$A$ plane is in level flight at constant speed and each of its two wings has an area of $25 \; m^{2}$. If the speed of the air is $180 \; km/h$ over the lower wing and $234 \; km/h$ over the upper wing surface,determine the plane's mass in $kg$. (Take air density to be $1 \; kg \; m^{-3}$ and $g = 9.8 \; m/s^{2}$).

The figure shows a liquid of given density flowing steadily in a horizontal tube of varying cross-section. The cross-sectional areas at $A$ is $1.5 \, cm^2$,and at $B$ is $25 \, mm^2$. If the speed of the liquid at $B$ is $60 \, cm/s$,then find $(P_A - P_B)$ in $Pa$. (Given: $P_A$ and $P_B$ are liquid pressures at points $A$ and $B$ respectively. Density $\rho = 1000 \, kg/m^3$. $A$ and $B$ are on the axis of the tube.)

Water is pumped through the hose shown below, from a lower level to an upper level. Compared to the water at point $1$, the water at point $2$:

Water flows in a streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between $P$ and $Q$ is $15 \text{ Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \text{ cm}^2$ and $20 \text{ cm}^2$, respectively. The rate of flow of water through the pipe, in $\text{cm}^3\text{s}^{-1}$, is : [Take density of water = $1000 \text{ kg m}^{-3}$]

An aeroplane of mass $4.5 \times 10^4 \,kg$ and total wing area of $600 \,m^2$ is travelling at a constant height. The pressure difference between the upper and lower surfaces of its wings is (Acceleration due to gravity $= 10 \,m \,s^{-2}$)

Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region,the bubbles