The speed of the water in a river is $V$ near the surface. If the coefficient of viscosity of water is $\eta$ and the depth of the river is $H$, then the shearing stress between the horizontal layers of water is

$A$ thin square plate of side $2\ m$ is moving at the interface of two very viscous liquids of viscosities $\eta_1 = 1 \text{ poise}$ and $\eta_2 = 4 \text{ poise}$ respectively, as shown in the figure. Assume a linear velocity distribution in each fluid. The liquids are contained between two fixed plates. $h_1 + h_2 = 3\ m$. $A$ force $F$ is required to move the square plate with a uniform velocity $10\ m/s$ horizontally. The value of the minimum applied force will be ........ $N$.

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

$A$ metal plate of area $10^{-2} \,m^2$ rests on a layer of castor oil, $2 \times 10^{-3} \,m$ thick, whose coefficient of viscosity is $1.55 \,Ns\, m^{-2}$. The approximate horizontal force required to move the plate with a uniform speed of $3 \times 10^{-2} \,ms^{-1}$ is (in $N$)

$A$ 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 ......... $cm/s$.

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 $\eta = 10^{-2}\, \text{poise}$.