In a major human artery with an internal diameter of 5mm, the flow of blood, averaged over the cardiac cycle is 5cm3·s−1. The artery bifurcates (splits) into two identical blood vessels that are each 3mm in diameter. What are the average velocity and the mass flow rate upstream and downstream of the bifurcation? The density of blood is 1.06g·cm−3

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Explanation:

Assuming flow is uniform across the cross section of the artery, the mass flow rate is the product of the volumetric flow rate and the density.

  (5 cm³/s)(1.06 g/cm³) = 5.3 g/s

If we assume the blood splits evenly at the bifurcation, then the downstream mass flow rate in each artery is half that:

  (5.3 g/s)/2 = 2.65 g/s

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The average velocity will be the ratio of volumetric flow rate to area. Upstream, that is ...

  (5 cm³/s)/(π(0.25 cm)²) ≈ 25.5 cm/s

Downstream, we have half the volumetric flow and a smaller area.

  (2.5 cm³/s)/(π(0.15 cm)²) ≈ 35.4 cm/s

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