Intravenous infusions are often made under gravity.
At what height should the bottle be placed so the liquid pressure is 700 mm-H2O?
To determine at what height the bottle should be placed so the liquid pressure is 700 mm-H2O, we need to consider the relationship between liquid pressure and height.
The pressure exerted by a liquid at a given height is determined by the hydrostatic pressure equation:
P = ρgh
Where:
P is the pressure (in Pascals)
ρ (rho) is the density of the liquid (in kg/m³)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height of the liquid column (in meters)
In this case, the unit of pressure given is mm-H2O (millimeters of water). To convert mm-H2O to Pascals, we need to first convert it to meters by dividing by 1000 (since there are 1000 millimeters in a meter), and then multiply by the density of water (ρ = 1000 kg/m³) and acceleration due to gravity (g = 9.8 m/s²).
So, let's convert 700 mm-H2O to Pascals:
700 mm-H2O = (700/1000) * ρ * g
Substituting ρ = 1000 kg/m³ and g = 9.8 m/s², we get:
700 mm-H2O = (0.7) * (1000 kg/m³) * (9.8 m/s²)
Simplifying, we find:
700 mm-H2O = 6860 Pascals
Therefore, the liquid pressure should be 700 mm-H2O or 6860 Pascals.
Now, to find the height of the liquid column, we rearrange the hydrostatic pressure equation:
h = P / (ρg)
Plugging in the values, we get:
h = 6860 Pascals / (1000 kg/m³ * 9.8 m/s²)
Calculating, we find:
h ≈ 0.701 meters
Therefore, for the liquid pressure to be 700 mm-H2O, the bottle should be placed at a height of approximately 0.701 meters.