cee4324-5984_lecture25

cee4324-5984_lecture25 - CEE 4324/5984 Open Channel Flow...

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Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Quantitative Surface Water Profiles CEE 4324/5984 –Open Channel Flow – Lecture 25
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Questions from Lecture 24? Quantitative Surface Water Profiles Review: Standard Step Method Learning from Spreadsheet Conjugate Curve Work Comments on Current Homework Assignment HEC-RAS Today’s Agenda:
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Begin Quantitative Surface Water Profiles: Standard Step Method: Distance calculated from depth Governing Equation: For convenience, we’ll use discrete version of derivative and solve for x . f S S dx dE - = 0 f S S E E x x - - + = 0 1 2 1 2
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Standard Step Method Main idea – at location, i : We will arbitrarily choose depths, y i and y i +1 , and use equation from previous slide to determine distance between these two depths. The method lends itself nicely to a spreadsheet operation. ) ( i y f E i =
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Standard Step Method At-a-Point Measurements (Row i ): English units assumed Column 1: Depth, y (feet). Arbitrarily chosen . (More to be discussed later) Column 2: Area, A (ft 2 ). Given the channel geometry, A is a function of y . For instance, in a rectangular channel, A=by . Column 3: Wetted Perimeter, P (ft). Given the channel geometry, P is a function of y . For instance, in a rectangular channel, P=b+2y .
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Standard Step Method Column 4: Hydraulic Radius, R (ft). Given the channel geometry, R is a function of y . For instance, in a rectangular channel, R=by/(b+2y) . In general, R = Column 2 ÷ Column 3. Column 5: Velocity, v (ft/s). Given the discharge ( Q ), v is determined by dividing by A . In general, v = Q ÷ Column 2.
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Column 6: Friction Slope, S f . Using the velocity from Column 5 and hydraulic radius from Column 4, apply a re-arranged version of Manning’s equation: Column 7: Velocity Head, v 2 /2 g (ft). Calculated using the velocity from
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cee4324-5984_lecture25 - CEE 4324/5984 Open Channel Flow...

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