Walden Pond! Ha! Math Assignment.
Nov. 21st, 2010 11:36 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
greenstorm21 November 2010
Environmental Services Technician
Highland Valley Copper (COMINCO)
Box 1500
Logan Lake BC
V0K 1W0
Dear Ms. Erin P:
Request for Information to Support our Habitat Conservation Project Proposal
As COMINCO has now granted our Federation access to the Highland Valley site, and permission to correspond directly with you, we would like your assistance so that we can complete our HCF proposal by deadline.
Projects funded by the Habitat Conservation Trust Fund are accepted on the basis of 1, 2, 3, or 4-year durations. When we submit our finalized Reclamation and Stocking of Walden Pond with Rainbow Trout proposal we must assign a definite project length to it.
As we understand from your Geologist, Walden Pond, an exhausted open quarry pit, will gradually fill with rainfall and rain runoff, and that earlier rock and earth “berms” have been removed from its circumference.
Our Federation’s individual clubs plan to regenerate riparian and aquatic vegetation, but we require your help to determine two hydrologic factors that will decide our project length:
(1.) The length of time required for Walden Pond to fill to the desired depth (see enclosure) from only natural rainfall and rain runoff.
(2.) The presumably shorter time required to fill the pond to the desired depth if the nearby unnamed creek were to be diverted into the pond. (For this scenario we would apply for a Ministry permit to divert).
As the Federation’s volunteer biologist, I have been assigned to correspond with you on behalf of the Federation and its President, Stephen Carper. Please provide me with a letter outlining the basic answers to these questions, with data and calculation sheets attached, and please ‘copy’ our President on the letter only.
As soon as our Federation decides on the project’s length, and has submitted the project proposal to the HCF (their deadline is 1 April 2009), I shall write to you again to schedule site reconnaissance visits by our members.
I look forward to receiving your reply by 8th December 2010.
Sincerely,
Roberto Shorto
Pond Data:
The diagram above shows the desired shape of the pond. The cross-sectional areas are approximated by measuring the desired depths given below using surveying techniques at regular intervals at the locations marked with a ¶ in the diagram above. Each crossing yields one cross-sectional area. You assume the areas at the ends of the pond () are zero.
In the diagram above, the total length L of the pond is 1006 m, and measurements on each crossing are taken 81 m apart.
Crossing 1:
Station # 0 1 2 3
Depth (m) 0.81999999999999995 3.8999999999999999 4.1299999999999999 0.17000000000000001
Crossing 2:
Station # 0 1 2
Depth (m) 1.8100000000000001 3.9100000000000001 1
Crossing 3:
Station # 0 1 2 3 4
Depth (m) 1.1899999999999999 3.3199999999999998 6.5499999999999998 4.4699999999999998 1.3100000000000001
Crossing 4:
Station # 0 1 2 3 4
Depth (m) 0.68999999999999995 5.8099999999999996 9.0999999999999996 5.5599999999999996 1.79
Crossing 5:
Station # 0 1 2 3 4
Depth (m) 0.97999999999999998 4 5.79 1.3799999999999999 1.6799999999999999
Your Data:
Average rainfall = 280 mm/year.
You may assume the rainfall is evenly distributed throughout the year.
The rain that falls on an area of 271 ha drains into the pond (this includes the rain that falls on the pond).
You may neglect evaporation and water leaking out of the pond.
Unnamed creek information:
Water in the creek moves at an average speed of 4.75 cm/s, and the creek has a cross-sectional profile as shown below. The creek is 1.8 m wide, and the depths (in meters) shown in the profile are as follows:
0.26000000000000001
0.95999999999999996
1.72
1.73
1.23
0.78000000000000003
Deliverables for Math Assignment:
Letter to Roberto Shorto summarizing your findings. Letter should be created in a word processor. It should follow an appropriate format, should be readable and clear, and should contain no spelling or grammatical errors.
Enclosure showing calculations used to approximate the volume of the pond.
Enclosure showing calculations used to find the flow rate and time for the pond to fill (in days, rounded to the nearest whole number of days), without diverting the creek.
Enclosure showing calculations used to find the flow rate and time for the pond to fill (in days, rounded to the nearest whole number of days), with diverting the creek.
Note: Diagrams given are not to scale.
All calculations may be done by hand, but must be presented very neatly and clearly, showing all steps. Remember, this is something you are sending to an important contact to show the work that you have done.
