$A$ space $2.5\ cm$ wide between two large plane surfaces is filled with oil. The force required to drag a very thin plate of area $0.5\ m^2$ just midway between the surfaces at a speed of $0.5\ m/s$ is $1\ N$. The coefficient of viscosity in $kg/(m \cdot s)$ is:

There is a $1$ $mm$ thick layer of glycerine between a flat plate of area $100$ $cm^2$ and a big fixed plate. If the coefficient of viscosity of glycerine is $1.0$ $kg/(m \cdot s)$,then what force in $N$ is required to move the plate with a velocity of $7$ $cm/s$?

The velocity of the upper layer of water in a river is $36 \, km/h$. The shearing stress between horizontal layers of water is $10^{-3} \, N/m^2$. The depth of the river is $h$. (The coefficient of viscosity of water is $10^{-2} \, Pa \cdot s$). Find the value of $h$ in meters.

Write one practical use of viscosity.

$A$ Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800$ $N$ is applied to the shaft,parallel to the sleeve,the shaft attains a speed of $1.5$ $cm/s$. If a force of $2.4$ $kN$ is applied instead,the shaft would move with a speed of ......... $cm/s$.

For the situation shown in the figure,water flows on the surface of a fixed plate. The velocity of water as a function of distance $y$ is given as: $u = \alpha \left[ \frac{y}{h} - 2\left( \frac{y}{h} \right)^2 \right]$. Determine the magnitude of the shear stress that the water applies at the base of the plate. The coefficient of viscosity is $\eta$.