Question

There is a 1 mm thick layer of glycerine between a flat plate of area 100 cm² & a big fixed plate. If the coefficient of viscosity of glycerine is 1.0kg/m-s, then how much force is required to move the plate with a velocity of 7cm/s
 A. 3.5N
B. 0.7N
C. 1.4N
D. None

Answer 1

Hint: Viscosity is a physical property which causes the resistance to flow for the fluid. Viscosity is a type of internal friction present in the fluid. The boundary layer in the laminar flow is a cause of viscosity only as the upper layers are stopped by the lower layers while flowing.

Complete step by step solution:
The thickness of the layer is dx=1mm.
The area of plate is A=100 cm².
The coefficient of viscosity of glycerine is $\eta $ =1.0kg/m-s.
The velocity of the place is dV=7cm/s

Express the relation for force of viscosity acting between the layers on plate.

$F = \eta A\dfrac{{dV}}{{dx}}$

Here F is the force of viscosity, A is the contact surface area, dx is the thickness of layer and dV is the change in velocity and $\eta $ is the coefficient of viscosity.

Substitute 1mm for dx, 10 cm² for A, 1.0kg/m−s for $\eta $ , 7cm/s for dV to find the value of force F.

\[\begin{array}{l}
F = 1 \times 100\,{\rm{c}}{{\rm{m}}^{\rm{2}}} \times \dfrac{{7{\rm{cm/s}}}}{{1{\rm{mm}}}}\\
F = 1 \times 100\,{\rm{c}}{{\rm{m}}^{\rm{2}}} \times \dfrac{{{{10}^{ - 4}}{{\rm{m}}^2}}}{{1\,{\rm{c}}{{\rm{m}}^2}}} \times \dfrac{{7{\rm{cm/s}} \times \dfrac{{{{10}^{ - 2}}\,{\rm{m}}}}{{1\,{\rm{cm}}}}}}{{1{\rm{mm}} \times \dfrac{{{{10}^{ - 3}}\,{\rm{m}}}}{{1\,{\rm{mm}}}}}}\\
F = 7 \times {10^{ - 1}}\,{\rm{N}}\\
F = 0.7\,{\rm{N}}
\end{array}\]

Therefore, an opposite force equal to 0.7N is to be applied to move the plate between the layers. Hence the correct option is (B).

Note: Viscosity is also defined as the ratio of shear stress to shear rate of the fluid particle. For Newtonian fluids, the viscosity is independent of the shear rate. Newtonian fluids follow Newton's law of viscosity but non-Newtonian fluids do not follow Newton's law of viscosity. In non-newtonian fluids the viscosity is dependent on the shear rate.