Model the arterial tree as a simple branching network in which each junction is composed of a parent vessel and daughter vessels, each having a diameter related to the parent's via the cube law (D_n-1)^3= (D_n*a)^3 + (D_n*b)^3 which is approx. equal to 2*(D_n)^3(adsbygoogle = window.adsbygoogle || []).push({});

a.) Show that D_n/D_0= 2^(-n/3)

b.) Show that 35 generations are required to model the arterial tree from aorta (D_0=2.6 cm) to the capillaries (D_34=10 um)

c.) Derive a formula for the mean transit time (ie vessel length divded by mean velociity) for an individual vessel. Based on this formula, how long does the model suggest it would take for blood to go from the aorta to the capillaries?

My work:

a.) since

(D_n-1)^3 is approximately equal to 2*(D_n)^3

therefore,

(D_n-1/D_n)^3= 2

therefore i Dn/Do= 2^(-n/3)

I'm not sure

i need help with the other questions, i'm confused how use this equation to solve the problem?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Hemodynamics Homework Help, Works shown please help!

**Physics Forums | Science Articles, Homework Help, Discussion**