cee4324-5984_lecture21

cee4324-5984_lecture21 - CEE 4324/5984 Open Channel Flow...

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Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Thoughts on the C 3 profile shape and gradually varied flow profiles near steps, constrictions, and shifts in normal depth CEE 4324/5984 –Open Channel Flow – Lecture 21
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Questions from Lecture 20? Surface Water Profiles Review: General “Recipe” The C3 Profile Shape – Saloni’s Question Return to Conjugate Curve Concept Steps and Constrictions Reminder: Exam 2 will be NEXT CLASS PERIOD : Tuesday, November 8. Exam will cover through early material on Surface Water Profiles. Today’s Agenda:
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Surface Water Profiles: General Recipe for Solution 1. Calculate normal depth ( y 0 ) and critical depth ( y c ) to determine if reach is mild, critical, or steep 2. Other useful depths: Conjugate depth to y 0 ( y conj ) Alternate depth to gate opening (if sluice gate is present) 1. Identify features in the reach that will affect depth (e.g. gate, step, constriction, change in channel characteristics, boundary conditions, hydraulic jump) 2. Apply energy, momentum, and continuity principles to determine depths at key locations within the reach.
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Surface Water Profiles: General Recipe for Solution (continued) 5. Where flow is subcritical , work upstream from known depths (the flow will tend towards normal depth). 6. Where flow is supercritical , work downstream from known depths. 7. Use “building block” profiles (see next slide) to connect between known depths: M 1 , M 2 , M 3 : S 1 , S 2 , S 3 : C 1 , C 3 : H 2 , H 3 :
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Surface Water Profiles: “Building Block” Profiles 8. For each profile, note that it has several key properties: a. Its letter designation ( M , S , C , H, A ) depends on y 0 relative to y c . b. The profile resides entirely in a particular depth range relative to y 0 and y c . c. The profile exclusively gains or loses depth in the downstream direction. For example: The M 2 curve occurs only on mild reaches for depths: y ≤ y ≤ y . This
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Consider several limiting cases for: When y y 0 (numerator approaches 0, so dy/dx approaches 0 asymptotically) When y y c [denominator approaches 0, Surface Water Profiles – Profile Shapes 3 3 10 0 0 1 1 - - = y y y y S dx dy c
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Surface Water Profiles – Profile Shapes From class text Let’s focus on C 3 profile shape
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cee4324-5984_lecture21 - CEE 4324/5984 Open Channel Flow...

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