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Question 6 A weir is a barrier that spans across the width of a river and is used to alter its flow characteristics. Typically, this results in a change in the height of the river level. The figure below shows the cross-section of a broad- crested weir. The symbols in the figure are Hw- the height of the weir (m), Hà – the head above the weir (m), and H = Hw + Hà – the depth of the river upstream of the weir. The flow across the weir (Qw) (m/s) can be computed using the following expression: Qw 3/2 Qu = C,BVg) Hw Weir Bw where Cw is a weir coefficient (dimensionless), Bw is the weir width (m), and g is the gravitational constant, taken as 9.81m/s'. The weir coefficient can be determined using the weir height (Hw): 1+ H/H 2+ H/H Cu = 1.125, In this problem, assume: g = 9.81m/s, Hw = 0.8 m, Bw = 8 m, and Q = 1.3 m/s. Complete the following: (a) Determine the upstream depth (H = Hw + Hà) using simple fixed-point iteration with an initial guess of Hx=0.5Hw. Complete two iterations. For each iteration, compute the approximate error (Ea). (b) Determine the upstream depth (H Hw + Hà) using the false position method with an initial bracket of H=[0.1Hw to Hw]. Complete two iterations. For each iteration, compute the approximate error. 2 13

Question 6 A weir is a barrier that spans across the width of a river and is used to alter its flow characteristics. Typically, this results in a change in the height of the river level. The figure below shows the cross-section of a broad- crested weir. The symbols in the figure are Hw- the height of the weir (m), Hà – the head above the weir (m), and H = Hw + Hà – the depth of the river upstream of the weir. The flow across the weir (Qw) (m/s) can be computed using the following expression: Qw 3/2 Qu = C,BVg) Hw Weir Bw where Cw is a weir coefficient (dimensionless), Bw is the weir width (m), and g is the gravitational constant, taken as 9.81m/s'. The weir coefficient can be determined using the weir height (Hw): 1+ H/H 2+ H/H Cu = 1.125, In this problem, assume: g = 9.81m/s, Hw = 0.8 m, Bw = 8 m, and Q = 1.3 m/s. Complete the following: (a) Determine the upstream depth (H = Hw + Hà) using simple fixed-point iteration with an initial guess of Hx=0.5Hw. Complete two iterations. For each iteration, compute the approximate error (Ea). (b) Determine the upstream depth (H Hw + Hà) using the false position method with an initial bracket of H=[0.1Hw to Hw]. Complete two iterations. For each iteration, compute the approximate error. 2 13

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question 6 A weir is a barrier that spans across the width of a river and is used to alter its flow characteristics. Typically, this results in a change in the height of the river level. The figure below shows the cross-section of a broad- crested weir. The symbols in the figure are Hw – the height of the weir (m), Hà – the head above the weir (m), and H = Hw + HA – the depth of the river upstream of the weir. The flow across the weir (Qw) (m'/s) can be computed using the following expression: 3/2 3/2 Qu = CuBug ) H Hw Weir 3 Bw where Cw is a weir coefficient (dimensionless), Bw is the weir width (m), and g is the gravitational constant, taken as 9.81m/s'. The weir coefficient can be determined using the weir height (Hw): 1+ H/H 2+ H/Hw Cu = 1.125. In this problem, assume: g = 9.81m/s", Hw = 0.8 m, Bw = 8 m, and Qw = 1.3 m/s. Complete the following: (a) Determine the upstream depth (H = Hw + Hà) using simple fixed-point iteration with an initial guess of Hi=0.5Hw. Complete two iterations. For each iteration, compute the approximate error (Ea). (b) Determine the upstream depth (H = Hw + Hà) using the false position method with an initial bracket of Hk=[0.1Hw to Hw]. Complete two iterations. For each iteration, compute the approximate error.
Transcribed Image Text:Question 6 A weir is a barrier that spans across the width of a river and is used to alter its flow characteristics. Typically, this results in a change in the height of the river level. The figure below shows the cross-section of a broad- crested weir. The symbols in the figure are Hw – the height of the weir (m), Hà – the head above the weir (m), and H = Hw + HA – the depth of the river upstream of the weir. The flow across the weir (Qw) (m'/s) can be computed using the following expression: 3/2 3/2 Qu = CuBug ) H Hw Weir 3 Bw where Cw is a weir coefficient (dimensionless), Bw is the weir width (m), and g is the gravitational constant, taken as 9.81m/s'. The weir coefficient can be determined using the weir height (Hw): 1+ H/H 2+ H/Hw Cu = 1.125. In this problem, assume: g = 9.81m/s", Hw = 0.8 m, Bw = 8 m, and Qw = 1.3 m/s. Complete the following: (a) Determine the upstream depth (H = Hw + Hà) using simple fixed-point iteration with an initial guess of Hi=0.5Hw. Complete two iterations. For each iteration, compute the approximate error (Ea). (b) Determine the upstream depth (H = Hw + Hà) using the false position method with an initial bracket of Hk=[0.1Hw to Hw]. Complete two iterations. For each iteration, compute the approximate error.
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