$A$ good lubricant should have

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.

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 $\eta$.

$A$ flat plate of area $10 \, cm^2$ is separated from a large plate by a layer of glycerine $1 \, mm$ thick. If the coefficient of viscosity of glycerine is $20 \, \text{poise}$, the force required to keep the plate moving with a velocity of $1 \, cm/s$ is .......... $dyne$.

Water is flowing on a horizontal fixed surface,such that its flow velocity varies with $y$ (vertical direction) as $v = k \left( \frac{2y^2}{a^2} - \frac{y^3}{a^3} \right)$. If the coefficient of viscosity for water is $\eta$,what will be the shear stress between the layers of water at $y = a$?

Define velocity gradient and give its unit. Also,write the dimensional formula of the velocity gradient.