Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 14 - Fluids - Problems - Page 412: 83a

Answer

$3.19\;m/s$

Work Step by Step

We consider a point P on the surface of the liquid in the container. Now applying the Bernoulli’s equation between the points C and D, we obtain $p_C+\frac{1}{2}\rho v_C^2+\rho gh_C=p_D+\frac{1}{2}\rho v_D^2+\rho gh_D$ Here, $p_C=p_D=p_0$, $h_C=0$, $h_D=(d+h_2)$ and the speed of the liquid on the open surface of the container can be assumed zero: $v_D=0$ Substituting the above values, we obtain $p_0+\frac{1}{2}\rho v_C^2+\rho g(0)=p_0+\frac{1}{2}\rho (0)^2+\rho g(d+h_2)$ or, $\frac{1}{2}\rho v_C^2=\rho g(d+h_2)$ or, $v_C=\sqrt {2 g(d+h_2)}$ or, $v_C=\sqrt {2\times9.81\times(0.12+0.40)}\;m/s$ or, $\boxed{v_C=3.19\;m/s}$ Therefore, the liquid emerges from the tube at C with a speed $3.19\;m/s$
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