Write one practical use of viscosity.

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.

$A$ flat plate of area $0.1 \,m^2$ is placed on a flat surface and is separated from it by a film of oil $10^{-5} \,m$ thick whose coefficient of viscosity is $1.5 \,N \cdot s \cdot m^{-2}$. The force required to cause the plate to slide on the surface at a constant speed of $1 \,mm \cdot s^{-1}$ is ............ $N$.

Water in a river $20 \ m$ deep is flowing at a speed of $10 \ ms^{-1}$. The shearing stress between the horizontal layers of water in the river in $Nm^{-2}$ is (Coefficient of viscosity of water $= 10^{-3} \ SI \ units$)

Explain velocity gradient and coefficient of viscosity and give their units.

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 $\eta$.