Imagine for a moment that a large artery formed two branches carrying blood to two different organs. Branch 1 has a radius of 0.5 cm and Branch 2 has a radius of 1.0 cm. If the blood flow rate in Branch 1 is 2ml/min, what do you expect the blood flow rate of Branch 2 to be

Answers

Answer 1

The flow rate through Branch 2 is 8·√2 ml/min

Reasons:

Radius of Branch 1 = 0.5 cm

Radius of Branch 2 = 1.0 cm

Flow rate, Q = Velocity, V × Area, A

The area of the Branch 1 = π × 0.5² = 0.25·π

We have;

[tex]\dfrac{v_1^2}{r_1} = \dfrac{v_2^2}{r_2}[/tex]

Which gives;

[tex]v_2 = \mathbf{\sqrt{\dfrac{v_1^2}{r_1} \times r_2}}[/tex]

[tex]The \ velocity \ of \ Branch 1 , \ v_1 = \dfrac{2}{\pi \times 0.5^2} = \dfrac{8}{\pi}[/tex]

Therefore;

[tex]v_2 = \sqrt{\dfrac{\left(\dfrac{8}{\pi} \right) ^2}{0.5} \times1} = 8 \cdot\dfrac{\sqrt{2} }{\pi}[/tex]

[tex]The \ flow \ rate, \ Q_2 = 8 \cdot\dfrac{\sqrt{2} }{\pi} \times \pi \times 1^2 = 8 \times \sqrt{2}[/tex]

The flow rate through Branch 2 = 8·√2 ml/min

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