Calculate the height, in feet, of a column of water that would exert the same pressure as a column of mercury that

is 754 mm high. (The density of mercury is 13.6 g/cm3 and the density of water is 100 g/cm3.)

1 inch = 254 mm

• Convert 754 mm Hg to inches Hg
• Convert the inches Hg to feet Hg (1 feet = 12 in)
• Multiply feet Hg to feet H2O by multiplying by 13.6 ft.H2O/ftHg

3.36 ft

874

To calculate the height of the column of water that would exert the same pressure as the column of mercury, we need to use the equation:

Pressure = density * gravity * height

Given that the density of mercury is 13.6 g/cm3 and the density of water is 1.0 g/cm3:

For mercury column:
Pressure_mercury = 13.6 g/cm3 * gravity * 754 mm

For water column:
Pressure_water = 1.0 g/cm3 * gravity * height_water

Since we want the pressures to be the same, we can equate the two equations:

13.6 g/cm3 * gravity * 754 mm = 1.0 g/cm3 * gravity * height_water

Now, we can solve for height_water:

height_water = (13.6 g/cm3 * gravity * 754 mm) / (1.0 g/cm3 * gravity)

Since gravity is the same on both sides of the equation, it cancels out:

height_water = 13.6 * 754 mm / 1.0

Converting mm to feet:
1 mm = 0.00328084 feet

height_water = 13.6 * 754 * 0.00328084 feet

Calculating this value:

height_water = 33.9068 feet

Therefore, a column of water that is approximately 33.9 feet high would exert the same pressure as a 754 mm column of mercury.