Calculate the velocity of efflux of water when a completely filled cylinder of height $20 \mathrm{m}$ is punched with a hole on the side wall near its bottom. (Take, $g=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$.)

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 $=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

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 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

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.

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 $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A light cylindrical vessel is kept on a horizontal surface. Area of the base is $A.$ A hole of cross-sectional area $a$ is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is

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 $=1000 \mathrm{kg}/{\mathrm{m}}^3$)