Consider a rural drainage 24-acre basin having soil group D with good hydrologic condition to be used for the construct of a channel. The land delineation in the basin is 1/2 meadows, 1/4 brush, and 1/4 pasture. If the time of concentration is 0.3-hrs, with a design rainfall of 4.5 in for type-II distribution, determine the peak flow for this basin for the design of the channel. Insert your graphs.
First, we need to calculate the CN for this basin. Using the given land delineation, we can calculate the weighted CN:
CN = (0.5 x 61) + (0.25 x 72) + (0.25 x 81) = 68.25
Next, we need to calculate the total rainfall depth for the design storm. Using the type-II distribution and the given design rainfall of 4.5 inches, we can use rainfall charts to find the total depth:
Total depth = 4.5 x 1.24 = 5.58 inches
Finally, we can use the Rational Method to calculate the peak flow:
Q = (0.0078) x (CN) x (A) x (I)
Where:
- Q = peak flow (cfs)
- A = area (acres)
- I = intensity (in/hr)
Converting the area to square feet:
24 acres = 1,045,440 square feet
Converting the intensity to inches per hour:
5.58 inches in 0.3 hours = 18.6 in/hr
Plugging in the values:
Q = (0.0078) x (68.25) x (1,045,440) x (18.6)
Q = 2783 cfs
So the peak flow for this basin for the design of the channel is 2783 cfs.
Graph:
See attached graph.
To determine the peak flow for the design of the channel in a rural drainage basin, we can use the Rational Method. The Rational Method is commonly used to estimate peak flows in small drainage basins where adequate streamflow data is not available.
Step 1: Calculate the runoff coefficient (C)
The runoff coefficient (C) represents the fraction of rainfall that becomes direct runoff. In this case, we need to determine the runoff coefficient for the specific land use types in the drainage basin.
Given:
Meadows: 1/2 of the basin area
Brush: 1/4 of the basin area
Pasture: 1/4 of the basin area
For each land use type, we need to determine the corresponding runoff coefficient. Runoff coefficients can vary depending on soil type and land conditions. In this case, since the soil group is D with good hydrologic condition, we can assume the following values:
Meadows (C_meadows) = 0.05
Brush (C_brush) = 0.15
Pasture (C_pasture) = 0.25
Step 2: Calculate the total weighted runoff coefficient (C_total)
To calculate the total weighted runoff coefficient, we multiply each runoff coefficient by its corresponding land use area and sum them up.
C_total = (C_meadows * Area_meadows) + (C_brush * Area_brush) + (C_pasture * Area_pasture)
Given:
Area_meadows = 1/2 * 24 acres = 12 acres
Area_brush = 1/4 * 24 acres = 6 acres
Area_pasture = 1/4 * 24 acres = 6 acres
C_total = (0.05 * 12) + (0.15 * 6) + (0.25 * 6)
= 0.6 + 0.9 + 1.5
= 3
Step 3: Calculate the peak flow (Q)
The peak flow can be calculated using the Rational Method equation:
Q = (C * I * A) / T
Where:
Q = Peak flow rate (cfs)
C = Total weighted runoff coefficient
I = Design rainfall intensity (in/hr)
A = Drainage area (acres)
T = Time of concentration (hr)
Given:
C = 3
I = 4.5 in/hr (Type II distribution)
A = 24 acres
T = 0.3 hr
Converting inches/hr to ft/hr, I = 4.5 / 12 ft/hr
Now, substitute the values into the equation:
Q = (C * I * A) / T
= (3 * (4.5 / 12) * 24) / 0.3
= (3 * 0.375 * 24) / 0.3
= 27 cfs
Therefore, the peak flow for the design of the channel in this basin is 27 cubic feet per second (cfs).