Water and Sanitation Engineering
Assignment 1 Answers
Semester 1 2024
08 APRIL 2024
DUE DATE
0027 65 934 4052
,
,
, 1. Given that the discharge decreased from 50 m3/s after 10 days to 25 m3/s after
an additional 30 days, the expected flow on day 120 is calculated as follows;
𝑄0 = 50𝑚3 /𝑠 (Initial discharge)
𝑄1 = 25𝑚3 /𝑠 discharge after 30 days
𝑡1 = 10 𝑑𝑎𝑦𝑠
𝑡2 = 40 𝑑𝑎𝑦𝑠
𝑡3 = 120 𝑑𝑎𝑦𝑠
𝑸𝟏 = 𝑸𝟎 𝒆−𝒌(𝒕𝟐 −𝒕𝟏 )
25 = 50𝑒 −(40−10)𝑘
25
= 𝑒 −30𝑡
50
ln(0.5) = −30𝑘 ln 𝑒 (ln 𝑒 = 1)
ln(0.5)
𝑘=
−30
𝑘 = 0.023
Discharge on day 120 (𝑄2 ) is given by;
𝑸𝟐 = 𝑸𝟏 𝒆−(𝟎.𝟎𝟐𝟑)(𝒕𝟑 −𝒕𝟐 )
𝑄2 = 25𝑒 −(0.023)(120−40)
𝑄2 = 25𝑒 −1.84
𝑄2 = 3.97 𝑚3 /𝑠
The expected flow on day 120 is 3.97 m3/s.
Assignment 1 Answers
Semester 1 2024
08 APRIL 2024
DUE DATE
0027 65 934 4052
,
,
, 1. Given that the discharge decreased from 50 m3/s after 10 days to 25 m3/s after
an additional 30 days, the expected flow on day 120 is calculated as follows;
𝑄0 = 50𝑚3 /𝑠 (Initial discharge)
𝑄1 = 25𝑚3 /𝑠 discharge after 30 days
𝑡1 = 10 𝑑𝑎𝑦𝑠
𝑡2 = 40 𝑑𝑎𝑦𝑠
𝑡3 = 120 𝑑𝑎𝑦𝑠
𝑸𝟏 = 𝑸𝟎 𝒆−𝒌(𝒕𝟐 −𝒕𝟏 )
25 = 50𝑒 −(40−10)𝑘
25
= 𝑒 −30𝑡
50
ln(0.5) = −30𝑘 ln 𝑒 (ln 𝑒 = 1)
ln(0.5)
𝑘=
−30
𝑘 = 0.023
Discharge on day 120 (𝑄2 ) is given by;
𝑸𝟐 = 𝑸𝟏 𝒆−(𝟎.𝟎𝟐𝟑)(𝒕𝟑 −𝒕𝟐 )
𝑄2 = 25𝑒 −(0.023)(120−40)
𝑄2 = 25𝑒 −1.84
𝑄2 = 3.97 𝑚3 /𝑠
The expected flow on day 120 is 3.97 m3/s.
