The pressure of water in a water pipe when the tap is closed and opened is $3.5 \times 10^5 \, N/m^2$ and $3 \times 10^5 \, N/m^2$ respectively. With the tap open,the velocity of water flowing is ........... $m/s$. (Take density of water $\rho = 10^3 \, kg/m^3$)

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

Is Bernoulli's equation unsteady? Explain.

$A$ Venturimeter is used to:

$A$ 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 $kg \ m^{-3}$)

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 $\pi \ W$)