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: 55

Answer

See answer.

Work Step by Step

Apply the equation of continuity to the openings. $$A_2v_2=A_1v_1$$ $$v_2=v_1\frac{A_1}{A_2}$$ Now apply Bernoulli’s equation. The pressure at each opening is atmospheric pressure. $$P_1+\frac{1}{2}\rho v_1^2+\rho g y_1= P_2+\frac{1}{2}\rho v_2^2+\rho g y_2$$ $$ v_1^2- v_2^2=2 g( y_2-y_1)=2gh$$ Substitute. $$ v_1^2- (v_1\frac{A_1}{A_2})^2=2gh$$ $$ v_1^2(1- (\frac{A_1}{A_2})^2)=2gh$$ $$ v_1=\sqrt{\frac{2gh }{(1- (A_1/A_2)^2)}}$$ This was to be shown.
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