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ENGR 326 Formal Lab Report 1 This assi gnm ent is wo rt h 2 0 0 pts (1 0 0 pts fo r technical m erit a nd 1 0 0 pts fo r the written qual ity )
The repo rt is d ue o n Wednesday Se ptem ber 1 6 , 1 1 .5 9 pm .
A consulting engineer has been hired to design a chlorine disinfection system for a small community water system.
The chlorination system is to be sized to provide sufficient capacity to treat the 95 percentile daily water demand, which
means that the probability that the average daily demand will be less than the design flow is 0.95. Flow data collected at
the plant show that the probability distribution of the average daily water demand is accurately modeled by a log
Pearson Type III probability distribution which has a probability density function (PDF) of:
𝑓𝑓𝑥𝑥(𝑥𝑥) = 1
𝛼𝛼𝑥𝑥Γ(𝛽𝛽) (ln 𝑥𝑥 − 𝛾𝛾)𝛽𝛽−1
𝛼𝛼𝛽𝛽−1 𝑒𝑒 −�ln𝑥𝑥−𝛾𝛾𝛼𝛼 �; 𝑥𝑥 > 𝑒𝑒𝛾𝛾
Where:
x is the average daily water demand in m3/day
α is a scale parameter
β is a shape parameter and
γ is a location parameter [units are ln(m3/day)] and
Γ(β) is the Gamma function evaluated at β
The plant data was used to estimate the PDF parameters with the results that α = 0.3204, β = 2.75 and γ = 2.96
[ln(m3/day)]. The chlorination system design flow (which is the 95 percentile daily water demand value, Q0.95) can be
calculated by finding Q0.95 such that:
𝑃𝑃𝑃𝑃(𝑋𝑋 ≤ 𝑄𝑄0.95) = � 𝑓𝑓𝑥𝑥(𝑥𝑥)𝑑𝑑𝑥𝑥 = 0.95
𝑄𝑄0.95
exp (𝛾𝛾)
Write a general program that can integrate a user-defined function (given in a user specified function subprogram)
using Romberg integration based on the trapezoidal rule. Using the program, determine the required design flow for the
disinfection system.
Perform sensitivity analysis on your results by evaluating the variation in the design flow when the treatment system
is designed to treat flow values from the 90th to the 98th percentile flow.
To test your program, use the integral that you solved by hand and using Excel solutions of the trapezoid method
and Romberg integration in HW 1. This evaluation and comparison of your HW 1 results to your program results should
be included as a report appendix titled “Program Verification” in your lab report.