Question

Consider the system shown in Fig. P2-70. If a change of 0.7 kPa in the pressure of air causes the brine-mercury interface in the right column to drop by 5 mm in the brine level in the right column while the pressure in the brine pipe remains constant, determine the ratio of A2/A1.

FIGURE P2–70

Answer 1

Now consider the pressure drop in the left and right hand side of the column at the area then pressure change in the column is given by

…… (1)

Now consider the pressure drop in the left and right hand side of the column at the area then pressure change in the column is given by

…… (2)

Here,

The Specific gravity of mercury is

Specific gravity of brine solution is

The Density of water is

Change in pressure of the air from the area to is

Change in brine level in the right column is

Mercury level in the right column is

Subtracting equation (1) from (2), we get

…… (3)

Since the mercury is incompressible, the volume of the mercury remains constant in the left and right limb

Therefore the total change of the mercury is given by

…… (4)

By substituting equation (4) from (3), we get

Substitute

Therefore, the ratio is