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Biosolids Project
Ditches System Dimensioning
One of the tasks I accomplished for the Biosolids Project was the calculation of the dimensions of the ditches system. The ditches system is supposed to collect the runoff water from each plot, carry it to the water sampling system, and then evacuate it without causing backwater conditions in the parshall flumes.
Each plot must constitute a separate watershed, so that the water of each plot can be analyzed separately. Therefore the water collection system contains some bearms also.
In this page I will explain step by step how did I selected the dimensions of the ditches.
All theory and calculations are based on
G. O. Schwab et al., Soil and Water Conservation
Engineering, 4th edition, J.Wiley & Sons, USA 1993.
Runoff
First of all let's specify that the goal of the project is to sample runoff water from a series of field plots. Runoff is that portion of the precipitation that makes its way toward as surface or subsurface flow. The project do not consider groundwater. This should be kept in mind going through this process.
Runoff is that part of the rain that flows on the ground surface after subtracting a) the interception, b) the infiltration and storage, c) the evaporation and d) the detention
The engineering design of runoff control systems is concerned by the following dimensions:
- Peak rates of runoff
- Runoff volumes
- Temporal distribution of rates and volumes
The rainfall intensity influences the runoff %, but not in linear proportions: in the following diagram the runoff is compared to rainfall amount and intensity. For more details see [Schab et al.]
Dimensioning
To calculate the design peak runoff we are going to use the "rational method". [Schwab et al.] According to this method the design peak runoff is given by the equation
q = 0.028 C i A
Where:
-
q = design peak runoff in [m^3/s]
-
C = runoff coefficient [-]. This parameter depends primarly from the infiltration rate, the surface coverage and the rainfall intensity.
-
i = rainfall intesity in mm/h for the design return period and for a duration equal to the "time of concentration" of the watershed
-
A = watershed area in [ha]
Time of concentration
Is the time that the water takes to flow from the most remote point (in time) to the outlet, once the soil is saturated. The time of concentration can be estimated with a method developed by Kirpich (1940):
Tc = 0.0195 L^0.77 Sg^(-0.385)
Where:
Tc = Time of
concentration
L = Max length of flow in [m]
Sg = Watershed gradient in [m/m], in
other words
[h(outlet) - h(most remote point)] / L
If the duration of the rainfall is shorter than the time of concentration the runoff will be smaller. The maximum runoff under a constant precipitation is reached at the time of concentration.
Runoff dimensioning at Kirton Ranch
The data in green refers to our specific case.
Using tables 4.1, 4.2, 4.3 [pages73-74 Schwab et al.] we can determine the coefficient C for a permanent pasture, with good hydraulic conditions and soil group B (Sandy, very little clay and silt, shallow). With this soil and an expected rainfall rate of 200mm/h we can assume
C = 0.23
Given that
A = 1/2 acre = 21780 ft^2 = 0.202 ha
Sg = 0.5 ft /
390 ft = 0.00126
Tc =
0.0195 * 130m^0.77 * 0.00126^(-0.385)
= 10.8 [min]
For the Lake Okeechobee region considering
a 2 Years return period the following rain events are to be expected:
1h --> 2.5 inches = 6.4 cm
10 min --> 20 cm/h
Primary ditches
The parshall flumes of the water
sampling units have a maximum capacity of 14.1 liters/second. This correspond to
a 108mm/h rain event for 11 min.
In case of a bigger rainfall: a) the sampler data
will be inacurate, b) runoff may overflow the flume, if the plot is correctly
isolated with berms will serve as storage, c) sedimentation may occour in
flume's area.
According to page 269 [Shwab et al] the maximum speed to avoid erosion is 0.46 m/s, the maximum grade for sandy soils 0.2% and the maximum sideslope for shallow open channels in sandy soils 2:1
This indications give us the dimensions of the primary ditches, whose function is to collect the water of the plot and bring it to the water sampler:
The minimal h is 8cm, however the dimensions of the primary ditches are given by construction factors. For this reason the depth is set to 30 cm. The side slope remains 2:1
The length slope is calculated according to page 270 [Schwab et al]:
T = w*h*s*K
Where
Tractive Force = 1.3 Pa
V = 0.5 m/s
s = slope = height / length
w = 9800 N/m^3
s = (1.3 N/m^3) / (9800 N/m^3 * 0.1 m * 0.5) = 0.27%
This means for a 311 ft length ditch, a 0.8 ft slope
Secondary ditches
L
= maximum distance = 490m
Sg = 0.6m / 490m = 0.0012m
Tc = 0.0195 * 490 ^ 0.77 * 0.0012 ^ (-0.385) = 30.6 min
Using the formula on page 26 of [Schwab et al.] it's possible to calculate a two years rain event to be expected at this location for the time of concentration. In our case we should expect a 104mm/h event for 30 min.
The runoff peak for this situation can be calculated with the rational method (see above).
q = 0.0028 C * i * A
where
C = 0.23
i = 104 mm/h
A = area of one block = 43240 m^2 =
4.3 ha
so
q = 0.28 m^3/s
Now, considered the particular situation with a very small area, the low slope and the partially unnatural water collection system with storage, and considered the mission of avoiding backflow conditions in the flume, we prefer to stay on the sure side with the calculations. Therefore we will consider the maximum possible flume's output of 28 l/s and we will assume that this output occurs for a time longer than the time of concentration. This assumption gives us
q = 28 l/s * 17 flumes = 476 l/s (= 0.476 m^3/s)
Therefore to dimension the secondary ditches we will assume a q of 0.5 m^3/s
Going through the same process as above, and assuming a velocity of 0.5 m/s (page 270) we get
h = 0.71 m
The secondary ditch will look as follow:
The length slope, calculated as above with
v = 0.5 m/s
T = 1.3 Pa
w = 9800 N/m^3
x = 0.71 m
K = 0.5
S = T / (w*x*K) = 0.043 % = ~ 0
Tertiary ditch
On the same principle the tertiary ditch should be able to evacuate the water from the three secondary ditches. The velocity of the water, to avoid erosion processes, should be again v = 0.5 m/s. Since the expected Q is 1,5 m^3/s, the water height will be 1.22m. With a side slope of 2:1, the width of the channel is approximately 5m.
Conclusion
This was a summary of the thought that are behind the ditch dimensioning. As you could notice, large safety factors were used, with the primary goal of avoiding backflow conditions in the parshal flumes. For more information about this phenomena, see D.M.Grant & B.D.Dawson, Isco Open Channel Flow Measurement Handbook, Fifth Edition, ISCO Inc., Lincoln Nebraska, 1997. Please note that the since the third edition this book contains many changes regarding the parshall flumes, some of them very important.