Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 10 - Fluids - General Problems - Page 290: 99

Answer

There is a 68 percent reduction in the blood flow rate,

Work Step by Step

Use Poiseuille’s equation. The volume flow rate is proportional to $R^4$, all else being equal. In other words, $\frac{Q}{R^4}$ remains constant. Note that when the diameter is reduced by 25 percent, so is the radius. $$\frac{Q_{final}}{R^4_{final}}=\frac{Q_{initial}}{R^4_{initial}}$$ $$\frac{Q_{final}}{ Q_{initial}}=\frac{ R^4_{final}}{R^4_{initial}}=(0.75)^4=0.32$$ The final flow rate is 32 percent of the original, which is a reduction of 68 percent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.