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Water flows over a dam into a rectangular channel of width b (out of page). At the bottom of the dam, the depth of flow is h₁. As you may have seen on watching rapid channel flow, the water may suddenly change elevation to height h2 as it passes through a highly disturbed region called the hydraulic jump. If velocity is assumed uniform at 1 and 2, compute the height h2 using the control volume analysis. Take the pressures at 1 and 2 as hydrostatic, and assume that the flow is steady. Neglect friction at the channel bed and walls. (Courtesy of the Wright Water Engineers, Inc. and ASDSO) Hydraulic jump h₁ = 3 ft V₁ = 25 ft/s h₂ =? V₂ =? (a) Find the cubic equation, in terms of h₁, V₁, and g, that you must solve for the downstream depth h₂ of the water channel. (b) For h₁ = 3 ft and V₁ = 25 ft/s, find the downstream depth h₂. Use the standard value for Note that you are solving a cubic equation, and only one of the solutions is correct.

Water flows over a dam into a rectangular channel of width b (out of page). At the bottom of the dam, the depth of flow is h₁. As you may have seen on watching rapid channel flow, the water may suddenly change elevation to height h2 as it passes through a highly disturbed region called the hydraulic jump. If velocity is assumed uniform at 1 and 2, compute the height h2 using the control volume analysis. Take the pressures at 1 and 2 as hydrostatic, and assume that the flow is steady. Neglect friction at the channel bed and walls. (Courtesy of the Wright Water Engineers, Inc. and ASDSO) Hydraulic jump h₁ = 3 ft V₁ = 25 ft/s h₂ =? V₂ =? (a) Find the cubic equation, in terms of h₁, V₁, and g, that you must solve for the downstream depth h₂ of the water channel. (b) For h₁ = 3 ft and V₁ = 25 ft/s, find the downstream depth h₂. Use the standard value for Note that you are solving a cubic equation, and only one of the solutions is correct.

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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Water flows over a dam into a rectangular channel of width b (out of page). At the bottom of the dam, the depth of flow is h₁. As you may have seen on watching rapid channel flow, the water may suddenly change elevation to height h₂ as it passes through a highly disturbed region called the hydraulic jump. If velocity is assumed uniform at 1 and 2, compute the height h2 using the control volume analysis. Take the pressures at 1 and 2 as hydrostatic, and assume that the flow is steady. Neglect friction at the channel bed and walls. (Courtesy of the Wright Water Engineers, Inc. and ASDSO) Hydraulic jump h₁ = 3 ft V₁ = 25 ft/s BE 2 h₂ =? V₂ = ? (a) Find the cubic equation, in terms of h₁, V₁, and g, that you must solve for the downstream depth h₂ of the water channel. (b) For h₁ = 3 ft and V₁ = 25 ft/s, find the downstream depth h₂. Use the standard value for g. Note that you are solving a cubic equation, and only one of the solutions is correct.
Transcribed Image Text:Water flows over a dam into a rectangular channel of width b (out of page). At the bottom of the dam, the depth of flow is h₁. As you may have seen on watching rapid channel flow, the water may suddenly change elevation to height h₂ as it passes through a highly disturbed region called the hydraulic jump. If velocity is assumed uniform at 1 and 2, compute the height h2 using the control volume analysis. Take the pressures at 1 and 2 as hydrostatic, and assume that the flow is steady. Neglect friction at the channel bed and walls. (Courtesy of the Wright Water Engineers, Inc. and ASDSO) Hydraulic jump h₁ = 3 ft V₁ = 25 ft/s BE 2 h₂ =? V₂ = ? (a) Find the cubic equation, in terms of h₁, V₁, and g, that you must solve for the downstream depth h₂ of the water channel. (b) For h₁ = 3 ft and V₁ = 25 ft/s, find the downstream depth h₂. Use the standard value for g. Note that you are solving a cubic equation, and only one of the solutions is correct.
Expert Solution
Step 1

To find:

(a) The cubic equation in terms of h1,V1 and g.

(b) The downstream depth h2.

Given:

The height is h1=3 ft.

The velocity is V1=25 ft/sec. 

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