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.