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cee4324-5984_lecture15

cee4324-5984_lecture15 - CEE 4324/5984 Open Channel Flow...

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Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Flow Resistance (continued) CEE 4324/5984 –Open Channel Flow – Lecture 15
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Questions from Lecture 14? Reminder: Please read Chaudhry: 4-1 – 4-3 Flow Resistance Shear Stress in an open channel Flow resistance equations Chézy Equation Manning Equation Normal Depth Definition Examples Calculator Tools Today’s Agenda:
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Flow Resistance – Definition Sketch Datum y z v 2 /2g T.E.L H.G.L 1 S f 1 S 0
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Non-Uniform Flow: S f relative to S 0 S 0 > S f S 0 < S f T.E.L. T.E.L. 1 S 0 1 S 0 Gaining energy downstream Losing energy downstream
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Uniform Flow: Non-Uniform Flow: <<derivation to be done on whiteboard>> Shear Stress in an Open Channel 0 0 RS γ τ = f RS γ τ = 0
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Chézy Equation Chézy (1768) based on water supply canals in Paris Equation: <<derivation to be done on whiteboard>> RS C v =
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Manning Equation Manning (1891) – various stories as to its origin Take Chézy “ C ”: Then, substituting in Chézy’s equation: n R C 6 1 = 2 1 3 2 S R n C v M = C M = 1 : metric units C M = 1.486 : English units
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Representative Manning’s n values: For more see link at class web page
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