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cee4324-5984_lecture4

# cee4324-5984_lecture4 - CEE 4324/5984 Open Channel Flow...

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Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Specific Energy: Critical Flow, Steps, and Constrictions CEE 4324/5984 –Open Channel Flow – Lecture 4

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Questions? Brief Review: Critical Flow Equations and Sluice Gate Animation Example 4: Sluice Gate (concept of choke) Example 5: Step Problem – subcritical flow Example 6: Step Problem – supercritical flow Example 7: Step Problem – supercritical flow Example 7: “Negative Step” problem Example 8: A step as a choke Example 9: A constriction (sub-critical) Example 10: A constriction (super-critical) Today’s Agenda
Critical Depth Equations - REVIEW Critical depth in a rectangular channel: Critical energy in a rectangular channel: Definition of Froude number in a rectangular channel: 3 / 1 2 = g q y c c c y E 5 . 1 = gy v F r =

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Sluice Gate Animation
Example 4: Sluice Gate as a Choke Settings: q = 10.0 ft 2 /s Incoming flow depth is y 1 =4.94 feet Gate opening, y g is set to y g =0.50 feet Recall, alternate depth to y 1 =4.94 feet is y 2 = 0.59 feet (so y g < y 2 ) What is depth downstream of gate? Are any other depths changed? With E =5.0 feet, at the instant y g =0.50 feet what is unit discharge? << to be derived on whiteboard >>

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Example 4 (cont): E-y diagram for choke 0 1 2 3 4 5 6 0 1 2 3 4 5 6 E (ft) y (ft) q = 8.51 ft 2 /s q = 10.0 ft 2 /s y 1 = 4.94 ft y 2 = 0.50 ft y 2 = 0.59 ft
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E (ft) y (ft) Example 4 (cont): E-y diagram for choke q = 8.51 ft 2 /s q = 10.0 ft 2 /s y 1 = 4.94 ft y 2 = 0.59 ft E = 5.00 ft E = 6.71 ft y 2 = 0.50 ft y 2 = 0.50 ft y 1 = 6.68 ft

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Example 4 (cont): Take-away facts This example shows the sluice gate acting as a “choke”.
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cee4324-5984_lecture4 - CEE 4324/5984 Open Channel Flow...

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