Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 15 - Fluids and Elasticity - Exercises and Problems - Page 437: 34

Answer

$\approx 847\;\rm mmHg$

Work Step by Step

When you are lying down, the absolute pressure inside the brain and the heart is $$P_1=P_{gauge}+P_A$$ where $P_1$ is the initial pressure in both the brain and the heart. So, $$ P_{\rm heart}=P_{1,\rm brain}=118+760=\bf 878\;\rm mmHg\tag 1$$ And when you are standing up, the pressure in the heart is constant and is then given by $$P_{\rm heart}=P_{2\rm,brain }+h\rho g$$ where $h$ is the height of the brain and $\rho$ is the blood's density. So, $$P_{2\rm,brain }=P_{\rm heart}-h\rho g $$ Plugging the known, and do not forget to convert the last term to the unit of mmHg. where $\rm 760\;\rm mmHg=1.013\times 10^5\;P_a$ $$P_{2\rm,brain }=878-\rm \left[(0.4)(1060)(9.8)\;\rm P_a\;\left(\dfrac{760\;\rm mmHg}{1.013\times 10^5\;P_a}\right)\right]$$ $$P_{2\rm,brain }=\color{red}{\bf 846.8}\;\rm mmHg$$
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