Alejandro L. answered • 11/26/16

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To answer this question you need to first start with the definition of pressure:

P = F/A (1)

where P is the pressure, F is the force exerted on the liquid column and A is the area. According to Newton's second law:

F = mg (2)

where m is the mass of the liquid column and g is the acceleration of gravity. Substituting equation (2) into (1) yields equation (3):

P = mg/A (3)

now multiply both numerator and denominator of (3) by the height of the liquid column that is raised as a result of the atmospheric pressure P:

P = mgh/Ah (4)

but the product of the area and height of a liquid column is simply the volume of the column, thus equation (4) becomes:

P = mgh/V (5)

finally, we recognize that the density of the liquid column is defined as m/V; so equation (5) takes the final form of equation (6):

P = dgh (6)

where d is the density. In your problem, regardless of the identity of the liquid, the pressure is always the same (1 bar), so the right side of the last equation must be equal for both water and mercury:

d1gh1 = d2gh2 (7)

or

d1h1 = d2h2 (8)

At this point you must first determine what the height of the mercury barometer is at 1 bar (100,000 N/m2) using equation (6):

h = P/dg = (100,000 kg/ms2)/[(13600 kg/m3)(9.8 m/s2)] = 0.75 m

where the units were changed to SI units (1 N = 1 kg/ms2). At this point you have everything you need to solve for the height of a water column using equation (8).

Hope this was of help.