Blood Flow in Arteries and Veins - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 154

after calculating the bifurcation angles. Also, validate the last equation from Murray's Law,
which relates both bifurcation angles to the radii of the three blood vessels (see Figure 5.15 ).

Solution

r 1 5 r 2 1 r 3

3 3

r 3 ð 175 μ m Þ 5 ð 125 μ m Þ 1

3 q

ð

3 3

r 3 5 175 μ m Þ

2 ð

125 μ m Þ 150 : 5 μ m

5

4 4 4

r 1 1 r 2 2 r 3 ð 175 μ m Þ 1 ð 125 μ m Þ 2 ð 150 : 5 μ m Þ

cos 2 1 cos 2 1 6

θ 5 5 5 45 :

2 r 1 r 2

2 2

2 ð 175 μ m Þ ð 125 μ m Þ

4 4 4

r 1 2 r 2 1 r 3 ð 175 μ m Þ

2 ð

125 μ m Þ

1 ð

150 : 5 μ m Þ

cos 2 1 cos 2 1 5

φ 5 :

5 5 29

2 r 1 r 3

2 2

2 ð 175 μ m Þ ð 150 : 5 μ m Þ

6 1 5 Þ 5 1 Þ 5 cos ðθ 1 φÞ 5 cos ð 45 : 29 : cos ð 75 : 0 : 256

4 4 4

r 1 2 r 2 2 r 3

5 ð

175 μ m Þ 2 ð 125 μ m Þ 2 ð 150 : 5 μ m Þ

5 0 : 256

2 r 2 r 3

2 150 2

2 125 ð μ m Þ ð : 5 μ m Þ

Therefore,

r 1 2 r 2 2 r 3

cos ðθ 1 φÞ 5

2 r 2 r 3

FIGURE 5.15 Schematic of the bifurcation found in
the sample problem.

250 μ m

45.6 °

350 μ m

29.5 °

301 μ m