Explanation Given information: The flow is uniform and hydrostatic. The height of the water level at section (1) is 0.45 ft , the velocity at section (1) is 16 ft/s and the height of spillway is 2.2 ft , The losses are neglected. The Figure-(1) shown below defines the section (1) and section (2) in the given system. Figure-(1) Write the expression for the continuity equation between the section (1) and section (2) of the given system. A 1 V 1 = A 2 V 2 .... (I) Here, the area at section (1) is A 1 , the area at section (2) is A 2 , the velocity at section (1) is V 1 , and the Velocity at section (1) is V 2 . Write the expression for the area at section (1) for unit width. A 1 = h 1 Here, the area at section (1) is A 1 , The height at section (1) is h 1 . Write the expression for the area at section (2) for unit width. A 2 = h 2 Here, the area at section (2) is A 2 , The height at section (2) is h 2 . Substitute h 1 for A 1 and h 2 for A 2 in Equation (I). V 1 h 1 = V 2 h 2 V 2 = V 1 × h 1 h 2 …… (II) Write the expression for the Bernoulli’s equation between the section (1) and section (2) of the given system. p 1 ρ g + V 1 2 2 g + z 1 = p 2 ρ g + V 2 2 2 g + z 2 p 1 − p 2 ρ g + V 1 2 2 g − V 2 2 2 g + z 1 − z 2 = 0 …… (III) Here, the pressure at section (1) is p 1 , the velocity at section (1) is V 1 , the height of the section (1) from the datum is z 1 , the pressure at section (2) is p 2 , the velocity at section (2) is V 2 , the height of the section (2) from the datum is z 2 , the density of water is ρ , and the acceleration due to gravity is g . Since the pressure at the section (1) and section (2) is atmospheric, so the difference between the pressures is zero. p 1 − p 2 = 0 Substitute 0 for p 1 − p 2 in Equation (I). 0 ρ g + V 1 2 2 g − V 2 2 2 g + z 1 − z 2 = 0 V 1 2 2 g − V 2 2 2 g + z 1 − z 2 = 0 …… (IV) Substitute V 1 × h 1 h 2 for V 2 in Equation (III). V 1 2 2 g − V 1 × h 1 / h 2 2 2 g + z 1 − z 2 = 0 ... (V) Calculation: Substitute 0.45 ft for h 1 , 2.2 ft for H , 0

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ISBN: 9789385965494

Author: Frank White

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 3, Problem 3.141P

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The downstream depth h2 and whether two realistic solution are possible.

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Chapter 3, Problem 3.140P

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The downstream depth h 2 and whether two realistic solution are possible.

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The downstream depth h2 and whether two realistic solution are possible.

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