Question

What is the S.I unit of viscosity coefficient $(\eta )$ ?
A. Pascal
B. $N\,s{m^{ - 2}}$
C. $k{m^{ - 2}}s$
D. $N{m^{ - 2}}$

Answer 1

Hint:In order to the question, first we will explain about the coefficient of viscosity or viscosity coefficient then only on the basis of the definition of viscosity coefficient, we will conclude the S.I unit.

Complete answer:
Every liquid has its own specific viscosity and the measure of this attribute is called the coefficient of viscosity. The coefficient of viscosity $(\eta )$ is defined as the tangential force $F$ required to maintain a unit velocity gradient between two parallel layers of liquid of unit area $A$ .
The S.I unit of $\eta $ is Newton- second per square metre $(N\,s{m^{ - 2}})$ . Hence, the coefficient of viscosity is the measure of the resistance of the fluid to deformation at the given rate due to internal friction.
The unit of coefficient of viscosity can be understood by defining the coefficient of viscosity. The coefficient of viscosity is characterized for two equal layers of fluid as the tangential force needed to keep unit speed angles between these layers.
The alternate method of characterizing the coefficient of viscosity is as the proportion of shear pressure to the speed slope of the liquid. Mathematical representation is:
$\eta = \dfrac{{Fr}}{{Av}}$
where, $\eta = coefficient\,of\,vis\cos ity$
$F = \tan gential\,force$
$A = area$
$v = velocity$
$r = dis\tan ce\,between\,the\,layers$
Hence, the correct option is B. $N\,s{m^{ - 2}}$ .

Note:The coefficient of viscosity is utilized to completely decide the level of consistency of some random liquid. For any liquid, this coefficient stays steady and is a characteristic property of that fluid.