Question

A layer of glycerine of thickness 1mm is enclosed between a big plate and another plane of area ${10^{ - 2}}{m^2}$. If coefficient of viscosity of glycerine is $1kg/(m-s)$, then the force in newton required to move plate with a velocity of $0.07m/s$ will be:
A) $7$
B) $0.7$
C) $70$
D) $0.07$

Answer 1

Hint: The viscosity of a fluid represents the obstruction offered to the flow of the fluid by the subsequent layers. The layers of the fluid undergo shear stress when the force is applied to move the fluid. The relationship is given by:
Newton’s law of viscosity i.e. $\tau = \mu \dfrac{{du}}{{dy}}$
$\mu $= coefficient of viscosity of the fluid and $\dfrac{{du}}{{dy}}$= velocity gradient.

Complete step by step by solution:
Given that, layer thickness
\[dy = 1mm = {10^{ - 3}}m\]
Area $A = {10^{ - 2}}{m^2}$
Coefficient of viscosity $\mu = 1kg/ms$
Velocity $du = 0.07m/s$
Using the equation of Newton’s law of viscosity i.e. $\tau = \mu \dfrac{{du}}{{dy}}$ where
$\mu $= dynamic viscosity of the fluid, and $\dfrac{{du}}{{dy}}$= velocity gradient.
The shear stress is given as the ratio of the force applied to the area on which the force is applied.
Shear stress,
$\tau = \dfrac{F}{A}$
where F= force and A= Area
Substituting,
$\Rightarrow$ $F = \mu \dfrac{{du}}{{dy}}A$
Put all the values in the above equation.
$\Rightarrow$ $F=(1)\times \dfrac{0.07}{{{10}^{-3}}}\times {{10}^{-2}}=0\cdot 7N$

Which is required Force; Hence option (B) is the correct option.

Additional information: Dynamic viscosity is the force required to maintain the fluid flow at a particular rate. Dynamic viscosity is usually used when the fluid is subjected to any external force. The unit of dynamic viscosity is Pa-s, where Pa is $N/{m^2}$- SI unit of pressure.
Kinematic viscosity is defined as dynamic viscosity to the density of the fluid. It shows the rate of momentum transfer (how fast the fluid is moving) when the fluid is subjected to deformation. The unit of Kinematic viscosity is ${m^2}/s$ in SI units.

Note: Not all fluids follow Newton's law of viscosity. There is a special category of fluids called non-Newtonian fluids where the Newton’s law of viscosity is not applicable. Example of such a fluid is quicksand.