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

Consider a completely full cylindrical water tank of height $1.6 \ m$ and cross-sectional area $0.5 \ m^2$. It has a small hole in its side at a height $90 \ cm$ from the bottom. Assume the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load of $50 \ kg$ is applied at the top surface of the water in the tank,then the velocity of the water coming out at the instant when the hole is opened is ......... $m/s$ $(g=10 \ m/s^2)$.

At a hydroelectric power plant,the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m^{3} s^{-1}.$ If the turbine generator efficiency is $60\%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8\; m s^{-2}\right).$

Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is $P$ at a point where flow speed is $v$,the pressure at another point where the flow speed is $2v$,is (Take density of water as $\rho$)

Water is flowing through a horizontal pipe of non-uniform cross-section. In the region of the narrowest part inside the pipe,the water will have

An aeroplane of mass $4.5 \times 10^4 \,kg$ and total wing area of $600 \,m^2$ is travelling at a constant height. The pressure difference between the upper and lower surfaces of its wings is (Acceleration due to gravity $= 10 \,m \,s^{-2}$)