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).

Question

asked May 10, 2020 150k views

1 Answer

Manas Sahu · Answer 1 · 2020-05-16T07:03:14+0000

Answer:

100.71 cm H2O

Step-by-step explanation:

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

P=(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
is the density and V is the volume.

Replacing this in the pressure definition:

P=(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=(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:

$h_(w)=(p_(Hg)h_(Hg))/(p_(w) ) \\h_(w)=(13.5*746)/(1.00)=10071$ mm

It is equal to 1007,1 cm.