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 $2$:

Determine the pressure difference in a tube of non-uniform cross-sectional area as shown in the figure. $\Delta P = ?$ (in $Pa$)
$d_{1} = 5 \, cm, V_{1} = 4 \, m/s, d_{2} = 2 \, cm, V_{2} = ?$
Assume the fluid is water with density $\rho = 1000 \, kg/m^{3}$.

What is the nature of the pressure-distance graph for the pipe shown in the figure?

$A$ plane is in level flight at constant speed and each of its two wings has an area of $40 \,m^2$. If the speed of the air is $180 \,km/h$ over the lower wing surface and $252 \,km/h$ over the upper wing surface,the mass of the plane is . . . . . . $kg$. (Take air density to be $1 \,kg \,m^{-3}$ and $g=10 \,ms^{-2}$)

Why is Bernoulli's equation not applicable to turbulent flow? Explain.

Water flows in a streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between $P$ and $Q$ is $15 \text{ Nm}^{-2}$. The area of cross-section at $P$ and $Q$ are $40 \text{ cm}^2$ and $20 \text{ cm}^2$, respectively. The rate of flow of water through the pipe, in $\text{cm}^3\text{s}^{-1}$, is : [Take density of water = $1000 \text{ kg m}^{-3}$]