Pa⋅s\text{Pa}{\cdot}\text{s}

pascal second

Dynamic viscosityexact by definition

The pascal second is the coherent SI unit of dynamic (absolute) viscosity, the ratio of shear stress to shear rate. Its factor is 1 by construction. It is a large unit for ordinary liquids: water at 20 °C is about 0.001 Pa·s, while honey is a few Pa·s.

Watch out: Dynamic viscosity (Pa·s) and kinematic viscosity (m²/s) are different quantities related by the density: ν=μ/ρ\nu = \mu/\rho. Reynolds number can be computed with either, using the matching form of the equation, but substituting one value for the other is a genuinely common and consequential error.

1 Pa⋅s\text{Pa}{\cdot}\text{s} 1 Pa⋅s\text{Pa}{\cdot}\text{s}

About the pascal second

The pascal second is what a rheometer prints, and its size makes it the unit of thick things. Water at 20 °C is 0.001 Pa·s, olive oil about 0.08, honey a few, and molten glass at working temperature around a thousand. Polymer melts entering an injection mould run from a hundred to ten thousand Pa·s, which is why mould filling is governed by viscosity long before strength enters the picture, and lubrication, coatings and food-texture work all specify in this unit or its thousandth, the mPa·s.

Its most famous measurement is the pitch drop experiment at the University of Queensland, running since 1927: a funnel of room-temperature pitch, a material that shatters under a hammer blow, has released nine drops in nearly a century, from which the viscosity comes out on the order of 10810^{8} Pa·s, around a hundred billion times water. Solid and liquid are statements about timescale, and the viscosity in Pa·s is the number that sets the timescale.

Two things about the unit itself. It never received a name: the poiseuille was proposed for 1 Pa·s but no CGPM ever adopted it, so dynamic viscosity remains a workhorse quantity with a nameless SI unit. And it is the viscosity that shear stress wants, τ=μ γ˙\tau = \mu\,\dot{\gamma}, the form the Hagen-Poiseuille and Stokes drag results are built on; the kinematic value in m²/s is this divided by density and must never be substituted for it.

One pascal second in every dynamic viscosity unit

1,000,000micropascal second (μPa·s)
10,000millipoise (mP)
2,419.09pound per foot hour (lb/(ft·h))
1,000millipascal second (mPa·s)
1,000centipoise (cP)
145.038microreyn (μreyn)
10poise (P)
1pascal second (Pa·s)this unit
0.671969pound per foot second (lb/(ft·s))
0.0208854pound-force second per square foot (lbf·s/ft²)
0.001kilopascal second (kPa·s)
0.000145038reyn (reyn)