Department of Soil-, Crop-, and Climate Sciences
Faculty of Agriculture
University of the Free State
AGEG 2624: Soil & Water Conservation Engineering
TL Dirwai
Room 1.202, LandBou Building
DirwaiTL@ufs.ac.za
Tutorial 3: (13/10/2021) Modelling/Estimating Soil Loss, Soil & Water Conservation
Planning, Open Channel Flow for Soil & Water Conservation Engineering, Runoff
Control (Disposal) Planning
A. MODELLING SOIL LOSS
1. The Figure below shows the framework for the SLEMSA model. For this framework (i)
itemize the 5 control variables (1 – 5), and (ii) indicate the symbols used (V1 – V5).
Answer
i)
ii)
(see L6b)
1 = energy interception, 2 = rainfall energy, 3 = soil erodibility, 4 = slope
steepness and 5 = slope length
V1 = I, V2 = E, V3 = F, V4 = S and V5 = L
2. The following data obtains for a given location in South Africa:
Mean annual precipitation (MAP)
= 750 mm
Mean annual rainfall energy (E) equation (J/m2/yr) E = 10 (MAP) + 12000
Soil type
= Avalon series Av31 Mooiveld
Soil erodibility (F)
= 3.0
The relationship between mean annual soil loss (K) to mean annual rainfall (E) is given by
the equation:
ln K = b ln E + a
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where; a = 2.8840 – 8.1209 F and b = 0.4681 + 0.7663 F
Calculate the value of the K sub-model in the SLEMSA model for the above conditions.
Answer
Rainfall energy = 10(750) +12000 = 19500 J/m2/yr
a = 2.8840 – 8.1209(3) = -21.4787
b = 0.4681 + 0.7663(3) = 2.7670
ln K = 2.7670(ln 19500) + (-21.4787) = 5.8542
K=exp(5.8542) = 348.696 t/ha/yr
3. Determine the topographic factor (X) in the SLEMSA model for a slope 150 m long and a
7° slope.
Answer
Slope steepness of 7° equates to a slope steepness of 12.2%.  from the Sine formula
X = 150½ (0.76 + 0.53(12.2/100) + 0.076(12.2/100)2)/25.65 = 0.394
4. What are the crop management (C) factors for the following conditions:
(i)
Grain maize with potential yield of 7.5 t/ha?
From Table 4b, C = 0.053
(ii)
Kikuyu grass with a 90% average cover during the rainy season?
From Table 4b, C ≈ 0.043
or C = e(-0.06i) = C = e(-0.06*90) =
(iii)
 does not agree with Table 4b results!!
Clean cultivated orchard in its 2nd year of growth?
From Table 4b, C = 0.407
5. Determine the annual mean soil loss (Z) from the determinations you undertook in Q2, Q3
and Q4(i).
Answer
Z = K.X.C = 348.696 * 0.394 * 0.053 = 7.287 t/ha/yr
B. SOIL AND WATER CONSERVATION PLANNING
1. State the main objective of Soil and Water Conservation Planning.
2. Differentiate between Land Classification and Land Capability Classification and applied
with soil and water conservation planning.
3. Differentiate between Land Use Planning (LUP) and Soil and Water Conservation
Planning.
4. List and briefly discuss 4 key factors to consider when defining conservation needs.
C. OPEN CHANNEL FLOW (NB: If needed, refer to Figure 4.2 at the end of the tutorial)
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1. In open channel flow:
(i)
The Reynolds Number (Re) is a ratio of which forces?
Re = Inertial forces/Viscous forces
(ii)
The Froude Number (Fr) is a ratio of which forces?
Fr = Inertial/Gravitational
2. The Continuity Equation is presented as follows;
𝑄 = 𝐴𝑣
Where Q = flow rate, A = flow cross-sectional area and v = flow velocity. Flow velocity is
generally given by the Manning’s Equation as follows;
1 2/3 1/2
𝑅 𝑆𝑜
𝑛
Where n = Manning’s roughness coefficient, R = hydraulic radius, So = channel longitudinal
slope. Clearly labelling the axes, graphically sketch how flow rate (Q) varies with hydraulic
radius (R).
𝑣=
Answer
Direct relationship
3. In Open Channel Hydraulics it is stated that “… hydraulic efficiency decreases with an
increase in channel bed width”. State two technical reasons why the above statement is
true.
Answer
As bed width increases, R decreases
More contact surface hence resistance to flow, so decreased efficiency of conveyance.
4. Classify or categorise (time and space) the following types of open channel flow:
i) Flow in a trapezoidal shaped channel past a flow control gate that is being opened
gradually/slowly.
ii) Flow in a straight parabolic shaped channel laid on a gradient of 1:1000.
iii) Flow of runoff water in a stormwater drain during a rain storm.
5. A rectangular channel with a base width (b) of 75 cm carries water at a flow rate of 1 m 3/s
and a flow depth (d) of 0.5 m.
i) Determine the critical state of flow of the water in the channel?
Answer
Flow velocity, v = Q/A = 1/(0.5 * 0.75) = 2.667 m/s
Fr = v/(gy)1/2 = 2.667/(0.5*9.82)1/2 = 1.204
 supercritical flow
ii) Are the conditions obtaining in the above channel acceptable in normal soil & water
conservation channel design? Why?
Answer
No. Because the flow is supercritical and not desirable in SWC channel design.
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5. A rough unlined rectangular channel 4.6 m wide (b) carries water at a depth (d) of 0.6 m
on a longitudinal slope (So) of 0.0025 and Manning’s roughness coefficient (n) of 0.04.
Determine the discharge (Q) in the channel (m3/s).
Answer
Q = Av = A*1/n*R2/3*So1/2 = (4.6*0.6)((4.6*0.6)/(0.6+4.6+0.6))2/3*(0.0025)1/2 = 2.103 m3/s
6. Design a best hydraulic section for a trapezoidal shaped channel to convey 12 m3/s for a
channel with a side slope Z:1 = 1.5:1, channel longitudinal slope (So) = 1:5000 and
Manning’s roughness coefficient (n) = 0.01. In this question ‘design’ means determine b,
d, t, D and T. Assume a 15% freeboard. [NB: Best trapezoidal hydraulic section has b
related to d as flows: b = 2d/{Z+(1+Z2)1/2}]
Answer (See Figure 4.2 for formulae)
Note: b = 2d/{Z+(1+Z2)1/2}] = 2d/{1.5+(1+1.52)1/2}] = 0.606d  substitute this for b.
Flow x-sectional area, A = bd +Zd2 = 0.606d(d) + 1.5d2 = 2.106d2
Flow wetted perimeter, P = b + 2d(1 + Z2)1/2 = 0.606d + 2d(1 + 1.52)1/2 = 4.212d
Hydraulic radius, R = A/P = (2.106d2)/( 4.212d) = 0.5d
Now, Q = Av = A(1/n*R2/3*So1/2) = 2.106d2 (1/0.01)*(0.5d)2/3*(0.00021/2)
i.e. 12 = 1.414(2.106d2)( (0.5d)2/3)  solve for d by iteration or Excel solver
From d  determine b
d  determine D as D = d + 15%(d)
t = b + 2Zd
T = b + 2zD
7. Is there a link between Vmax applied in open channel design and Vcr found in processes
and mechanics of erosion? If so, what is the link?
D. RUNOFF CONTROL PLANNING
1. Define Runoff Control Planning.
2. State any 2 conditions under which an RCP is needed.
3. What is the practical purpose of the Principle of Natural Liability Acceptance (NLA)?
4. Differentiate between a K1-type and K3-type artificial waterway.
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