Environmental Services Technician
Highland Valley Copper (COMINCO)
Box 1500
Logan Lake BC
V0K 1W0
Dear Ms. Erin P:
Request for Information to Support our Habitat Conservation Project Proposal
As COMINCO has now granted our Federation access to the Highland Valley site, and permission to correspond directly with you, we would like your assistance so that we can complete our HCF proposal by deadline.
Projects funded by the Habitat Conservation Trust Fund are accepted on the basis of 1, 2, 3, or 4-year durations. When we submit our finalized Reclamation and Stocking of Walden Pond with Rainbow Trout proposal we must assign a definite project length to it.
As we understand from your Geologist, Walden Pond, an exhausted open quarry pit, will gradually fill with rainfall and rain runoff, and that earlier rock and earth “berms” have been removed from its circumference.
Our Federation’s individual clubs plan to regenerate riparian and aquatic vegetation, but we require your help to determine two hydrologic factors that will decide our project length:
(1.) The length of time required for Walden Pond to fill to the desired depth (see enclosure) from only natural rainfall and rain runoff.
(2.) The presumably shorter time required to fill the pond to the desired depth if the nearby unnamed creek were to be diverted into the pond. (For this scenario we would apply for a Ministry permit to divert).
As the Federation’s volunteer biologist, I have been assigned to correspond with you on behalf of the Federation and its President, Stephen Carper. Please provide me with a letter outlining the basic answers to these questions, with data and calculation sheets attached, and please ‘copy’ our President on the letter only.
As soon as our Federation decides on the project’s length, and has submitted the project proposal to the HCF (their deadline is 1 April 2009), I shall write to you again to schedule site reconnaissance visits by our members.
I look forward to receiving your reply by 8th December 2010.
Sincerely,
Roberto Shorto
Pond Data:
The diagram above shows the desired shape of the pond. The cross-sectional areas are approximated by measuring the desired depths given below using surveying techniques at regular intervals at the locations marked with a ¶ in the diagram above. Each crossing yields one cross-sectional area. You assume the areas at the ends of the pond () are zero.
In the diagram above, the total length L of the pond is 1006 m, and measurements on each crossing are taken 81 m apart.
Crossing 1:
Station # 0 1 2 3
Depth (m) 0.81999999999999995 3.8999999999999999 4.1299999999999999 0.17000000000000001
Crossing 2:
Station # 0 1 2
Depth (m) 1.8100000000000001 3.9100000000000001 1
Crossing 3:
Station # 0 1 2 3 4
Depth (m) 1.1899999999999999 3.3199999999999998 6.5499999999999998 4.4699999999999998 1.3100000000000001
Crossing 4:
Station # 0 1 2 3 4
Depth (m) 0.68999999999999995 5.8099999999999996 9.0999999999999996 5.5599999999999996 1.79
Crossing 5:
Station # 0 1 2 3 4
Depth (m) 0.97999999999999998 4 5.79 1.3799999999999999 1.6799999999999999
Your Data:
Average rainfall = 280 mm/year.
You may assume the rainfall is evenly distributed throughout the year.
The rain that falls on an area of 271 ha drains into the pond (this includes the rain that falls on the pond).
You may neglect evaporation and water leaking out of the pond.
Unnamed creek information:
Water in the creek moves at an average speed of 4.75 cm/s, and the creek has a cross-sectional profile as shown below. The creek is 1.8 m wide, and the depths (in meters) shown in the profile are as follows:
0.26000000000000001
0.95999999999999996
1.72
1.73
1.23
0.78000000000000003
Deliverables for Math Assignment:
Letter to Roberto Shorto summarizing your findings. Letter should be created in a word processor. It should follow an appropriate format, should be readable and clear, and should contain no spelling or grammatical errors.
Enclosure showing calculations used to approximate the volume of the pond.
Enclosure showing calculations used to find the flow rate and time for the pond to fill (in days, rounded to the nearest whole number of days), without diverting the creek.
Enclosure showing calculations used to find the flow rate and time for the pond to fill (in days, rounded to the nearest whole number of days), with diverting the creek.
Note: Diagrams given are not to scale.
All calculations may be done by hand, but must be presented very neatly and clearly, showing all steps. Remember, this is something you are sending to an important contact to show the work that you have done.
