State Bernoulli's equation in words and write its mathematical formula.

$A$ venturimeter has a pipe diameter of $4 \,cm$ and a throat diameter of $2 \,cm$. The velocity of water in the pipe section is $10 \,m/s$. The pressure drop between the pipe section and the throat section is (use density of water $= 1000 \,kg/m^3$):

$A$ 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. . . . .

Blood velocity: The flow of blood in a large artery of an anesthetised dog is diverted through a Venturi meter. The wider part of the meter has a cross-sectional area equal to that of the artery,$A = 8 \; mm^2$. The narrower part has an area $a = 4 \; mm^2$. The pressure drop in the artery is $24 \; Pa$. What is the speed (in $m/s$) of the blood in the artery?

$A$ tank of height $15 \ m$ and cross-section area $10 \ m^2$ is filled with water. There is a small hole of cross-section area $a$ which is much smaller than the container, located at a height of $12 \ m$ from the base of the container. How much force should be applied with a piston at the top level, so that the water coming out of the hole hits the ground at a distance of $16 \ m$ (in $kN$)? (Take, density of water $\rho = 1000 \ kg \ m^{-3}$ and $g = 10 \ m/s^2$)

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: