Equation of Continuity

Water is filled in a cylindrical container to a height of $3 \mathrm{m}$. There is an orifice on the side of the container at a height $x \mathrm{m}$ from the base of the container. The ratio of the cross-sectional area of the orifice and the beaker is $0.1$. The square of the speed of the liquid coming out from the orifice is $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

A liquid flows through a pipe of non-uniform crosssection. If $A_1$ and $A_2$ are the cross-sectional areas of the pipe at two points, the ratio of velocities of the liquid at these points will be

Water is flowing continuously from a tap having an internal diameter $8\times {10}^{-3} \mathrm{m}$. The water velocity as it leaves the tap is $0.4 \mathrm{m}/\mathrm{s}$. The diameter of the water stream at a distance $2\times {10}^{-1} \mathrm{m}$ below the tap is close to

Two pipes $P$ and $Q$ having diameters $2\times {10}^{-2} \mathrm{m}$ and $4\times {10}^{-2} \mathrm{m}$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is

A tube has two areas of cross-section as shown in Fig. The diameters of the tube are $8 \mathrm{mm}$ and $2 \mathrm{mm}$. Find range of water falling on horizontal surface, if piston is moving with a constant velocity of $0.25 \mathrm{m}/\mathrm{s}, h=1.25 \mathrm{m}\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$.

A horizontal pipeline carries water in a streamline flow. At a point along the pipe where the cross-sectional area is $1\times {10}^{-3}{ \mathrm{m}}^2$, the water velocity is $1{ \mathrm{ms}}^{-1}$ and the pressure is $2000 \mathrm{Pa}$. Find the pressure on water at another point-where the cross-sectional area is $5\times {10}^{-4}{ \mathrm{m}}^2$. Density of water $={10}^3 \mathrm{kg}·{\mathrm{m}}^{-3}$.

Calculate the rate of flow of glycerine of density $1.25\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ through the conical section of a pipe if the radii of its ends are $0.1 \mathrm{m}$ and $0.44 \mathrm{m}$ and the pressure-drop across its length is $10 \mathrm{N}/{\mathrm{m}}^2$

A garden hose has inside cross-sectional are $4{ \mathrm{cm}}^2$ and opening in the nozzle at other end is $0.5{ \mathrm{cm}}^2$. The velocity of water in the segment of the hose which lies on the ground is $1 \mathrm{m}/\mathrm{s}$. If a man holds the nozzle at a height $1 \mathrm{m}$ from the ground, find

the velocity with which water comes out of the nozzle and

Water flows through a pipe whose internal diameter is $4 \mathrm{cm}$ at the speed of $2 \mathrm{m}/\mathrm{s}$. What should be the diameter of the nozzle if the water is to emerge at a speed of $8 \mathrm{m}/\mathrm{s}$?

What is the equation of continuity? Establish this equation.

Explain why :

A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.

Explain why :

the size of the needle of a syringe controls flow rate better than the thumb pressure exerted by the doctor while administering an injection.

Explain why :

When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers.

Explain why :

To keep a piece of paper horizontal, we should blow over, not under it.

How you can demonstrate the principle of continuity in a simple way?

Write down the equation of continuity and explain the symbols. How it takes a simpler form for an incompressible fluid?

What is equation of continuity? Which basic principle this equation stands for?

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $h$ from the top and the other is a circular hole of radius $R$ at a depth $4h$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, $R$ is equal to