First, determine the total volume of water that has flowed from the river in the first five days of the observation period; in the first ten days; in the entire fourteen day period.

1. First, determine the total volume of water that has flowed from the river in the first five days of the observation period; in the first ten days; in the entire fourteen day period.
Question 2 and 3 are individual parts
2. Estimate the average rate of flow from 3 days before your day until your day; from 2 days before your day until you day; from 1 day before your day until your day.
Also estimate the average rate of flow from your day until 3 days after your day; from your day until 2 days after your day; from your day until 1 day after your day.
Member1: Day 4, Member2: Day 6, Member3: Day 8, Member4: Day 10
3. Estimate the instantaneous rate of flow on your day
4. Using the flow graph on the first page and your group’s answer to # 3, construct a graph of the rate of flow of the river for the fourteen day period.
5. Determine all the time periods when the rate at which the water is flowing is increasing. (By graph and words)
6. Determine all the time periods when the rate at which the water is flowing is decreasing. (By graph and words)
7. Your group’s client is considering building a small hydroelectric plant near the mouth of the river. For the project to be feasible, the plant needs to be able to operate at full capacity at least 70% of the time and at reduced capacity at least another 15% of the time.
To operate at full capacity, a flow rate of at least 200 million gallons per day is required. However, if the flow rate rises above 400 million gallons per day, the equipment is stressed, and the plant must close down.
If the flow rate is too small for full capacity operation, the plant can still operate at reduced capacity as long as the flow rate remains above 125 million gallons per day.
Although a statistical analysis is what is needed for a final decision on the plant, what can you tell your client about the two-week observation period that would be relevant to the hydroelectric project?
Write-up direction
• You should write up your project as if you were doing a professional recommendation to a client of your company.
• The report should have a typed cover page, with a title, the full names of your team members
• Your reported must include the following:
1. A typed answer to question#7 that summarizes your findings and makes a recommendation to the client. This answer should be written in paragraph form.
2. Pages neatly showing the calculation done for question 1-5.
1. Total volume of water that has flowed into the lake from the river
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7
billion gallons 0.5 1.1 1.5 2.0 2.3 2.5 2.6
Day 8 Day 9 Day 10 Day 11 Day 12 Day 13 Day 14
billion gallons 2.7 2.75 2.8 2.9 3.0 3.25 3.4

2. Rate of the water that flow into the river
Member 1: Day 4
3 days before Day 4 2 days before Day 4 1 days before Day 4
Average rate of flow
(billion gallons) (0.5+1.1+1.5+2.0)÷4
= 1.275 (1.1+1.5+2.0)÷3
= 1.533 (1.5+2.0)÷2
= 1.75
3 days after Day 4 2 days after Day 4 1 days after Day 4
Average rate of flow
(billion gallons) (2.0+2.3+2.5+2.6)÷4
= 2.35 (2.0+2.3+2.5)÷3
= 2.266 (2.0+2.3)÷2
= 2.15

Member 2: Day 6
3 days before Day 6 2 days before Day 6 1 days before Day 6
Average rate of flow
(billion gallons) (1.5+2.0+2.3+2.5)÷4
= 2.075 (2.0+2.3+2.5)÷3
= 2.266 (2.3+2.5)÷2
= 2.4
3 days after Day 6 2 days after Day 6 1 days after Day 6
Average rate of flow
(billion gallons) (2.5+2.6+2.7+2.75)÷4
= 2.6375 (2.5+2.6+2.7)÷3
= 2.6 (2.5+2.6)÷2
= 2.55

Member 3: Day 8
3 days before Day 8 2 days before Day 8 1 days before Day 8
Average rate of flow
(billion gallons) (2.3+2.5+2.6+2.7)÷4
= 2.525 (2.5+2.6+2.7)÷3
= 2.6 (2.6+2.7)÷2
= 2.65
3 days after Day 8 2 days after Day 8 1 days after Day 8
Average rate of flow
(billion gallons) (2.7+2.75+2.8+2.9)÷4
= 2.7875 (2.7+2.75+2.8)÷3
= 2.75 (2.7+2.75)÷2
= 2.725

Member 4: Day 10
3 days before Day 10 2 days before Day 10 1 days before Day 10
Average rate of flow
(billion gallons) (2.6+2.7+2.75+2.8)÷4
= 2.7125 (2.7+2.75+2.8)÷3
= 2.75 (2.75+2.8)÷2
= 2.775
3 days after Day 10 2 days after Day 10 1 days after Day 10
Average rate of flow
(billion gallons) (2.8+2.9+3.0+3.25)÷4
= 2.9875 (2.8+2.9+3.0)÷3
= 2.9 (2.8+2.9)÷2
= 2.85

 
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