Aras Ibrahim
Module Leader: Geoff Grenyer Student Number: 100303438
Module code: 5HX500 BEng (Hons) Civil and Infrastructure Engineering
College of Engineering and Technology
Department of Engineering
Programme Title(s): BEng (Hons) Civil and Infrastructure Engineering
Programme Code(s): H292
Module Title: Advanced Engineering Mathematics 2
Module Code: 5HX500
Module Leader: Geoff Grenyer
Lecturer: Geoff Grenyer
Assignment No: ONE
Assessment tasks
1. 20% the depth of a river flowing in a rectangular channel 5m. Wide is measured over a period of 11 hours following a storm. The tables show depth of the river in mm.
Time T hours
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Depth D mm
325
330
326
320
345
393
420
451
490
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
532
582
600
626
633
637
645
641
a) Using excel plot a graph of this data, state the function representing the 5th order polynomial line of best fit and show this on the graph. (For accuracy the line of best fit constants should be expressed to 6 decimal places).
b) Comment on the differences between the actual data and the line of best fit function including largest differences.
The purpose of plotting the line of best fit is to simply spot the errors of data on the graph and the accuracy of the line or curve will be affected by order of the function. When increasing the order of the line of best fit reduces the error created from actual data. Therefore there will be a very small error, when setting line of best fit with an order of 5. depending on the correlation of the data. Furthermore, increasing the amount of decimal places of the coefficients increases the accuracy. As well as this, the data points seem to be equally above and below the line of best fit, thus further decreasing the error. The correlation coefficient (R2) is very close to 1, therefore proving the accuracy between the actual data and the line of best fit.
c) Differentiate the best fit function and find the rate (mm/hour) at which the water is rising after 4.5 hours
d) Determine the maximum river depth suggested by the best fit function and the time at which this occurs and compare these values with the information suggested by the data.
e) Integrate the best fit function between 1 and 11 hours to give an area (A) and multiply by the channel width (W) and velocity (V) (assumed to be 1m/s) to give the volume of water flowing in the 11 hour period. State the answer in cubic metres. Volume = A x W X V
f) Find the area under the actual data line using Simpson’s rule and use this to determine the volume of water flowing as above.
g) Comment of the accuracy the volume calculation using the best fit model when compared to the volume using the actual data.
2. 20% a ready mixed concrete supplier has 2 batching plants P and Q being supplied by 3 quarries A, B and C.
Quarry capacities and plant requirements together with distances between quarries and plants.
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