Consider the rectangular channel having width b and depth y.
Calculate width and depth of the trapezoidal channel:
From the Manning’s equation for flow
…… (1)
Where, Flow rate
Manning’s roughness coefficients
Flow area
Hydraulic radius
Side slope
From the diagram,Angle made with the horizontal surface
Calculate angle:
From the table, geometric properties of common open-channel shapes
Area …… (2)
Wetted Perimeter
To obtain optimum condition, eliminate b
From equation (2)
Substitute the value of in wetted perimeter, we get
Differentiate the above equation with respect to y
…… (3)
Let, apply the optimum conditions,
for equation (3)
…… (4)
Equate equations (2) and (4)
…… (5)
Substitute equation (5) in (1)
Now substitute the value of A in wetted perimeter, then
Calculate hydraulic radius,
Calculate depth of the trapezoidal section:
Substitute: for
,
for
,
for
in (1)
Simplify the above equation
Calculate width of the channel:
Therefore, the depth of channel isand Width of the channel is
.
Determine the cross section of the greatest hydraulic efficiency for a trapezoidal channel with side slope...
Determine the cross-section of the greatest hydraulic efficiency for a trapezoidal channel with side slope of 1 vertical to 2 horizontal if the design discharge is 10 m3/s. The channel slope is 0.001 and Manning’s roughness factor is 0.020.
Please help ,,,,, water resources
Determine the cross-section of the greatest hydraulic efficiency for a trapezoidal channel with side slope of I vertical to 2 horizontal if the design discharge is 12 m^3/s. The channel slope is 0.001 and Manning's roughness factor is 0.020.
A 2.44 wide channel with a bed slope of 0.0004 has a depth of flow of 0.61 m. (a) Determine the discharge of the channel. The manning coefficient is 0.015. (b) Determine the normal depth if the channel has a flow rate of 2.85 m3/s. (c) Determine the cross section of greatest hydraulic efficiency for a trapezoidal channel if the design discharge is 10 m3/s, the channel slope is 0.0052 and manning’s n = 0.025.
QUESTION 1 A trapezoidal, concrete lined channel is to be constructed to carry floodwater. The slope of the ground surface is 1 in 500. The design discharge is 10 m3/s. Calculate the dimensions of the trapezoidal channel that will minimize excavation and results in the optimum hydraulic section. (Take Manning’s n = 0.015).
A trapezoidal channel has a bottom width, b, of 10.0 m and a side slope ratio of 3:1. The Manning’s n of the channel is 0.025, and it is laid on a slope of 0.001. If the water depth is 2 m at the downstream end, write and submit an R script to compute the water surface profile for a discharge of 30 m3 /s. Also submit a plot of the water profile in elevation (m) for 1000 m channel...
#4 [5 points] A trapezoidal channel of bottom width 25 ft and side slope 1:2.5 carries a discharge of 450 cfs with a normal depth of 3.5 ft. The elevations at the beginning and end of the channel are 685 and 650 ft., respectively. Determine the length of the channel if n = 0.02. #5 [5 points] Water is flowing at a rate of 4.5 m3/s in a trapezoidal channel whose bottom width is 2.4 m and side slopes are...
A trapezoidal channel has a side slope of 1:1 and a bed width of 6.0 m. A hydraulic jump with a height of 0.5 m (i.e. the difference between water surface elevation upstream and downstream of the jump) is encountered in the channel. If the channel has a discharge of 10 m3/s, determine the critical depth in the channel. Plot the momentum curve and determine the flow depth immediately upstream and downstream of the jump.
A concrete-lined (smooth) trapezoidal channel with a bottom width of 10 ft and side slope 2 horizontal to 1 vertical has a slope 0,002 and is designed for a discharge of 160 cts. Determine the water depth in the channel,
Design a concrete trapezoidal channel with best hydraulic cross-section that can handle the flow from the development above. The slope of the channel is 0.05. Describe the flow condition in the channel. 3. art ii-open books and notes (20 points each - use NRCS methods to solve these problems) A proposed 40 ha development in Jackson, Mississippi, includes 10 ha parking lot, 10 ha buildings, and the rest is grass area which includes 1 ha detention pond. The runoff from...
Question 6 A concrete-lined trapezoidal channel with uniform flow has a normal depth of 1.5 m. The base width is 4 m and the side slopes are equal at 1 vertical to 2 horizontal. Mannin‘s n-0015. The bed slope 0.001 Compute the mean velocity and discharge. If the above channel were to be designed for flooding, it may have a section like in Figure below 8 m 8 m 4 m When the flow goes over the top of the...