An engine pump is used to pump a liquid of density $\rho$ continuously through a pipe of cross-sectional area $A$. If the speed of flow of the liquid in the pipe is $v$,then the rate at which kinetic energy is being imparted to the liquid is

$A$ steady flow of a liquid of density $\rho$ is shown in the figure. At point $1$,the area of cross-section is $2A$ and the speed of flow of liquid is $\sqrt{2} \ m \ s^{-1}$. At point $2$,the area of cross-section is $A$. Between the points $1$ and $2$,the pressure difference is $100 \ N \ m^{-2}$ and the height difference is $10 \ cm$. The value of $\rho$ is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg \ m^{-3}$)

If the velocity of flow is $4 \, m/s$,then the velocity head is ......... $m$.

Application of Bernoulli's theorem can be seen in

In this figure,an ideal liquid flows through a tube of uniform cross-section. The liquid has velocities $v_A$ and $v_B$,and pressures $P_A$ and $P_B$ at points $A$ and $B$ respectively.

Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipe,