A collapsible plastic bag contains a glucose solution. If the average gauge pressure in the vein is 1.21 103 Pa, what must be the minimum height h of the bag in order to infuse glucose into the vein? Assume the specific gravity of the solution is 1.03.
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To find the minimum height of the bag, we need to consider the pressure exerted by the column of glucose solution. The pressure exerted by a fluid column is given by:
P = ρgh
Where:
P is the pressure exerted (in pascals)
ρ is the density of the fluid (in kg/m³)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height of the fluid column (in meters)
In this case, the fluid is the glucose solution and its density is given by the specific gravity of the solution. The specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance, usually water. In this case, the reference substance is water.
ρ_fluid = SG × ρ_water
Given that the specific gravity of the solution is 1.03, and the density of water is approximately 1000 kg/m³, we can find the density of the glucose solution:
ρ_glucose_solution = 1.03 × 1000 kg/m³
Now, let's substitute these values into the pressure equation:
P = ρgh
1.21 * 10³ = (1.03 * 1000) * 9.8 * h
Now, solving for h:
h = (1.21 * 10³) / ((1.03 * 1000) * 9.8)
Calculating this expression will give us the minimum height required for the bag in order to infuse glucose into the vein.