An aeroplane of mass $3 \times 10^4 \, kg$ and total wing area of $120 \, m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is $(g = 10 \, m/s^2)$.

$A$ closed water tank has a cross-sectional area $A$. It has a small hole at a depth of $h$ from the free surface of the water. The radius of the hole is $r$ such that $r \ll \sqrt{\frac{A}{\pi}}$. If $p_o$ is the pressure inside the tank above the water level and $p_a$ is the atmospheric pressure,the rate of flow of the water coming out of the hole is ($\rho$ is the density of water).

The weight of an aeroplane flying in the air is balanced by:

To get the maximum flight (Magnus effect),a ball must be thrown as:

$A$ train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0$ $(S_0 = 4S_t)$. Assume that almost all the air (density $\rho$) in front of the train flows back between its sides and the walls of the tunnel. Also,the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be $p_0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$,then $p_0 - p = \frac{7}{2N} \rho v_t^2$. The value of $N$ is. . . . .

Water flows in a horizontal tube (see figure). The pressure of water changes by $700 \; Nm^{-2}$ between $A$ and $B$ where the area of cross-section are $40 \; cm^{2}$ and $20 \; cm^{2},$ respectively. Find the rate of flow of water through the tube in $cm^{3} / s$. (Density of water $= 1000 \; kgm^{-3}$)