millipascal-seconds (mPa-s) to centipoises (cP) conversion

What is the Millipascal-Second?

The millipascal-second is a submultiple of the SI unit of dynamic viscosity, equal to one thousandth of a pascal-second. It is the everyday unit for the viscosity of liquids such as water, oils, and beverages.

Definition

One millipascal-second is one thousandth of a pascal-second, the SI derived unit of dynamic viscosity.

$$1\ \text{mPa-s} = 0.001\ \text{Pa·s}$$

In SI base units this is 10⁻³ kg·m⁻¹·s⁻¹. The millipascal-second is numerically identical to the centipoise (cP), the widely used CGS-based unit, so 1 mPa·s = 1 cP exactly.

Origin and History

The unit follows from the SI prefix "milli-" applied to the pascal-second, which itself was defined when the International System of Units systematized viscosity in terms of the pascal. Its convenience comes from matching the pre-existing centipoise, letting historical viscosity data carry over unchanged.

Law and Notable Facts

As an SI-sanctioned submultiple, the millipascal-second is fully standard. Its enduring popularity rests on a near-coincidence: liquid water at 20 °C has a dynamic viscosity of about 1.002 mPa·s, making the unit an intuitive reference point.

Real-World Examples and Conversions

• Water at 20 °C: about 1.0 mPa·s.
• Whole milk: roughly 2 to 3 mPa·s.
• Light motor oil (SAE 10 at operating temperature): tens of mPa·s.
• 1 mPa·s equals exactly 1 centipoise and 0.001 Pa·s.

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, $500\ \text{cP} = 0.5\ \text{Pa·s} = 500\ \text{mPa·s}$.