Water flows through the tube shown. The cross-sectional areas of the wide and narrow parts are $5 \text{ cm}^2$ and $2 \text{ cm}^2$,respectively. The rate of flow is $500 \text{ cm}^3/\text{s}$. Find the difference in the mercury level of the $U$-tube in $\text{cm}$.

$A$ fluid is flowing through a horizontal pipe of varying cross-section,with speed $v \ m/s$ at a point where the pressure is $P \ Pa$. At another point where pressure is $\frac{P}{2} \ Pa$,its speed is $V \ m/s$. If the density of the fluid is $\rho \ kg/m^3$ and the flow is streamline,then $V$ is equal to

Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli's equation? Explain.

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

$A$ closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened,the pressure was reduced to $P_2$. The speed of water flowing out of the pipe is ( $\rho=$ density of water )

Write the limitations and uses of Bernoulli's equation.