viscosity, measuring a fluid's resistance to flow. It quantifies the shear stress needed to produce a unit velocity gradient in a fluid.

Definition

One pascal-second is the viscosity of a fluid in which a shear stress of one pascal produces a velocity gradient of one reciprocal second between adjacent layers.

$$1\ \text{Pa-s} = 1\ \text{Pa·s}$$

Expressed in SI base units, 1 Pa·s = 1 kg·m⁻¹·s⁻¹ = 1 N·s/m². It is the coherent SI unit of dynamic viscosity and is exactly equal to 10 poise (the CGS unit), so 1 Pa·s = 1000 mPa·s = 1000 centipoise.

Origin and History

Viscosity was first characterized quantitatively through the work of Newton and later Poiseuille in the nineteenth century, with the CGS poise (named for Poiseuille) long serving as the standard unit. The pascal-second entered use with the adoption of the SI, tying viscosity directly to the pascal of pressure.

Law and Notable Facts

The pascal-second is the officially sanctioned SI unit of dynamic viscosity, though the millipascal-second (equal to the once-ubiquitous centipoise) remains far more common in practice because water at 20 °C has a viscosity of almost exactly 1 mPa·s.

Real-World Examples and Conversions

• Water at 20 °C: about 0.001 Pa·s (1 mPa·s).
• Air at room temperature: about 0.0000181 Pa·s.
• Olive oil at 20 °C: roughly 0.084 Pa·s.
• Honey: commonly 2 to 10 Pa·s depending on temperature and water content.

What is the centipoise?

The centipoise (cP) is a CGS unit of dynamic (absolute) viscosity, equal to one hundredth of a poise. It is the most widely used practical viscosity unit in industry because water at about 20 °C has a viscosity of very nearly 1 cP.

Definition

One centipoise equals one hundredth of a poise, which in SI units is exactly one millipascal-second:

$$1\ \text{cP} = 0.001\ \text{Pa·s}$$

Since $1\ \text{P} = 0.1\ \text{Pa·s}$ (the poise being defined as $1\ \text{g}\,\text{cm}^{-1}\,\text{s}^{-1}$), the centipoise is $10⁻²$ of that, i.e. $1\ \text{cP} = 1\ \text{mPa·s}$ exactly. The unit is dimensionally mass per length per time.

Origin and History

The poise is named after the French physician and physiologist Jean Léonard Marie Poiseuille (1797–1869), who studied the flow of liquids (blood) through narrow tubes and formulated what became the Hagen–Poiseuille law. The centipoise arose as a convenient submultiple because water conveniently sits near 1 cP, making comparisons intuitive.

Law and Notable Facts

The centipoise is a CGS-derived unit and is not part of the SI, which prefers the pascal-second (Pa·s) or millipascal-second (mPa·s). Because $1\ \text{cP} = 1\ \text{mPa·s}$ exactly, conversion between the everyday industrial unit and the SI unit requires no arithmetic beyond a change of name — a coincidence that has helped the centipoise survive.

Real-World Examples and Conversions

Water at 20 °C is about 1.002 cP. Whole milk is roughly 3 cP, olive oil around 60–80 cP, and honey near 2,000–10,000 cP. SAE 30 motor oil at 20 °C is on the order of 200 cP. To convert, $500\ \text{cP} = 0.5\ \text{Pa·s} = 500\ \text{mPa·s}$.