Two immiscible liquids are filled in a conical flask as shown in the figure. The cross-sectional area is shown. $A$ small hole of area $a$ is made in the lower end of the cone. Find the speed of liquid flow from the hole.

The lift of an airplane is based on

Which types of energies are present in the streamline flow of an ideal fluid?

Write the limitations and uses of Bernoulli's equation.

$A$ horizontal pipe line carries water in a streamline flow. At a point along the tube where the cross-sectional area is $10^{-2} \ m^2$,the water velocity is $2 \ m/s$ and the pressure is $8000 \ Pa$. The pressure of water at another point where the cross-sectional area is $0.5 \times 10^{-2} \ m^2$ is ........ $Pa$.

An ideal gas of density $\rho_1=0.2 \ kg \ m^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=0.8 \ kg \ s^{-1}$ from its lower end,and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1=0.1 \ m^2$ and the upper end is $A_2=0.4 \ m^2$. The pressure and the temperature of the gas at the lower end are $600 \ Pa$ and $300 \ K$,respectively,while its temperature at the upper end is $150 \ K$. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g=10 \ ms^{-2}$ and the ratio of specific heats of the gas $\gamma=2$. Ignore atmospheric pressure. Which of the following statement$(s)$ is(are) correct?