Question

The segment on the left has diameter 1.6 mm, and each of the segments on the right has diameter 0.4 mm. Assume the blood can be treated as an ideal fluid. If blood enters the segment on the left with speed v, at what speed does the blood leave the segments on the right?

Answer 1

Answer:

Explanation:

The flow entering the first segment will be the same as the flow exiting the second segment, and in both cases it will be equal to the velocity multiplied by the area of the segment. If $Flow_{a} = Flow_{b}$ and Flow = VxA, then you have:

$V_{a} x A_{a} = V_{b} x A_{b}$ (1)

You can also calculate the transversal area of each segment, because blood vessels are cylinders and you know each segment's diameter. The formula to calculate this is:

$A = \pi /4 x d^{2}$

Replacing d for each segment you have:

$Area_{a} = 2.01 mmArea_{b} = 0.13 mm$

Now, replacing these values on (1), you have:

$V_{a} x 2.01 mm = V_{b} x 0.13 mm$

$(V_{a} x 2.01 mm)/0.13 mm = V_{b}$

$15.4 x V_{a} = V_{b}$

This means that velocity in the second segment is 15.4 times the velocity in which blood entered the first segment.