Water is pumped steadily out of a flooded basement at a speed of $10 \ m \ s^{-1}$ through a hose (tube) of radius $1 \ cm$, passing through a window $3 \ m$ above the water level. The power of the pump is (Assume $g = 10 \ m \ s^{-2}$, density of water $= 1000 \ kg \ m^{-3}$): (in $\pi \ W$)

Water is filled in a cylindrical container to a height of $3 \ m$. 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 ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.

Air streams horizontally past an airplane. The speed over the top surface is $60 \, m/s$ and that under the bottom surface is $45 \, m/s$. The density of air is $1.293 \, kg/m^3$. The difference in pressure is ....... $N/m^2$.

$A$ bottle has a thin nozzle on top. It is filled with water,held horizontally at a height of $1 \,m$ and squeezed slowly by hands,so that the water jet coming out of the nozzle hits the ground at a distance of $2 \,m$. If the area over which the hands squeeze it is $10 \,cm^{2}$,the force applied by hand is close to .......... $N$ (take $g=10 \,m/s^{2}$ and density of water $=1000 \,kg/m^{3}$).

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 ......... $m/s$ $(g=10 \ m/s^2)$.

Bernoulli's principle is based on the law of conservation of