A cylinder of height $ 20\; m$ is completely filled with water. The velocity of efflux of water (in $ m/s$) through a small hole on the side wall of the cylinder near its bottom is ....... $m/s$
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From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid
A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ $w.r.t.$ water, the value of $r$ is$......R$
The relative velocity of two consecutive layers is 8 cm/s. If the perpendicular distance between the layers is $0.1\, cm$, then the velocity gradient will be ......... $sec^{-1}$
Two water pipes $P$ and $Q$ having diameters $2$$ \times 10^{-2} $ $m$ and $4$ $\times 10^{-2}$ $m$, respectively, are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is
Different physical quantities are given in Column - $\mathrm{I}$ and their dimensional formula are given in Column - $\mathrm{II}$. Match them appropriately.
The diameter of an air bubble which was initially $2\,mm$, rises steadily through a solution of density $1750\,kg\,m\,m ^{-3}$ at the rate of $0.35\,cms ^{-1}$. The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).
Water flows in a streamlined manner through a capillary of radius $'a'$, the pressure difference being $'p'$ and the rate of flow $Q$. If the radius is reduced to $'a/2'$ and the pressure increased to $'4p'$, the rate of flow becomes :-