If the average gauge pressure in the vein is
14400 Pa, what must be the minimum height
of the bag in order to infuse glucose into the
vein? Assume that the specific gravity of the
solution is 1.05. The acceleration of gravity is
9.8 m/s
115807m
1.399m
To determine the minimum height of the bag required to infuse glucose into the vein, we can use the equation for hydrostatic pressure:
P = ρgh,
where P is the gauge pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
First, let's calculate the absolute pressure in the vein:
P_absolute = P + P_atm,
where P_atm is the atmospheric pressure. Assuming that P_atm is 0 Pa, as it is not given in the question, we can simplify the equation to:
P_absolute = P.
Now, we can rearrange the hydrostatic pressure equation to solve for h:
h = P / (ρg).
Given that the average gauge pressure (P) is 14400 Pa, the specific gravity (SG) of the glucose solution is 1.05, and the acceleration due to gravity (g) is 9.8 m/s^2, we have all the values we need to calculate the minimum height:
h = 14400 Pa / (1.05 kg/m^3 * 9.8 m/s^2).
Let's calculate the value of h:
h = 14400 Pa / (10.92 kg/m^2/s^2).
h ≈ 1319.35 meters.
Therefore, the minimum height of the bag in order to infuse glucose into the vein is approximately 1319.35 meters.