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?

In a streamline flow,

Water coming out of the mouth of a tap and falling vertically in streamline flow forms a tapering column,i.e.,the area of cross-section of the liquid column decreases as it moves down. Which of the following is the most accurate explanation for this?

$A$ laminar stream is flowing vertically down from a tap of cross-section area $1 \ cm^2$. At a distance $10 \ cm$ below the tap,the cross-section area of the stream has reduced to $0.5 \ cm^2$. The volumetric flow rate of water from the tap is about ........ $litre/min$.

Water enters through end $A$ with speed $v_1$ and leaves through end $B$ with speed $v_2$ of a cylindrical tube $AB$. The tube is always completely filled with water. In case $I$,the tube is horizontal; in case $II$,it is vertical with end $A$ upwards; and in case $III$,it is vertical with end $B$ upwards. We have $v_1 = v_2$ for:

$A$ pipe having an internal diameter $D$ is connected to another pipe of the same size. Water flows into the second pipe through $n$ holes,each of diameter $d$. If the water in the first pipe has speed $v$,what is the speed of water leaving the second pipe?