A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ${\mathrm{m}\mathrm{s}}^{-1}$) through a hole on the side wall of the cylinder near its bottom, is

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 bottle has a thin nozzle on top. It is filled with water, held horizontally at a height of $1 \mathrm{m}$ and squeezed slowly by hands so that the water jet coming out of the nozzle hits the ground at a distance of $2 \mathrm{m}.$ If the area over which the hands squeeze it, is $10 {\mathrm{cm}}^2,$ the force applied by hands is close to: (take $g=10 \mathrm{m}/{\mathrm{s}}^2$ and density of water $=1000 \mathrm{kg}/{\mathrm{m}}^3$)

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 $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below:

Artery is contracted in region $\mathrm{II}$. Choose the correct statement.

Consider a water tank as shown in the figure. It's cross-sectional area is $0.4{ \mathrm{m}}^2$. The tank has an opening $B$ near the bottom whose cross-section area is $1{ \mathrm{cm}}^2$. A load of $24 \mathrm{kg}$ is applied on the water at the top when the height of the water level is $40 \mathrm{cm}$ above the bottom, the velocity of water coming out the opening $B$ is $\mathrm{v} \mathrm{m} {\mathrm{s}}^{-1}$. The value of $v$, to the nearest integer, is ___ .[Take the value of $g$ to be $10{ \mathrm{m} \mathrm{s}}^{-2}$]

A cylindrical container containing water has a small hole at height of $H=8 \mathrm{cm}$ from the bottom and at a depth of $2 \mathrm{cm}$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $\left(x\right)$ is

In the diagram shown, the difference in the two tubes of the manometer is $5 \mathrm{cm}$, the cross-section of the tube at $A$ and $B$ is $6 {\mathrm{mm}}^2$ and $10 {\mathrm{mm}}^2$ respectively. The rate at which water flows through the tube is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$