To find the height of water that corresponds to a pressure of 760 mm Hg, we can use the formula for pressure:
P = ρgh
Where:
- P = pressure (in pascals)
- ρ = density of the fluid (in kg/m³)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height of the fluid column (in meters)
First, we need to convert the pressure from mm Hg to pascals. The pressure of 760 mm Hg is equivalent to:
P = 760 mm Hg × 133.322 Pa/mm Hg = 101325 Pa
Now, we have the following values:
- P = 101325 Pa
- g = 9.81 m/s²
- Density of water (ρ) = 1.00 g/cm³ = 1000 kg/m³
- Density of mercury (ρHg) = 13.79 g/cm³ = 13790 kg/m³
We can solve for h using the density of water because we are looking for the height of the water column:
101325 Pa = (1000 kg/m³)(9.81 m/s²)(h)
Rearranging the equation gives:
h = 101325 Pa / (1000 kg/m³ × 9.81 m/s²)
h = 10.34 m
Therefore, a height of approximately 10.34 meters of water is necessary to measure a pressure of 760 mm Hg.