UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
HYDROLOGY AND WATER
ENGINEERING
Rainfall-Runoff Analysis, Water Demand and Network Design
⋄
Module: Hydrology and Water Engineering
Assignment No.: 01
Due Date: 2026
Submitted in partial fulfilment of the requirements for Hydrology and Water Engineering
at the University of South Africa.
, UNISA | Hydrology & Water Engineering Rainfall-Runoff and Network Analysis
Question 1: Rainfall-Runoff Analysis and Hyetograph
Separating gross rainfall into losses and effective runoff is one of the foundational steps in
flood hydrology. The phi-index (ϕ) method offers a practical way to estimate a uniform infil-
tration rate that, when subtracted from each rainfall interval, reproduces the observed surface
runoff (Bedient, Huber and Vieux, 2013).
1.1 Phi-Index and Direct Surface Runoff
Given data
• Total recorded rainfall: P = 35,0 cm
• Equivalent excess rainfall (direct surface runoff depth): Pe = 27,5 cm
• Total losses: F = P − Pe = 35,0 − 27,5 = 7,5 cm
• Storm duration: 10 hours (incremental values in 1-hour intervals)
Step 1: Identify hours where rainfall exceeds ϕ
The ϕ-index is defined such that:
n
X
(1)
max pi − ϕ, 0 · ∆t = Pe
i=1
where pi is the rainfall intensity in hour i and ∆t = 1 hr. Because hours 1 and 10 have to-
tals of 0,60 cm and 0,40 cm respectively, any trial ϕ > 0,40 cm/hr means those two hours
contribute zero excess. The effective storm duration therefore spans hours 2 through 9.
Step 2: Trial value ϕ = 0,75 cm/hr
At ϕ = 0,75 cm/hr the excess sums to 28,00 cm, which is slightly above the required 27,5 cm.
The ϕ-index must therefore be increased marginally.
Step 3: Refine to ϕ = 0,80 cm/hr
Increasing ϕ by 0,05 cm/hr reduces the excess in each of the eight active hours by 0,05 cm:
Page 1 of 11
College of Science, Engineering and Technology
⋄
HYDROLOGY AND WATER
ENGINEERING
Rainfall-Runoff Analysis, Water Demand and Network Design
⋄
Module: Hydrology and Water Engineering
Assignment No.: 01
Due Date: 2026
Submitted in partial fulfilment of the requirements for Hydrology and Water Engineering
at the University of South Africa.
, UNISA | Hydrology & Water Engineering Rainfall-Runoff and Network Analysis
Question 1: Rainfall-Runoff Analysis and Hyetograph
Separating gross rainfall into losses and effective runoff is one of the foundational steps in
flood hydrology. The phi-index (ϕ) method offers a practical way to estimate a uniform infil-
tration rate that, when subtracted from each rainfall interval, reproduces the observed surface
runoff (Bedient, Huber and Vieux, 2013).
1.1 Phi-Index and Direct Surface Runoff
Given data
• Total recorded rainfall: P = 35,0 cm
• Equivalent excess rainfall (direct surface runoff depth): Pe = 27,5 cm
• Total losses: F = P − Pe = 35,0 − 27,5 = 7,5 cm
• Storm duration: 10 hours (incremental values in 1-hour intervals)
Step 1: Identify hours where rainfall exceeds ϕ
The ϕ-index is defined such that:
n
X
(1)
max pi − ϕ, 0 · ∆t = Pe
i=1
where pi is the rainfall intensity in hour i and ∆t = 1 hr. Because hours 1 and 10 have to-
tals of 0,60 cm and 0,40 cm respectively, any trial ϕ > 0,40 cm/hr means those two hours
contribute zero excess. The effective storm duration therefore spans hours 2 through 9.
Step 2: Trial value ϕ = 0,75 cm/hr
At ϕ = 0,75 cm/hr the excess sums to 28,00 cm, which is slightly above the required 27,5 cm.
The ϕ-index must therefore be increased marginally.
Step 3: Refine to ϕ = 0,80 cm/hr
Increasing ϕ by 0,05 cm/hr reduces the excess in each of the eight active hours by 0,05 cm:
Page 1 of 11
