Explanation Write the expression to determine the flow rate at section (1), (2), (3), and (4). Q 1 = A 1 V 1 Q 2 = A 2 V 2 Q 3 = A 3 V 3 Q 4 = A 4 V 4 (I) Here, velocity of the sections (1), (2), (3), and (4) are V 1 , V 2 , V 3 , and V 4 , area of the sections (1), (2), (3), and (4) are A 1 , A 2 , A 3 , and A 4 , and discharge of the sections (1), (2), (3), and (4) are Q 1 , Q 2 , Q 3 , and Q 4 . Write the Bernoulli's equation for the inlet and outlet streams for points (1) and (2). p 1 γ H 2 O + V 1 2 2 g + Z 1 = p 2 γ H 2 O + V 2 2 2 g + Z 2 (II) Here, the pressure at section 1 is p 1 , the pressure at section 2 is p 2 , the specific gravity of water is γ H 2 O , acceleration due to gravity is g , datum in section 1 is Z 1 , and the datum in section 2 is Z 2 . Write the expression for discharge for the branching pipe. Q 1 = Q 2 + Q 3 + Q 4 Q 4 = Q 1 − Q 2 − Q 3 Q 4 = Q 1 − A 2 V 2 + A 3 V 3 (III) Write the Bernoulli's equation for the inlet and outlet streams for points (1) and (3). p 1 γ H 2 O + V 1 2 2 g + Z 2 = p 3 γ H 2 O + V 3 2 2 g + Z 3 (IV) Here, the pressure in section 3 is p 3 and the datum in section 3 is Z 3 . Conclusion: Substitute 10 ft 3 / s for Q 1 and 1 ft 2 for A 1 in Equation (I). 10 ft 3 / s = 1 ft 2 × V 1 V 1 = 10 ft 3 / s 1 ft 2 V 1 = 10 ft / s Substitute 32.2 ft / s 2 for g , 10 psi for p 1 , 5 psi for p 2 , 10 ft / s for V 1 , 62.4 lb / ft 3 for γ H 2 O , 0 m for Z 1 , 0 m for Z 2 in Equation (III)

8th Edition

ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 3.6, Problem 112P

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The velocity at section (2), the pressure at section (3), and flow rate at section (4)

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Chapter 3.6, Problem 111P

Chapter 3.6, Problem 113P

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