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: 98

Answer

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Work Step by Step

a. Apply Bernoulli’s equation to the two ends. $$P_{sink}+\frac{1}{2}\rho v_{sink}^2+\rho gy_{sink}= P_{pail}+\frac{1}{2}\rho v_{pail}^2+\rho gy_{pail}$$ Assume the pressure at the tube ends is the same. $$v_{pail}=\sqrt{2g(y_{sink}-y_{pail})}=\sqrt{2(9.80\;m/s^2)(0.40m)}=2.8\;m/s$$ b. The volume flow rate at the bottom end, multiplied by the time to empty the sink, equals the volume of water in the sink. $$(Av)_{pail}t=V_{sink}$$ $$t=\frac{V_{sink}}{(Av)_{pail}}=\frac{(0.38\;m^2)(0.04\;m)}{\pi(0.0115\;m)^2(2.8\;m/s)}=13\;s$$
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