Open Channel Problems

7/29/2019 Open Channel Problems

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An open channel has a trapezoidal cross-section with a bottom width of 5 m and side slopesof 2:1 (H:V). If the depth of flow is 2 m and the average velocity in the channel is 1 m/s,calculate the discharge in the channel.

A trapezoidal channel is to be excavated at a site where permit restrictions require that thechannel have a bottom width of 5 m, side slopes of 1.5:1 (H:V) and a depth of flow of 1.8m. If the soil material erodes when the shear stress on the perimeter of the channel exceeds3.5 N/m2, determine the appropriate slope and flow capacity of the channel. Use the Darcy-Weisbach equation and assume that the excavated channel has an equivalent sand roughnessof 3 mm.


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Water flows at a depth of 2.20 m in a trapezoidal, concrete-lined section (ks = 2 mm) with

a bottom width of 3.6 m and side slopes of 2:1 (H:V). The slope of the channel is 0.0006and the water temperature is 20C. Assuming uniform-flow conditions, estimate the averagevelocity and flowrate in the channel. Use both the Darcy-Weisbach and Manning equationsand compare your answers.


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A trapezoidal irrigation channel is to be excavated to supply water to a farm. The designflowrate is 1.8 m3/s, the side slopes are 2:1 (H:V), the longitudinal slope of the channel is

0.1%, Mannings n is 0.025, and the geometry of the channel is to be such that the length

of each channel side is equal to the bottom width. (a) Specify the dimensions of the channelrequired to accommodate the design flow under normal conditions; and (b) If the channellining can resist an average shear stress of up to 4 Pa, under what flow conditions is thechannel lining stable?


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Water flows at 8.4 m3/s in a trapezoidal channel with a bottom width of 2 m and side slopesof 2:1 (H:V). Over a distance of 100 m, the bottom width expands to 2.5 m, with the sideslopes remaining constant at 2:1. If the depth of flow at both of these sections is 1 m andthe channel slope is 0.001, calculate the head loss between the sections. What is the powerin kilowatts that is dissipated?


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Determine the critical depth for 30 m3/s flowing in a rectangular channel with width 5 m. Ifthe depth of flow is equal to 3 m, is the flow supercritical or subcritical?


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A rectangular channel 2 m wide carries 3 m3/s of water at a depth of 1.2 m. If an obstruction40 cm wide is placed in the middle of this channel, find the elevation of the water surface atthe constriction. What is the minimum width of the constriction that will not cause a rise inthe water surface upstream?


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Water flows at 4.3 m3/s in a rectangular channel of width 3 m and depth of flow 1 m. Ifthe channel width is decreased by 0.75 m and the bottom of the channel is raised by 0.25 m,what is the depth of flow in the constriction?


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Water flows at 36 m3/s in a rectangular channel of width 10 m and a Manning n of 0.030. If

the depth of flow at a channel section is 3 m and the slope of the channel is 0.001, classify thewater-surface profile. What is the slope of the water surface at the observed section? Wouldthe shape of the water-surface profile be much different if the depth of flow were equal to 2m?


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If 100 m3/s of water flows in a channel 8 m wide at a depth of 0.9 m, calculate the downstreamdepth required to form a hydraulic jump and the fraction of the initial energy lost in the jump.


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Derive the hydraulic jump equation for a trapezoidal channel:

Water flows in a horizontal trapezoidal channel at 21 m3/s, where the bottom width of the

channel is 2 m, side slopes are 1:1, and depth of flow is 1 m. Calculate the downstream depthrequired for a hydraulic jump to form at this location. What would be the energy loss in theump?


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Open Channel Problems

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