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 $\pi \ W$)

$A$ liquid of density $600 \text{ kg/m}^3$ is flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0 \text{ cm}^2$ and that at $B$ is $20 \text{ mm}^2$. Both the points $A$ and $B$ are in the same horizontal plane, and the speed of the liquid at $A$ is $10 \text{ cm/s}$. The difference in pressures at $A$ and $B$ points is . . . . . . $\text{Pa}$.

The speeds of air above and below the wing of an airplane are $120\, m/s$ and $90\, m/s$,respectively. The density of air is $1.3\, kg/m^3$. If the wing has a length of $10\, m$ and a width of $2\, m$,the pressure difference between the top and bottom of the wing is ......... $Pascal$.

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 $\rho$)

An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$

Consider a cylindrical tank of radius $1\,m$ filled with water. The top surface of the water is at $15\,m$ from the bottom of the cylinder. There is a hole on the wall of the cylinder at a height of $5\,m$ from the bottom. $A$ force of $5 \times 10^{5}\,N$ is applied on the top surface of the water using a piston. Calculate the speed of efflux from the hole. (Given: atmospheric pressure $P_{A} = 1.01 \times 10^{5}\,Pa$,density of water $\rho_{w} = 1000\,kg/m^{3}$,and gravitational acceleration $g = 10\,m/s^{2}$) (in $,m/s$)