Question

# Which of the following is equal to 1 $kgm^{ -1 }s^{ -1 }$?a.) 0.01 poiseb.) 0.001 poisec.) 1 poised.) 10 poise

Hint: The unit given in the options is related to viscosity. Try to recall the formula of viscosity and try to convert the units in terms of poise using the relation between $kgm^{ -1 }s^{ -1 }$ and poise. You will definitely get your answer.

Viscosity - The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, the syrup has a higher viscosity than water.
Viscosity (represented by the symbol $\eta$ "eta") is the ratio of the shearing stress (F/A) to the velocity gradient ( ${ dv_{ x } }/{ dz }$) in a fluid.
$\eta \quad =\quad \dfrac { F/A }{ { dv_{ x } }/{ dz } }$
The SI unit of viscosity is the pascal second [Pa s].
The most common unit of viscosity is the dyne second per square centimeter [dyne $s/cm^{ 2 }$], which is given the name poise [P] after the French physiologist Jean Poiseuille (1799–1869).
We know that 1 Pa = 1 $N\quad m^{ -2 }$ and 1 N = 1 $kgms^{ -2 }$
So, from these relations we can get,
1 Pa-s = 1 N $m^{ -2 }$ s = 1 $kgm^{ -1 }s^{ -1 }$
Ten poise equal one pascal second [Pa s] making the centipoise [cP] and millipascal second [mPa s] identical.
Hence, 10 poise = 1 $kgm^{ -1 }s^{ -1 }$
So, the correct answer is “Option D”.

Note: As we know, the viscosity is the measure of the friction of fluids. There are two ways to measure a fluid’s viscosity as follows:
Dynamic Viscosity (Absolute Viscosity)
Kinematic Viscosity
Many are confused between the two viscosity measures and consider them to be one and the same. In reality, they have significant differences between them. For a few applications, kinematic viscosity is more useful than absolute or dynamic viscosity.