University of South Africa — Universiteit van Suid-Afrika
College of Science, Engineering and Technology
⋄ ⋄
WSE4801 / TRN3701
Stormwater Drainage & Flood Analysis
Gutter Flow, Spread Calculations & Hydrological Statistics
⋄ ⋄
Module: WSE4801
Title: Transportation Engineering
Assignment: Assignment 1
Total Marks: 75 Marks
Due: 2026
Institution: University of South Africa (UNISA)
Citation: APA 7th Edition
Submitted in partial fulfilment of the requirements for the degree in Engineering Technology
,UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Contents
1 Question 1: Triangular Gutter Flow and Spread Analysis [25 Marks] 2
1.1 1.1 Spread T Using the Triangular Gutter Equation . . . . . . . . . . . . . . . . . 2
1.2 1.2 Flow Depth at the Curb: y = Sx T . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 1.3 Compliance Check Against Tallow = 2.20 m . . . . . . . . . . . . . . . . . . . 4
1.4 1.4 Why Gutter Flow is Analysed as Steady and Uniform at Peak Discharge . . . 5
2 Question 2: Depressed Gutter and Composite Discharge [25 Marks] 6
2.1 2.1 Depressed Cross Slope SW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 2.2 Spread Over the Undepressed Portion TS = T − W . . . . . . . . . . . . . . . 7
2.3 2.3 Discharge Over Undepressed Section QS . . . . . . . . . . . . . . . . . . . . . 7
2.4 2.4 Total Composite Discharge Q = QS / (1 − Eo ) . . . . . . . . . . . . . . . . . . 8
2.5 2.5 Two Reasons Why Depressed Gutters Improve Inlet Performance and Pavement
Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Question 3: Hydrological Flood Statistics [25 Marks] 10
3.1 3.1 Mean Annual Flood Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 3.2 Standard Deviation of the Flood Series . . . . . . . . . . . . . . . . . . . . . . 11
3.3 3.3 Coefficient of Variation Cv and Comment on Variability . . . . . . . . . . . . 12
3.4 3.4 Standard Error of the Mean Flood Discharge . . . . . . . . . . . . . . . . . . 13
3.5 3.5 Summary of Statistical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Corrections Summary 15
Reference List 16
Page 1 of 16
,UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Question 1: Triangular Gutter Flow and Spread Analysis [25 Marks]
Scenario: A municipality is upgrading a collector road. During storms, water spreads across
the traffic lane, reducing skid resistance and causing splash hazards. The road has a triangular
gutter that must be checked against an allowable spread criterion.
Given:
• Longitudinal slope: SL = 0.010
• Cross slope: Sx = 0.020
• Manning roughness: n = 0.016
• Design gutter discharge: Q = 0.060 m3 /s
• Kn = 0.376 (SI units, per HEC-22)
1.1 Spread T Using the Triangular Gutter Equation
The HEC-22 triangular gutter flow equation in SI units is (Brown, Stein & Warner, 2009):
Kn 5/3 1/2 8/3
Q= S SL T (1)
n x
where Kn = 0.376 for SI units, Sx is the cross slope, SL is the longitudinal slope, n is Man-
ning’s roughness, and T is the spread (m).
Step 1: Rearrange Equation 1 for T
!3/8
Qn Qn
T 8/3 = 1/2 5/3
=⇒ T = 1/2 5/3
(2)
Kn SL Sx Kn SL Sx
Step 2: Compute the slope terms
5 5
Sx5/3 = (0.020)5/3 = e 3 ln(0.020) = e 3 ×(−3.912) = e−6.520 = 0.001474 (3)
1/2
SL = (0.010)0.5 = 0.10000 (4)
Page 2 of 16
, UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Step 3: Compute the numerator and denominator
Numerator = Q · n = 0.060 × 0.016 = 0.000960 (5)
1/2
Denominator = Kn · SL · Sx5/3 = 0.376 × 0.10000 × 0.001474 = 5.542 × 10−5 (6)
Step 4: Solve for T 8/3 and then T
0.000960
T 8/3 = = 17.33 (7)
5.542 × 10−5
3
T = (17.33)3/8 = e 8 ×ln(17.33) = e0.375×2.853 = e1.070 ≈ 2.91 m (8)
The water spread across the pavement under the design discharge is approximately 2.91 m
(SANRAL, 2013).
1.2 Flow Depth at the Curb: y = Sx T
The depth at the curb is directly proportional to the cross slope and the spread (Brown, Stein
& Warner, 2009):
y = Sx · T (9)
Substituting:
y = 0.020 × 2.91 = 0.058 m = 58 mm (10)
The maximum gutter flow depth at the curb face is 58 mm. This is noticeably deeper than
the 40 mm obtained in the original solution (which used the incorrect T = 2.02 m), and has
implications for splash hazard assessment.
