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 $\text{cm}$.

Write the limitations and uses of Bernoulli's equation.

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

An $L$-shaped tube with a small orifice is held in a water stream as shown in the figure. The upper end of the tube is $10.6 \ cm$ above the surface of the water. What will be the height (in $cm$) of the jet of water coming from the orifice? The velocity of the water stream is $2.45 \ m/s$. (Take $g = 9.8 \ m/s^2$)

Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross-section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively,then:

The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are $v$ and $2v$ respectively. The density of air is $\rho$ and the surface area of the wing is $A$. The dynamic lift on the wing is: