Bernoulli’s theorem is a consequence of

Water is pumped through the hose shown below, from a lower level to an upper level. Compared to the water at point $1$, the water at point $2$:

Glycerine of density $1.25 \times 10^3 \ kg/m^3$ is flowing in a conical-shaped horizontal pipe. The cross-sectional area of the pipe at its two ends is $10 \ cm^2$ and $5 \ cm^2$ respectively. The pressure difference between the two ends is $3 \ N/m^2$. The rate of flow of the liquid in the pipe is:

In a horizontal tube, the water pressure changes by $1500 \text{ N m}^{-2}$ between points $A$ and $B$ as shown in the figure below. The cross-sectional areas at $A$ and $B$ of the tube are $40 \text{ cm}^2$ and $20 \text{ cm}^2$, respectively. Find the rate of flow of water through the tube.

$A$ 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 . . . . . . $\times 10^{-3}\,m^{3}\,s^{-1}$.

Water is flowing through a horizontal pipe in streamline flow. At the narrowest part of the pipe,