The Bernoulli's equation is given by $p + \frac{1}{2} \rho v^{2} + h \rho g = k$,where $p =$ pressure,$\rho =$ density,$v =$ speed,$h =$ height of the liquid column,$g =$ acceleration due to gravity,and $k$ is a constant. The dimensional formula for $k$ is the same as that for:

Water is flowing through a horizontal tube having cross-sectional areas of its two ends as $A$ and $A'$ such that the ratio $A/A'$ is $5$. If the pressure difference of water between the two ends is $3 \times 10^5 \, N \, m^{-2}$,the velocity of water with which it enters the tube will be ......... $m \, s^{-1}$ (neglect gravity effects).

According to Bernoulli's equation $\frac{P}{\rho g} + h + \frac{v^2}{2g} = \text{constant}$,the terms $\frac{P}{\rho g}$,$h$,and $\frac{v^2}{2g}$ are generally called respectively:

Why does an airplane run a certain length on the runway first before taking off?

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?

The correct Bernoulli's equation is (symbols have their usual meaning):