On national fried butterstick day, Buttercup the dog eats too many fried butters

Question

On national fried butterstick day, Buttercup the dog eats too many fried buttersticks. One of the dog's arteries is completely clogged. You are working with the veterinarian to perform a bypass. Artery A flows into B and C. Calculate the diameter of vein C, as well as area, volumetric and mass flow rates for all 3 vessels.Do NOT assume that the mass flow rate from A is divided evenly between B & C. Assume density of blood is 1.056 g/cm^3

Round Answers to 2 decimal places. Do not include units in your answer boxes as they are given.

Area Artery A = ? cm^2

Volumetric Flow A = ? cm^3/s

Mass Flow Rate A = ? g/s

Area Artery B = ? cm^2

Volumetric Flow B = ? cm^3/s

Mass Flow Rate B = ? g/s

Area Artery C = ?

Volumetric Flow C = ? cm^3/s

Mass Flow Rate C = ? g/s

Diameter C = ?

Artery A Artery B Artery C Velocity 25.00 cm/s Velocity 30.00 cm/s Velocity 30.00 cm/s Diameter 0.30 cm Diameter 0.21 cm Diameter ??? cm Area ???    cm^2 Area ???    cm^2 Area ???    cm^2 Volumetric Flow ??? cm^3/s Volumetric Flow ??? cm^3/s Volumetric Flow ???    cm^3/s Mass Flow ??? g/s Mass Flow ???    g/s Mass Flow ???    g/s

Explanation / Answer

i. Area Artery A = 3.141 x diameter2 /4 = 3.141 x 0.32 / 4 = 0.07 cm2

ii. volumetric flow A= area x velocity = 0.07 x 25 = 1.75 cm3/s

iii. Mass flow rate A = volumetric flow A x density = 1.75 x 1.056 = 1.85 g/s

iv. Area Artery B = 3.141 x diameter2 /4 = 3.141 x 0.212 / 4 = 0.035 cm2

v. volumetric flow B= area x velocity = 0.035 x 30 = 1.05 cm3/s

vi. Mass flow rate B = volumetric flow A x density = 1.05 x 1.056 = 1.11 g/s

vii. volumetric flow C = volumetric Flow A - volumetric flow B

= 1.75 - 1.05 =0.7 cm3 /s

viii. mass flow rate C = Mass flow rate A - mass flow rate B

= 1.85 - 1.11

=0.74 g/s

ix. Area of Artery C = volumetric flow rate C/ velocity C

= 0.7 / 30 = 0.023 cm2

x. area of artery C =3.141 x diameter C2 /4 = 0.023

so, diameter C = 0.009 cm or 0.01 cm

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