In the case of a fluid,Bernoulli's theorem expresses the application of the principle of conservation of :

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 $\pi \ W$)

Air is blowing across the horizontal wings of an aeroplane in such a way that its speeds below and above the wings are $90\, m/s$ and $120\, m/s$ respectively. If the density of air is $1.3\, kg/m^3$,then the pressure difference between the lower and upper sides of the wings will be ........ $N/m^2$.

Water is flowing in a conical tube as shown in the figure. The velocity of water at area $A_2$ is $60 \,cm/s$. The values of $A_1$ and $A_2$ are $10 \,cm^2$ and $5 \,cm^2$ respectively. The pressure difference between the two cross-sections is: (in $\,N/m^2$)

Write the limitations of Bernoulli's equation.

Bernoulli’s theorem is a consequence of