Question

Suppose you were to construct a barometer using a fluid with a density of 1.22 g/mL. How high would the liquid level be in this barometer if the atmospheric pressure was 755 torr? (Mercury has a density of 13.6 g/mL.)

Answer 1

The liquid in this barometer would be 8416.393 milimeters.

Step-by-step explanation:

Since hydrostatic pressure is directly proportional to fluid density (
`\rho`), measured in grams per mililiter, and height of fluid (
`h`), measured in milimeters. Two barometers with distinct fluids are equivalent when both have the same hydrostatic pressure. Then, we construct the following relationship:

`\rho_(w)\cdot h_(w) = \rho_(Hg)\cdot h_(Hg)` (1)

Where:

`\rho_(w)`,
`\rho_(Hg)` - Densities of fluid and mercury, measured in grams per mililiter.

`h_(w)`,
`h_(Hg)` - Heights of fluid and mercury columns, measured in milimeters.

If we know that
`\rho_(w) = 1.22\,(g)/(mL)`,
`\rho_(Hg) = 13.6\,(g)/(mL)` and
`h_(Hg) = 755\,mm`, then the liquid level of this barometer is:

`h_(w) = (\rho_(Hg)\cdot h_(Hg))/(\rho_(w))`

`h_(w) = (\left(13.6\,(g)/(mL) \right)\cdot (755\,mm))/(1.22\,(g)/(mL) )`

`h_(w) = 8416.393\,mm`

The liquid in this barometer would be 8416.393 milimeters.