---

Why can you convert delta h to (P delta h) using densities?

---

Consider a gas sample trapped in a tube filled with Hg and an identical pressure gas sample trapped in an identical tube filled with water. The pressures these identical gas samples exert on the Hg and water "columns" are equal:

P on a Hg column = P on a water column

Since pressure is a force per unit area

force/area of Hg = force/area of water

Since force is equal to mass * the gravitational acceleration constant (g):

(mass Hg)(g)/area of Hg = (mass of water)(g)/area of water

or just

(mass Hg)/area of Hg = (mass of water)/area of water

Because mass is the product of volume and density:

(volume of Hg)(density of Hg)/area of Hg = (volume of water)(density of water)/area of water

and because the volume of a column is the product of its height and area:

(height of Hg column)(area of Hg column)(density of Hg)/(density of Hg)

= (height of water column)(area of water column)(density of water)/(density of water)

the height of the Hg column is related to the height of the water column through the inverse ratio of their densities:

height of Hg column = (density of water/density of Hg)(height of water column)

or

P delta h in mm of Hg = (density of water/density of Hg)(delta h in mm of water)