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a rectangular concrete channel, the equilibrium depth is 3.2 m. The channel is 2 m wide and the bed slope is 0.0006. Compute and give the values (and units) of the following quantities: (a) uniform equilibrium flow velocity, (b) Darcy friction factor, (c) discharge.

a rectangular concrete channel, the equilibrium depth is 3.2 m. The channel is 2 m wide and the bed slope is 0.0006. Compute and give the values (and units) of the following quantities: (a) uniform equilibrium flow velocity, (b) Darcy friction factor, (c) discharge.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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3.1 In a rectangular concrete channel, the uniform equilibrium flow depth is 3.2 m. The channel is 2 m wide and the bed slope is 0.0006. Compute and give the values (and units) of the following quantities: (a) uniform equilibrium flow velocity, (b) Darcy friction factor, (c) discharge. Solution: The problem is solved using the momentum principle. The bed shear stress must be estimated using the Darcy- Weisbach friction factor. See textbook pp. 69-77. Note that the calculations are iterative. Numerical solution: Vo = 1.53 m/s, do = 3.2 m, f= 0.0154 (kg = 1 mm), to = 4.43 Pa 3.2. A rectangular channel (12-m wide) is faced with rubble masonry (kg = 50 mm). The total flow rate is 12.5 m³/s and the bed slope is 0.001. (3.2.1) Compute and give the values and units of the following quantities: (a) uniform equilibrium flow depth, (b) Darcy friction factor, (c) boundary shear stress (3.2.2) Is the uniform equilibrium flow sub- or super-critical? (3.2.3) From where would you control the flow? Numerical solution: V₁1.17 m/s, do=0.891 m (for kg = 50 mm)
Transcribed Image Text:3.1 In a rectangular concrete channel, the uniform equilibrium flow depth is 3.2 m. The channel is 2 m wide and the bed slope is 0.0006. Compute and give the values (and units) of the following quantities: (a) uniform equilibrium flow velocity, (b) Darcy friction factor, (c) discharge. Solution: The problem is solved using the momentum principle. The bed shear stress must be estimated using the Darcy- Weisbach friction factor. See textbook pp. 69-77. Note that the calculations are iterative. Numerical solution: Vo = 1.53 m/s, do = 3.2 m, f= 0.0154 (kg = 1 mm), to = 4.43 Pa 3.2. A rectangular channel (12-m wide) is faced with rubble masonry (kg = 50 mm). The total flow rate is 12.5 m³/s and the bed slope is 0.001. (3.2.1) Compute and give the values and units of the following quantities: (a) uniform equilibrium flow depth, (b) Darcy friction factor, (c) boundary shear stress (3.2.2) Is the uniform equilibrium flow sub- or super-critical? (3.2.3) From where would you control the flow? Numerical solution: V₁1.17 m/s, do=0.891 m (for kg = 50 mm)
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