Question

On a cool, rainy day, the barometric pressure is 746 mmHg. Calculate the barometric pressure in centimeters of water (cmH2O) (d of Hg = 13.5 g/mL; d of H2O = 1.00 g/mL).

Answer 1

Answer:

100.71 cm H2O

Explanation:

In a fluid column barometer, the height of the fluid column is proportional to the pressure. The pressure is by definition:

$P=\frac{F}{A}$, where F is a force and A is the area.

In a column barometer the force is given by the weight of the fluid:

$F=m*g$, and the mass may be expressed as $m=p*V$, where $p$ is the density and V is the volume.

Replacing this in the pressure definition:

$P=\frac{pVg}{A}$

In a constant cross section area column, the volume may be calculated as:

$V=A*h$ where A is the area and h the height. Replacing this in the previous equation:

$P=\frac{pAhg}{A}=pgh$

Different columns may be over the same pressure, so:

$P_{w}=P_{Hg}\\ p_{w}h_{w}g=p_{Hg}h_{Hg}g$

Dividing each part for gravity constant:

$p_{w}h_{w}=p_{Hg}h_{Hg}$

And isolating hw:

$h_{w}=\frac{p_{Hg}h_{Hg}}{p_{w} } \\h_{w}=\frac{13.5*746}{1.00}=10071$ mm

It is equal to 1007,1 cm.