The venturi-meter works on:

$A$ steady flow of a liquid of density $\rho$ is shown in the figure. At point $1$,the area of cross-section is $2A$ and the speed of flow of liquid is $\sqrt{2} \ m \ s^{-1}$. At point $2$,the area of cross-section is $A$. Between the points $1$ and $2$,the pressure difference is $100 \ N \ m^{-2}$ and the height difference is $10 \ cm$. The value of $\rho$ is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $kg \ m^{-3}$)

$A$ 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 $g = 10 \ m/s^2$)

What is the Magnus effect?

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

An ideal fluid of density $800 \; kg \cdot m^{-3}$ flows smoothly through a bent pipe (as shown in the figure) that tapers in cross-sectional area from $a$ to $\frac{a}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4100 \; Pa$. At the wider section,the velocity of the fluid is $\frac{\sqrt{x}}{6} \; m \cdot s^{-1}$. Find the value of $x$. (Given $g = 10 \; m \cdot s^{-2}$)