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: 60

Answer

The new time will be 13 percent of the old, cutting the time by a factor of 7.7.

Work Step by Step

Use Poiseuille’s equation, 10-9, to find the reduced time. We see that the volume flow rate is proportional to $R^4$, all else being equal. $\frac{Q}{R^4}=\frac{V}{t}\frac{1}{R^4}$ is constant. Assuming that the total volume V to water the garden is the same, we see that $tR^4$ is constant. $$t_1R_1^4=t_2R_2^4$$ $$t_2=t_1(\frac{R_1}{R_2})^4= t_1(\frac{3/8}{5/8})^4=0.13t_1$$ The new time will be 13 percent of the old, cutting the time by a factor of 7.7.
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