Collapsible plastic bags are used in hospitals for infusions. We want to use such a bag to infuse a electrolyte solution into the artery of a patient. For this we mount the bag at a height h above the arm of the patient. Assuming that the particular gauge pressure in the artery is 14.4 kPa and the density of the electrolyte solution is 1.03 g/cm3, what is the minimum height h in order for the infusion to work?
2342341234234
To determine the minimum height h required for the infusion to work, we need to consider the hydrostatic pressure difference between the height of the bag and the artery.
The hydrostatic pressure is given by the equation:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the height or depth of the fluid.
In this case, we know the gauge pressure in the artery is 14.4 kPa, which means the pressure referenced to atmospheric pressure is 14.4 kPa + 101.3 kPa (standard atmospheric pressure).
Converting the density from g/cm³ to kg/m³, we have:
ρ = 1.03 g/cm³ × 1000 kg/m³ / 1 cm³
ρ = 1030 kg/m³
Plugging in the values, we can rearrange the equation to solve for h:
P = ρgh
h = P / (ρg)
Converting the gauge pressure into absolute pressure:
P = 14.4 kPa + 101.3 kPa
P = 115.7 kPa
Using the value for gravity:
g = 9.8 m/s²
Plugging in the known values:
h = (115.7 × 10³ Pa) / (1030 kg/m³ × 9.8 m/s²)
h ≈ 11.6 meters
Therefore, the minimum height h required for the infusion to work is approximately 11.6 meters.