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What height of mercury column is equivalent to a pressure of 100 psig? The density of mercury is 848 lbm/ft³.

A. 2 ft
B. 4 ft
C. 11 ft
D. 17 ft

Answer :

Final answer:

To find the equivalent height of a mercury column for 100 psig, convert the pressure to psia and then to psf, use the hydrostatic pressure formula, and solve for height. The correct height is approximately 0.604 feet (7.25 inches), much less than any of the choices provided. None of the options match the right answer.

Explanation:

To calculate the height of a mercury column that corresponds to a pressure of 100 psig (pounds per square inch gauge), we can use the hydrostatic pressure equation p = ρgh, where p is the pressure, ρ (rho) is the density of the fluid, g is the acceleration due to gravity (32.2 ft/s²), and h is the height of the column.

First, we need to convert psig to psi absolute (psia) by adding atmospheric pressure, which is approximately 14.7 psi. Therefore, 100 psig is equal to 114.7 psia. We also need to convert psia to pounds per square foot (psf) since we are working with the density in lbm/ft³. There are 144 sq in in 1 sq ft, so the pressure in psf is

114.7 psi × 144 = 16516.8 psf.

Now we apply the formula

p = ρgh.

Plugging in the values we get

16516.8 psf = (848 lbm/ft³)(32.2 ft/s²)h.

Solving for h, we get h = 16516.8 psf / (848 lbm/ft³ × 32.2 ft/s²) which is approximately 0.604 ft or 7.25 inches.

This indicates that the original choices a through d are incorrect, as the correct height of the mercury column is less than 1 foot.

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