What is the effect of pressure on the boiling point of water?

The density of the atmosphere at sea level is $1.29 \; kg/m^3$. Assume that it does not change with altitude. Then how high (in $km$) would the atmosphere extend?

$A$ cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$) and its neck is filled with immiscible oil (density $\rho_0$). Then,the pressure at

$A$ thin uniform tube is bent into a circle of radius $r$ in the vertical plane. Equal volumes of two immiscible liquids,whose densities are ${\rho _1}$ and ${\rho _2}$ $({\rho _1} > {\rho _2})$,fill half the circle. The angle $\theta$ between the radius vector passing through the common interface and the vertical is

Explain why:
$(a)$ The blood pressure in humans is greater at the feet than at the brain.
$(b)$ Atmospheric pressure at a height of about $6 \; km$ decreases to nearly half of its value at sea level,though the height of the atmosphere is more than $100 \; km$.
$(c)$ Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

In Guericke's experiment to show the effect of atmospheric pressure,two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create a vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$,then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is