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Unformatted text preview: Question 1. 3 Water flows at a rate of 100 ft /s and at a depth of 4 ft in a 5ft diameter circular culvert. Determine whether the flow is subcritical or supercritical. Determine, also, the flow rate that would cause critical flow at this depth in this culvert. θ x 2.5 θ 1.5 1.5 x 2.5 X2 = 2.52  1.52 = 6.25 – 2.25 = 4 x = 2 ft θ = tan1(1.5/2) = 0.6435 rad A = (π +2θ )/2π x π x2.52 + 1.5x2 = 16.84 ft2 Since the Froude Number is less than 1, flow is subcritical For critical flow Froude Number is 1 Q = 138.63 ft3/s
Question 2. Water flows at a depth of 3.5 ft in a rectangular channel with a base width of 4 ft. 3 The rate of flow is 140 ft /s. Determine whether the flow is sub critical or supercritical. Determine, also, the second depth of flow that is possible for the same specific energy in the same channel. A=3.5 x 4 = 14 sq.ft V= Q/A = 140/14 = 10 ft/s D = d = 3.5 ft V2/gD = 100/(32.2 x 3.5) = 0.89 > 1 Therefore Subcritical Flow 5.053d2 = 19.02 + d3 Known solution (d=3.5) can be factored out
= (d  3.5) (d2 – 1.553 d – 5.434) = 0 = = d = 3.233 Question 3. A horizontal rectangular channel expands smoothly (no friction) from a width of 6' to 12'. The upstream velocity and flow depth are 7 ft/s and 5 ft, respectively. Determine the downstream depth of flow. (You will obtain 2 values but only one is possible under the given conditions. Why?) Q = v x A = 7 x 6 x 5 = 210 ft3/s For the downstream section, the flow rate and energy are the same. 5.761d2 = 4.755 + d3 d = 1.0 ft, 5.61 ft For the upstream section, v2/gD = 49/32.2/5 = 0.3 Subcritical flow Since v2/gD is less than 1, the downstream depth is most likely 5.61 ft, where v2/gD is also less than 1 ...
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 Spring '08
 Cooke,R
 Fluid Dynamics, 5 ft, 2 ft, 5ft

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