Question

What is the $SI$ unit of viscosity coefficient $\left(\eta \right)$?

• A. $Ns{m}^{-2}$
• B. $k{m}^{-2}s$
• C. Pascal
• D. $N{m}^{-2}$

Answer 1

The correct option is A $Ns{m}^{-2}$

$\text{Coefficient of viscosity}$

Coefficient of viscosity is defined as the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

We have;

$f=\eta \times A\times dv/dx$

Where, $f=$ Tangential force

$A=$ Area
$\eta =$ Viscosity coefficient
$dv/dx=$ Velocity gradient

Here, we are finding the unit of viscosity coefficient.

So, $\eta =f/(A\times (dv/dx\left)\right)$

$\eta =(f\times dx)/(A\times dv)$

$\because$ The unit of $f,A,dx$ (distance), and $dv$ (velocity) are $N,m^2,m$ and $m{s}^{-1}$ respectively.

$\therefore \eta =\frac{N\times m}{m^2\times m{s}^{-1}}$

$\Rightarrow \eta =Ns{m}^{-2}$

Hence, the unit of viscosity coefficient is $Ns{m}^{-2}$.