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 $= 1000 \; kgm^{-3}$)

An engine pump is used to pump a liquid of density $\rho$ continuously through a pipe of cross-sectional area $A$. If the speed of flow of the liquid in the pipe is $v$,then the rate at which kinetic energy is being imparted to the liquid is

The figures below show water flowing through a horizontal pipe from left to right. Note that the pipe in the middle is narrower. Choose the most appropriate depiction of water levels in the vertical pipes.

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

The Bernoulli's equation is given by $p + \frac{1}{2} \rho v^{2} + h \rho g = k$,where $p =$ pressure,$\rho =$ density,$v =$ speed,$h =$ height of the liquid column,$g =$ acceleration due to gravity,and $k$ is a constant. The dimensional formula for $k$ is the same as that for:

The Pitot tube shown in the figure is used to measure fluid flow velocity in a pipe of cross-sectional area $S$. It was invented by a French engineer Henri Pitot in the early $18^{th}$ century. The volume of the gas flowing across the section of the pipe per unit time is (The difference in the liquid columns is $\Delta h$,$\rho_0$ and $\rho$ are the densities of liquid and the gas respectively):