Given below are two statements:
Statement $I$: When the speed of a liquid is zero everywhere,the pressure difference at any two points depends on the equation $P_1-P_2=\rho g(h_2-h_1)$.
Statement $II$: In the venturi tube shown,$2gh=v_2^2-v_1^2$.
In the light of the above statements,choose the most appropriate answer from the options given below.

We are able to squeeze snow and make balls out of it because of

$A$ cylindrical furnace has height $(H)$ and diameter $(D)$ both $1 \ m$. It is maintained at temperature $T=360 \ K$. The air gets heated inside the furnace at constant pressure $P_a$ and its temperature becomes $T=360 \ K$. The hot air with density $\rho$ rises up a vertical chimney of diameter $d=0.1 \ m$ and height $h=9 \ m$ above the furnace and exits the chimney. As a result,atmospheric air of density $\rho_a=1.2 \ kg \ m^{-3}$,pressure $P_a$ and temperature $T_a=300 \ K$ enters the furnace. Assume air as an ideal gas,neglect the variations in $\rho$ and $T$ inside the chimney and the furnace. Also ignore the viscous effects. [Given: The acceleration due to gravity $g=10 \ ms^{-2}$ and $\pi=3.14$]
$(1)$ Considering the air flow to be streamline,the steady mass flow rate of air exiting the chimney is . . . . .$g \ s^{-1}$.
$(2)$ When the chimney is closed using a cap at the top,a pressure difference $\Delta P$ develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air,due to the stoppage of air flow,are negligible then the value of $\Delta P$ is . . . . .$N \ m^{-2}$.

In a turbulent flow,the velocity of the liquid molecules in contact with the walls of the tube is

$27$ equal small water drops combine to form a big drop. If the surface tension of water is $T$ and the radius of a small drop is $r$,then:
$(A)$ The excess pressure inside the big drop is three times the excess pressure inside the small drop.
$(B)$ Surface energy decreases in this process.
$(C)$ In this process,$72 \pi r^2 T$ energy is released.
$(D)$ The radius of the big drop is $3r$.
The true statements are:

On opposite sides of a wide vertical vessel filled with water (density $\rho$), two identical holes are drilled, each having cross-section area $A$. The height difference between holes is $x$. The resultant force of reaction of water flowing out of the vessel is ($g$ = acceleration due to gravity).