Water flows through a pipe as shown in the figure. The areas of cross-section of sections $A$ and $B$ respectively are $4 {\mathrm{cm}}^2$ and $1 {\mathrm{cm}}^2$. The gauge pressure in the pipe at the centre of section $\mathrm{A}$ is $1.25\times {10}^5 \mathrm{Pa}$  and the flow rate is $800 {\mathrm{cm}}^3 {\mathrm{s}}^{-1}$. The difference in heights of the water levels in the vertical pipes is_____ $\mathrm{m}$. (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A $U$-tube open at both the ends is partially filled with a liquid $\left(A\right)$ of density $950 \mathrm{k} {\mathrm{gm}}^{-3}$. Another liquid $\left(B\right)$ of density $820 \mathrm{k} {\mathrm{gm}}^{-3}$ is poured into one of the arms and it forms a column of length $10 \mathrm{cm}$ as shown in the figure. If the arm into which liquid $B$ is poured is shielded from any air motion, the speed with which air should be blown across the top of the other arm till the levels of the two liquids are at same height in $\mathrm{m} {\mathrm{s}}^{-1}$ is (Density of air is $1.3 \mathrm{k} {\mathrm{gm}}^{-3}$, Acceleration due to gravity $=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A flat plate of area $10{ \mathrm{cm}}^2$ is separated form a large plate by a layer of Glycerine $1 \mathrm{mm}$ thick. If the coefficient of viscosity of Glycerine is $20$ poise, the force required to keep the plate moving with a velocity of $1 \mathrm{cm} {\mathrm{s}}^{-1}$ is $\underline{ }$