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 - Problems - Page 288: 65

Answer

0.89 Pa/cm.

Work Step by Step

Use Poiseuille’s equation with a length of 1 cm. The volume flow rate is the area of the aorta multiplied by the speed of the moving blood. $$Q=\frac{\pi R^4 (P_1-P_2)}{8 \eta \mathcal{l}}$$ $$ \frac{ P_1-P_2}{l}=\frac{8 \eta Q}{\pi R^4}=\frac{8 \eta \pi R^2 v}{\pi R^4}$$ $$ \frac{ P_1-P_2}{l}=\frac{8 (4\times10^{-3}\;Pa \cdot s) (0.40\;m/s)}{ (0.012\;m)^2}=88.9\;Pa/m=0.89\;Pa/cm$$
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