Question

If water were used to construct a barometer, what would be the height of the water column at standard atmospheric pressure $76\,cm$ of mercury?

Answer 1

Hint: The term "density" refers to the amount of mass per unit of volume.An object's average density is proportional to its total mass divided by its total volume. An object composed of a more dense material (such as iron) would have less volume than one made of a less dense substance of comparable mass (such as water).

Complete step by step answer:
The physical force applied on an object is known as pressure. The force exerted per unit area is perpendicular to the surface of the materials. $\dfrac{F}{A}$ is the fundamental formula for pressure (Force per unit area). Pascals is the unit of strain (Pa). Absolute, atmospheric, differential, and gauge pressures are examples of pressure types.

The pressure would be the same if mercury or water is used; the only distinction is the density of the solvent and the fluid's height. Mercury stands at a height of 76 cm. We know that for Mercury,
${\operatorname{P} _1} = {h_1}{\rho _1}g$
Given $h = 76\,cm$, $\rho = 13.6\;{\text{g}}/{\text{c}}{{\text{m}}^2}$.....(Density of Mercury)
Now, let the height of the water column be assumed as $h\,m$.Now for water
${\operatorname{P} _2} = {h_2}{\rho _2}g$
Where Density of water = $\rho = 1\;{\text{g}}/{\text{c}}{{\text{m}}^2}$
Since
${P_1} = {P_2}$
$\Rightarrow {h_1}{\rho _1} = {h_2}{\rho _2}$
Substituting the values we get,
\[{{\text{h}}_2} \times 1 = 76 \times 13.6 \\
\Rightarrow {{\text{h}}_2} = 1033.6\,cm.\]
$\therefore {h_2} = 10.336\,m$

Hence, the height of the water column at standard atmospheric pressure $76\,cm$ of mercury is $10.336\,m$.

Note: A barometer is a scientific device that measures air pressure in a specific area. Short-term weather variations can be predicted using pressure trends. Surface weather mapping employs a variety of atmospheric pressure sensors to locate surface troughs, pressure systems, and frontal borders.