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

Answer:

The liquid in this barometer would be 8416.393 milimeters.

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 $\rho_{w} = 1.22\,\frac{g}{mL}$, $\rho_{Hg} = 13.6\,\frac{g}{mL}$ and $h_{Hg} = 755\,mm$, then the liquid level of this barometer is:

$h_{w} = \frac{\rho_{Hg}\cdot h_{Hg}}{\rho_{w}}$

$h_{w} = \frac{\left(13.6\,\frac{g}{mL} \right)\cdot (755\,mm)}{1.22\,\frac{g}{mL} }$

$h_{w} = 8416.393\,mm$

The liquid in this barometer would be 8416.393 milimeters.