# What is the unit of viscosity? Please explain/

Aug 31, 2017

The SI unit of viscosity is the pascal-second (Pa·s).

#### Explanation:

The viscosity of a fluid is a measure of its resistance to flow.

We usually think of the viscosity of a liquid as its "thickness".

For example, we say that honey is "thicker" (has a higher viscosity) than water.

One way to measure viscosity is to place the fluid between two flat parallel plates and slide one plate past the other.

In terms of the above diagram, the formula for viscosity $\eta$ is

color(blue)(barul|stackrel(" ")(eta = (Fδ)/(Av))|)

Thus, the units of viscosity are ("N" × color(red)(cancel(color(black)("m"))))/("m"^2 × color(red)(cancel(color(black)("m")))·"s"^"-1") = "N·s·m"^"-2" = "Pa·s".

If a fluid is placed between two ${\text{1 m}}^{2}$ plates that are 1 m apart and one plate is pushed sideways with a force of 1 N and it moves at a velocity of $1 \textcolor{w h i t e}{l} \text{m·s"^"-1}$, then the fluid has a viscosity $\eta = \text{1 Pa·s}$.

Many chemists still use an old unit of viscosity, the poise (P), named after the French physician Jean Poiseuille.

It is a convenient unit because $\text{1 mPa·s" = "1 cP}$.

For example, the viscosity of water at 20 °C is $\text{1.002 mPa·s}$ or $\text{1.002 cP}$.

Honey has a viscosity of about $\text{10 Pa·s}$ or $\text{10 000 cP}$.