UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄
STORMWATER DRAINAGE ANALYSIS
WSE4801
Assignment 1 – Corrected Solutions – Semester 1, 2026
⋄
Module WSE4801 – Civil Engineering: Stormwater & Drainage
Assignment Assignment 1 (Corrected Solutions)
Semester Semester 1, 2026
Topics Triangular Gutters, Depressed Gutters, Flood Frequency
Statistics
Total Marks 75 Marks (3 Questions × 25)
Institution University of South Africa (UNISA)
Format Engineering Problem-Solving – APA 7th Edition
Submitted in partial fulfilment of the requirements for WSE4801 – UNISA, 2026
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
Contents
Question 1: Triangular Gutter Spread Analysis 2
Question 2: Depressed Gutter Discharge Analysis 8
Question 3: Flood Frequency Statistical Analysis 16
Summary of Corrected Results 23
Reference List 24
Page 1 of 24
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
Question 1 [25 Marks] – Triangular Gutter Spread Analysis
Given data:
• Longitudinal slope: SL = 0.010
• Cross slope: Sx = 0.020
• Manning’s roughness: n = 0.016
• Design gutter discharge: Q = 0.060 m3 /s
1.1 Calculate the Spread T Using the Triangular Gutter Equation [10]
Governing Equation – Triangular Gutter (SI)
The correct SI form of the triangular gutter flow equation (FHWA, 2009; SANRAL, 2013)
is:
0.375 1/2 5/3 8/3
Q= SL Sx T
n
Rearranging for spread T :
!3/8
Qn
T = 1/2 5/3
0.375 SL Sx
1/2
Step 1: Compute SL
1/2 √
SL = 0.010 = 0.10000
5/3
Step 2: Compute Sx
5/3
Using the exponent rule Sx = e(5/3) ln(Sx ) :
Sx5/3 = (0.020)5/3 = e(5/3)×ln(0.020) = e1.6667×(−3.9120) = e−6.5200 = 0.001478
Step 3: Compute the numerator
Q × n = 0.060 × 0.016 = 0.000960
Step 4: Compute the denominator
Page 2 of 24
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
1/2
0.375×SL ×Sx5/3 = 0.375×0.10000×0.001478 = 0.375×0.0001478 = 5.543×10−5 = 0.00005543
Step 5: Form the ratio
Qn 0.000960
1/2 5/3
= = 17.32
0.375 SL Sx 0.00005543
Step 6: Raise to the power 3/8
T = (17.32)3/8 = e(3/8) ln(17.32) = e0.375×2.8524 = e1.0697 = 2.914
T ≈ 2.91 m
Page 3 of 24
, UNISA | WSE4801 Stormwater & Drainage – Assignment 1
1.2 Flow Depth at the Curb: y = Sx T [5]
The flow depth at the curb face is the vertical rise of water from the gutter lip to the curb. It
is given directly by the geometric relationship between the cross slope and the spread (SAN-
RAL, 2013):
y = Sx × T
Substituting:
y = 0.020 × 2.91
y = 0.0582 m ≈ 58 mm
This depth of 58 mm is shallow but represents a notable increase over the original submission’s
40 mm value, consistent with the larger spread. It remains within the range of typical urban
gutter flow depths.
Page 4 of 24
College of Science, Engineering and Technology
⋄
STORMWATER DRAINAGE ANALYSIS
WSE4801
Assignment 1 – Corrected Solutions – Semester 1, 2026
⋄
Module WSE4801 – Civil Engineering: Stormwater & Drainage
Assignment Assignment 1 (Corrected Solutions)
Semester Semester 1, 2026
Topics Triangular Gutters, Depressed Gutters, Flood Frequency
Statistics
Total Marks 75 Marks (3 Questions × 25)
Institution University of South Africa (UNISA)
Format Engineering Problem-Solving – APA 7th Edition
Submitted in partial fulfilment of the requirements for WSE4801 – UNISA, 2026
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
Contents
Question 1: Triangular Gutter Spread Analysis 2
Question 2: Depressed Gutter Discharge Analysis 8
Question 3: Flood Frequency Statistical Analysis 16
Summary of Corrected Results 23
Reference List 24
Page 1 of 24
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
Question 1 [25 Marks] – Triangular Gutter Spread Analysis
Given data:
• Longitudinal slope: SL = 0.010
• Cross slope: Sx = 0.020
• Manning’s roughness: n = 0.016
• Design gutter discharge: Q = 0.060 m3 /s
1.1 Calculate the Spread T Using the Triangular Gutter Equation [10]
Governing Equation – Triangular Gutter (SI)
The correct SI form of the triangular gutter flow equation (FHWA, 2009; SANRAL, 2013)
is:
0.375 1/2 5/3 8/3
Q= SL Sx T
n
Rearranging for spread T :
!3/8
Qn
T = 1/2 5/3
0.375 SL Sx
1/2
Step 1: Compute SL
1/2 √
SL = 0.010 = 0.10000
5/3
Step 2: Compute Sx
5/3
Using the exponent rule Sx = e(5/3) ln(Sx ) :
Sx5/3 = (0.020)5/3 = e(5/3)×ln(0.020) = e1.6667×(−3.9120) = e−6.5200 = 0.001478
Step 3: Compute the numerator
Q × n = 0.060 × 0.016 = 0.000960
Step 4: Compute the denominator
Page 2 of 24
,UNISA | WSE4801 Stormwater & Drainage – Assignment 1
1/2
0.375×SL ×Sx5/3 = 0.375×0.10000×0.001478 = 0.375×0.0001478 = 5.543×10−5 = 0.00005543
Step 5: Form the ratio
Qn 0.000960
1/2 5/3
= = 17.32
0.375 SL Sx 0.00005543
Step 6: Raise to the power 3/8
T = (17.32)3/8 = e(3/8) ln(17.32) = e0.375×2.8524 = e1.0697 = 2.914
T ≈ 2.91 m
Page 3 of 24
, UNISA | WSE4801 Stormwater & Drainage – Assignment 1
1.2 Flow Depth at the Curb: y = Sx T [5]
The flow depth at the curb face is the vertical rise of water from the gutter lip to the curb. It
is given directly by the geometric relationship between the cross slope and the spread (SAN-
RAL, 2013):
y = Sx × T
Substituting:
y = 0.020 × 2.91
y = 0.0582 m ≈ 58 mm
This depth of 58 mm is shallow but represents a notable increase over the original submission’s
40 mm value, consistent with the larger spread. It remains within the range of typical urban
gutter flow depths.
Page 4 of 24
