Introduction
The ideal spread of an accident pollution at a particular
position of a canal between two lakes could be calculated by using the
‘transport canal’ model. The model could be built by a spreadsheet.
The basic data of the transport canal shows as below,
Canal length, distance between Lake A and Lake B, is 12
kilo-meters which is 12000 meters. Width is 10 meters. Depth of the canal is 5
meters. The position where accident happens is 4 kilo-meters away from Lake A.
Village is 4 kilo-meters away from Lake B which means 80000 meters away from
Lake A. Total amount of pollutant is 20000 kilograms. Concentrations of Lake A
and Lake B are 10 mg/l and 20mg/l, respectively. The dispersion coefficient is
25000 m2/hour.
By my calculation which shows in the attached spreadsheet,
(i) the highest concentration of pollutant in the water near the village is
39.8414 mg/l. (ii) The peak of concentration near the village is 273 hours
after the accident. (iii) The variation of pollutant concentration with time at
the accident point, the center of the canal and at the village is Figure 3.
(iv) The variation of concentration of pollutant along the canal at the time of
the highest concentration at the village is Figure 4.
Method
Step 1. Write the data into the spreadsheet. Transform the
original data with the uniform units as below.
Figure
1
Step 2. Draw the Lake A and Lake B into the appropriate cells in the spreadsheet. Use the
set Time step and set Space step to give out the data of other cells vertically
and horizontally as below.
Figure 2
Step 3. Calculate ‘r’ and ‘1-2r’. r is equal to the
product of ‘dispersion
coefficient’ and ‘Time step’ divided by the power of ‘space step’.
Step 4. In the first time step, the concentration of the
accident point is equal to the product of ‘1-2r’ and concentration of the
accident point (when time is 0, by my calculation the concentration is 800
mg/l) adding the product of ‘r’ and the sum of 2 cell values beside accident
point.
Step 5. Use the format in the first-time-step accident point
cell and spread the format to all other cells expect the Lake A and B’s cells.
Because the concentrations of Lake A and B will remain the same without any
change.
Step 6. Select the data from accident point along to the
village point, use the ‘insert chart’ to create the Variation of pollutant
concentration with time below.
Figure 3
Step 7. Select several horizontal data (with different time
steps) in the spreadsheet to create the concentration variation of pollutant
along the canal.
Figure
4
Conclusion
The transport canal model could show the significant
concentration change in the canal after the accident.
