The drawing shows an intravenous feeding. With the distance of 0.610 m, nutrient solution (ρ = 1010 kg/m3) can just barely enter the blood in the vein. What is the gauge pressure of the venous blood? Express your answer in millimeters of mercury.

To determine the gauge pressure of the venous blood, we can start by considering the hydrostatic pressure difference between the nutrient solution and the blood.

First, we need to calculate the hydrostatic pressure of the nutrient solution. We can use 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 distance.

Given:
Density of nutrient solution (ρ) = 1010 kg/m^3,
Distance or height (h) = 0.610 m,
Acceleration due to gravity (g) = 9.8 m/s^2.

Substituting these values into the equation:

P = (1010 kg/m^3) * (9.8 m/s^2) * (0.610 m)
P = 5980.6 kg*m^2/s^2.

Next, we need to convert the pressure from pascals (kg*m^2/s^2) to millimeters of mercury (mmHg). The conversion factor is:

1 mmHg = 133.322 pascals.

So, to convert the pressure to mmHg:

P(mmHg) = P(pascals) / (1 mmHg / 133.322 pascals)
P(mmHg) = (5980.6 kg*m^2/s^2) / (1 mmHg / 133.322 pascals)
P(mmHg) = 797876.912 mmHg.

Therefore, the gauge pressure of the venous blood is approximately 797876.912 mmHg.

To determine the gauge pressure of the venous blood in millimeters of mercury (mmHg), we can use the concept of hydrostatic pressure.

The hydrostatic pressure P at a certain depth in a fluid can be calculated using the equation:

P = ρgh

Where:
- P is the hydrostatic pressure
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the depth of the fluid

In this case, the fluid is the nutrient solution, with a density of ρ = 1010 kg/m3. We need to convert this density to mmHg, so we can use the conversion factor:

1 mmHg = 13,595.1 kg/m3

Now, we can calculate the gauge pressure at the given distance of 0.610 m.

Step 1: Convert the density of the fluid from kg/m3 to mmHg:
ρ_mmHg = ρ * (1 mmHg / 13,595.1 kg/m3)
ρ_mmHg = 1010 kg/m3 * (1 mmHg / 13,595.1 kg/m3)
ρ_mmHg = 0.074 mmHg

Step 2: Calculate the hydrostatic pressure using the formula:
P = ρgh

Since the fluid is just barely entering the blood in the vein, we can assume that the hydrostatic pressure P is equal to the gauge pressure.

P = ρ_mmHg * g * h
P = 0.074 mmHg * 9.8 m/s2 * 0.610 m
P ≈ 0.451 mmHg

Therefore, the gauge pressure of the venous blood is approximately 0.451 mmHg.

The guage pressure at the height h = ρgh

the atmospheric pressure = 1.013•10⁵ Pa

ρgh•760/1.013•10⁵ =1030• 9.8•0.61•760/1.013•10⁵=46.2 mmHg