The diagram shows a venturimeter through which water is flowing. The speed of water at $X$ is $2 \, cm/s$. The speed of water at $Y$ (taking $g = 1000 \, cm/s^2$) is ........ $cm/s$.

Consider the following equation of Bernoulli's theorem: $P + \frac{1}{2}\rho V^2 + \rho gh = K$ (constant). The dimensions of $K/P$ are the same as those of which of the following?

$A$ liquid of density $750\,kg\,m^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $A_{1} = 1.2 \times 10^{-2}\,m^{2}$ to $A_{2} = \frac{A_{1}}{2}$. The pressure difference between the wide and narrow sections of the pipe is $4500\,Pa$. The rate of flow of liquid is . . . . . . $\times 10^{-3}\,m^{3}\,s^{-1}$.

$A$ large cylindrical tank of cross-sectional area $1\ m^2$ is filled with water. It has a small hole at a height of $1\ m$ from the bottom. $A$ movable piston of mass $5\ kg$ is fitted on the top of the tank such that it can slide in the tank freely without friction. $A$ load of $45\ kg$ is applied on the top of the water by the piston,as shown in the figure. The value of $v$ when the piston is $7\ m$ above the bottom is $(g = 10\ m/s^2)$ ....... $m/s$

Water flows in a horizontal tube as shown in the figure. The pressure of water changes by $600\, N/m^2$ between $A$ and $B$ where the cross-sectional areas are $30\, cm^2$ and $15\, cm^2$ respectively. Find the rate of flow of water through the tube.

Prove Bernoulli's Principle.