If the average gauge pressure in the artery is 1.41E+4 Pa, what must be the minimum height, h of the bag in order to infuse glucose into the artery? Assume that the specific gravity of the solution is 1.04.

To find the minimum height (h) of the bag in order to infuse glucose into the artery, we can use the equation for pressure:

Pressure = Density x gravity x height

Given:
Average gauge pressure (P) = 1.41E+4 Pa
Specific gravity (SG) = 1.04

We can rearrange the equation to solve for height:

height = Pressure / (Density x gravity)

First, we need to determine the density of the solution. The specific gravity (SG) is the ratio of the density of the solution to the density of water. Since the density of water is 1000 kg/m^3, we can calculate the density of the solution as follows:

Density = SG x Density of water
Density = 1.04 x 1000 kg/m^3
Density = 1040 kg/m^3

Plugging in the values we have:

height = 1.41E+4 Pa / (1040 kg/m^3 x 9.8 m/s^2)

Simplifying the equation:

height = (1.41E+4 Pa) / (10192 kg/m^2/s^2)
height = (1.41E+4 Pa) / (10192 N/m^2)
height = 1.38 meters

Therefore, the minimum height (h) of the bag must be 1.38 meters in order to infuse glucose into the artery.

To determine the minimum height, h, of the bag required to infuse glucose into the artery, we need to consider two factors: the gauge pressure in the artery and the specific gravity of the solution.

First, let's understand what gauge pressure is. Gauge pressure is the pressure above atmospheric pressure. In this case, the average gauge pressure in the artery is given as 1.41E+4 Pa. It represents the pressure inside the artery relative to the atmospheric pressure.

Next, we need to calculate the absolute pressure in the artery by adding the atmospheric pressure. Atmospheric pressure is typically around 1.01E+5 Pa. So, we can calculate the absolute pressure in the artery as follows:

Absolute pressure = Gauge pressure + Atmospheric pressure
Absolute pressure = 1.41E+4 Pa + 1.01E+5 Pa
Absolute pressure = 1.15E+5 Pa

Now, let's consider the specific gravity of the glucose solution, which is given as 1.04. Specific gravity is the ratio of the density of a substance to the density of a reference substance. In this case, the reference substance is water. Since the specific gravity is greater than 1, it means that the glucose solution is denser than water.

To determine the minimum height, h, of the bag, we can use the hydrostatic pressure formula:

Hydrostatic pressure = Density × Gravity × Height

Since we know the density of the glucose solution is greater than water, we can replace the density with the product of the specific gravity and the density of water, which is approximately 1000 kg/m³.

Hydrostatic pressure = Specific gravity × Density of water × Gravity × Height

Now, we can equate the hydrostatic pressure to the absolute pressure in the artery and solve for the height, h:

Specific gravity × Density of water × Gravity × Height = Absolute pressure

Plugging in the known values:

1.04 × 1000 kg/m³ × 9.8 m/s² × Height = 1.15E+5 Pa

Simplifying the equation:

1.04 × 1000 × 9.8 × Height = 1.15E+5

Solving for Height:

Height = 1.15E+5 / (1.04 × 1000 × 9.8)

Calculating the value:

Height ≈ 11.3 meters

Therefore, the minimum height, h, of the bag must be approximately 11.3 meters in order to infuse glucose into the artery.