An engine pump ejects a liquid of density $\rho$ through a pipe of cross-sectional area $A$. If the velocity of the liquid coming out of the pipe is $v$,find the rate at which kinetic energy is imparted to the liquid.

The surface of water in a water tank of cross-sectional area $750 \,cm^2$ on the top of a house is '$h$' $m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \,mm^2$ is $30 \,cm/s$. At that instant, $\frac{dh}{dt}$ is $x \times 10^{-3} \,m/s$. The value of '$x$' will be:

Two pipes of radii $2 \, cm$ and $4 \, cm$ are connected in series. What is the ratio of the flow velocities of the fluid in these pipes?

An engine pumps a liquid of density $d$ continuously through a pipe of cross-sectional area $A$. If the speed of the liquid passing through the pipe is $V$,what is the kinetic energy per unit time imparted to the liquid?

An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A$ and radius $r$ at point $B$ further along the flow direction. If the velocity at point $A$ is $v$,what is its velocity at point $B$?

Explain streamlines and streamline flow.