A stream bed has a rectangular cross section 5 meters wide and a slope of 0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n = 0.015. y≈yn 2.5 m 1. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do not need to solve the equation by hand. To get full credit, show your equation with only one unknown. (10 pts) 2. Find the critical depth, yc. (10 pts) 3. The yn is found to be 1.8 m by solving the equation numerically. Identify the water surface profile upstream of the dam. Explain your answer for full credit. (10 pts)
A stream bed has a rectangular cross section 5 meters wide and a slope of 0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n = 0.015. y≈yn 2.5 m 1. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do not need to solve the equation by hand. To get full credit, show your equation with only one unknown. (10 pts) 2. Find the critical depth, yc. (10 pts) 3. The yn is found to be 1.8 m by solving the equation numerically. Identify the water surface profile upstream of the dam. Explain your answer for full credit. (10 pts)
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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Transcribed Image Text:A stream bed has a rectangular cross section 5 meters wide and a slope of
0.0002 m/m. The flow rate in the stream is 8.75 m³/s. A dam is built across the stream, causing
the water surface to rise to 2.5 meters just upstream of the dam, as shown below. Assume n =
0.015.
y≈yn
2.5 m
1. Find the normal depth, yn, corresponding to this flow rate and channel geometry. You do
not need to solve the equation by hand. To get full credit, show your equation with only
one unknown. (10 pts)
2. Find the critical depth, yc. (10 pts)
3. The yn is found to be 1.8 m by solving the equation numerically. Identify the water
surface profile upstream of the dam. Explain your answer for full credit. (10 pts)
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