$A$ liquid of density $600 \text{ kg/m}^3$ is flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0 \text{ cm}^2$ and that at $B$ is $20 \text{ mm}^2$. Both the points $A$ and $B$ are in the same horizontal plane, and the speed of the liquid at $A$ is $10 \text{ cm/s}$. The difference in pressures at $A$ and $B$ points is . . . . . . $\text{Pa}$.

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.

$A$ fully loaded Boeing aircraft has a mass of $3.3 \times 10^{5} \; kg$. Its total wing area is $500 \; m^{2}$. It is in level flight with a speed of $960 \; km/h$.
$(a)$ Estimate the pressure difference between the lower and upper surfaces of the wings.
$(b)$ Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface. [The density of air is $\rho = 1.2 \; kg/m^{3}$]

The diagram shows a venturimeter through which water is flowing. The speed of water at $X$ is $2 \, cm/s$. The speed of water at $Y$ (taking $g = 1000 \, cm/s^2$) is ........ $cm/s$.

Bernoulli’s theorem is a consequence of

$A$ wind with speed $40 \ m/s$ blows parallel to the roof of a house. The area of the roof is $250 \ m^2$. Assuming that the pressure inside the house is atmospheric pressure,the force exerted by the wind on the roof and the direction of the force will be $(\rho_{air} = 1.2 \ kg/m^3)$.