Page 3 of 16
College of Science, Engineering and Technology
⋄ ⋄
WSE4801 / TRN3701
Stormwater Drainage & Flood Analysis
Gutter Flow, Spread Calculations & Hydrological Statistics
⋄ ⋄
Module: WSE4801
Title: Transportation Engineering
Assignment: Assignment 1
Total Marks: 75 Marks
Due: 2026
Institution: University of South Africa (UNISA)
Citation: APA 7th Edition
Submitted in partial fulfilment of the requirements for the degree in Engineering Technology
,UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Contents
1 Question 1: Triangular Gutter Flow and Spread Analysis [25 Marks] 2
1.1 1.1 Spread T Using the Triangular Gutter Equation . . . . . . . . . . . . . . . . . 2
1.2 1.2 Flow Depth at the Curb: y = Sx T . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 1.3 Compliance Check Against Tallow = 2.20 m . . . . . . . . . . . . . . . . . . . 4
1.4 1.4 Why Gutter Flow is Analysed as Steady and Uniform at Peak Discharge . . . 5
2 Question 2: Depressed Gutter and Composite Discharge [25 Marks] 6
2.1 2.1 Depressed Cross Slope SW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 2.2 Spread Over the Undepressed Portion TS = T − W . . . . . . . . . . . . . . . 7
2.3 2.3 Discharge Over Undepressed Section QS . . . . . . . . . . . . . . . . . . . . . 7
2.4 2.4 Total Composite Discharge Q = QS / (1 − Eo ) . . . . . . . . . . . . . . . . . . 8
2.5 2.5 Two Reasons Why Depressed Gutters Improve Inlet Performance and Pavement
Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Question 3: Hydrological Flood Statistics [25 Marks] 10
3.1 3.1 Mean Annual Flood Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 3.2 Standard Deviation of the Flood Series . . . . . . . . . . . . . . . . . . . . . . 11
3.3 3.3 Coefficient of Variation Cv and Comment on Variability . . . . . . . . . . . . 12
3.4 3.4 Standard Error of the Mean Flood Discharge . . . . . . . . . . . . . . . . . . 13
3.5 3.5 Summary of Statistical Results . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Corrections Summary 15
Reference List 16
Page 1 of 16
,UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Question 1: Triangular Gutter Flow and Spread Analysis [25 Marks]
Scenario: A municipality is upgrading a collector road. During storms, water spreads across
the traffic lane, reducing skid resistance and causing splash hazards. The road has a triangular
gutter that must be checked against an allowable spread criterion.
Given:
• Longitudinal slope: SL = 0.010
• Cross slope: Sx = 0.020
• Manning roughness: n = 0.016
• Design gutter discharge: Q = 0.060 m3 /s
• Kn = 0.376 (SI units, per HEC-22)
1.1 Spread T Using the Triangular Gutter Equation
The HEC-22 triangular gutter flow equation in SI units is (Brown, Stein & Warner, 2009):
Kn 5/3 1/2 8/3
Q= S SL T (1)
n x
where Kn = 0.376 for SI units, Sx is the cross slope, SL is the longitudinal slope, n is Man-
ning’s roughness, and T is the spread (m).
Step 1: Rearrange Equation 1 for T
!3/8
Qn Qn
T 8/3 = 1/2 5/3
=⇒ T = 1/2 5/3
(2)
Kn SL Sx Kn SL Sx
Step 2: Compute the slope terms
5 5
Sx5/3 = (0.020)5/3 = e 3 ln(0.020) = e 3 ×(−3.912) = e−6.520 = 0.001474 (3)
1/2
SL = (0.010)0.5 = 0.10000 (4)
Page 2 of 16
, UNISA | Stormwater & Flood Analysis WSE4801— Assignment 1, 2026
Step 3: Compute the numerator and denominator
Numerator = Q · n = 0.060 × 0.016 = 0.000960 (5)
1/2
Denominator = Kn · SL · Sx5/3 = 0.376 × 0.10000 × 0.001474 = 5.542 × 10−5 (6)
Step 4: Solve for T 8/3 and then T
0.000960
T 8/3 = = 17.33 (7)
5.542 × 10−5
3
T = (17.33)3/8 = e 8 ×ln(17.33) = e0.375×2.853 = e1.070 ≈ 2.91 m (8)
The water spread across the pavement under the design discharge is approximately 2.91 m
(SANRAL, 2013).
1.2 Flow Depth at the Curb: y = Sx T
The depth at the curb is directly proportional to the cross slope and the spread (Brown, Stein
& Warner, 2009):
y = Sx · T (9)
Substituting:
y = 0.020 × 2.91 = 0.058 m = 58 mm (10)
The maximum gutter flow depth at the curb face is 58 mm. This is noticeably deeper than
the 40 mm obtained in the original solution (which used the incorrect T = 2.02 m), and has
implications for splash hazard assessment.
Page 3 of 16
