In the following figure,the flow of liquid through a horizontal pipe is shown. Three tubes $A, B$ and $C$ are connected to the pipe. The radii of the tubes $A, B$ and $C$ at the junction are respectively $2 \ cm, 1 \ cm$ and $2 \ cm$. It can be said that the:

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

$A$ horizontal pipeline carries water in a stream-line flow. At a point along the pipe, where the cross-sectional area is $10 \,cm^2$, the velocity of water is $1 \,m/s$ and the pressure is $2000 \,Pa$. The pressure of water at another point where the cross-sectional area is $5 \,cm^2$ is (Given: density of water $\rho = 1000 \,kg/m^3$) (in $\,Pa$)

Two light balls are suspended as shown in the figure. When a stream of air passes through the space between them,the distance between the balls will

$A$ 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. . . . .

$A$ manometer connected to a closed tap reads $4.5 \times 10^5 \text{ Pa}$. When the tap is opened,the reading of the manometer falls to $4 \times 10^5 \text{ Pa}$. The velocity of the flow of water is ........ $m/s$.