The velocity of water in a river is $18\, km/h$ near the surface. If the river is $5\, m$ deep,find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water is $\eta = 10^{-2}\, \text{poise}$.

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

The flow of water in a river at the banks is slower than at the middle of the river. Explain.

When stirring with a spoon is stopped in milk,it comes to rest after some time. Why?

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) true?
$(A)$ The resistive force of liquid on the plate is inversely proportional to $h$
$(B)$ The resistive force of liquid on the plate is independent of the area of the plate
$(C)$ The tangential (shear) stress on the floor of the tank increases with $u_0$
$(D)$ The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

$A$ thin plate is placed between two fixed plates,separating two liquids with coefficients of viscosity $\eta$ and $4\eta$,as shown in the figure. If the plate is to be pulled by applying the minimum force,then the ratio $\frac{d_2}{d_1}$ is: