I put the data needed to answer the questions under the questions.

QUESTIONS

1. Use the numbers for vessel diameters and volume flow rates from HW #4. For each structure and each type of vessel, calculate the pressure difference between the ends of the vessel needed because of viscosity (six calculations total, two for A and four for B). 10 points for correctness. 2. Use the volume flow rates and diameters from HW #4 to calculate the speed of the blood in each type of vessel in each structure (2 calculations for A, 4 for B). Then use the Bernoulli equation to calculate the pressure change at each junction between types of vessels (1 in A, 3 in B) because of the velocity change from one type of vessel to the next. Since this is just at the junction, height difference is zero. 10 points for correctness.

DATA NEEDED TO ANSWER QUESTIONS:

To use Murray's law to calculate the diameters of other types of vessels, we need to calculate the fourth root of the ratio of the cross-sectional area of each vessel to the cube of its length.

First, let's calculate the cross-sectional area of the aorta in Structure A:

Aorta diameter = 2.5 cm = 0.25 m

Cross-sectional area = r^2 = * (diameter / 2)^2 = * (0.25 / 2)^2 = 0.19635 cm^2 = 0.00019635 m^2

Next, let's calculate the cross-sectional area of the capillary in Structure A:

Capillary diameter = (fourth root of (0.5 cm^3 / 10 cm)) * 2.5 cm = (fourth root of (0.05)) * 2.5 cm = 0.5 cm

Cross-sectional area = r^2 = * (diameter / 2)^2 = * (0.5 / 2)^2 = 0.19635 cm^2 = 0.000019635 m^2

Next, let's calculate the cross-sectional area of the artery in Structure B:

Artery diameter = (fourth root of (8 cm^3 / 12 cm)) * 2.5 cm = (fourth root of (0.67)) * 2.5 cm = 1.5 cm

Cross-sectional area = r^2 = * (diameter / 2)^2 = * (1.5 / 2)^2 = 1.7678 cm^2 = 0.00017678 m^2

Next, let's calculate the cross-sectional area of the arteriole in Structure B:

Arteriole diameter = (fourth root of (0.5 cm^3 / 12 cm)) * 2.5 cm = (fourth root of (0.0417)) * 2.5 cm = 0.5 cm

Cross-sectional area = r^2 = * (diameter / 2)^2 = * (0.5 / 2)^2 = 0.19635 cm^2 = 0.000019635 m^2

Next, let's calculate the cross-sectional area of the capillary in Structure B:

Capillary diameter = (fourth root of (0.5 cm^3 / 12 cm)) * 2.5 cm = (fourth root of (0.0417)) * 2.5 cm = 0.5 cm

Cross-sectional area = r^2 = * (diameter / 2)^2 = * (0.5 / 2)^2 = 0.19635 cm^2 = 0.000019635 m^2

2. The volume flow rate of the aorta was 5 L/min = 5 x (10^-3 m^3/s). Using this volume flow rate, we can calculate the flow rate in each of the other types of vessels as follows:

For Structure A:

Capillary: 5 x 10^-3 m^3/s * (0.5 cm)^2 / (10 cm)^2 = 5 x 10^-3 m^3/s * (0.5 x 10^-2 m)^2 / (10 x 10^-2 m)^2 = 5 x 10^-3 m^3/s * 0.25 x 10^-4 / 1 = 5 x 10^-3 m^3/s * 0.25 * 10^-4 = 0.125 x 10^-3 m^3/s.

For Structure B:

Artery: 5 x 10^-3 m^3/s * (8 cm)^2 / (12 cm)^2 = 5 x 10^-3 m^3/s * (8 x 10^-2 m)^2 / (12 x 10^-2 m)^2 = 5 x 10^-3 m^3/s * 0.64 x 10^-4 / 1 = 5 x 10^-3 m^3/s * 0.64 * 10^-4 = 0.32 x 10^-3 m^3/s.

Arteriole: 5 x 10^-3 m^3/s * (0.5 cm)^2 / (12 cm)^2 = 5 x 10^-3 m^3/s * (0.5 x 10^-2 m)^2 / (12 x 10^-2 m)^2 = 5 x 10^-3 m^3/s * 0.25 x 10^-5 / 1 = 5 x 10^-3 m^3/s * 0.25 * 10^-5 = 0.0125 x 10^-3 m^3/s.

Capillary: 5 x 10^-3 m^3/s * (0.5 cm)^2 / (12 cm)^2 = 5 x 10^-3 m^3/s * (0.5 x 10^-2 m)^2 / (12 x 10^-2 m)^2 = 5 x 10^-3 m^3/s * 0.25 x 10^-5 / 1 = 5 x 10^-3 m^3/s * 0.25 * 10^-5 = 0.0125 x 10^-3 m^3/s.