Contents Page
Introduction--------------------------------------------------------------------------3
Individual Student Portfolio------------------------------------------------------3-4
Portfolio Activity Sheet 1 --------------------------------------------------------4
Portfolio Activity Sheet 2 --------------------------------------------------------4-5
Portfolio Activity Sheet 2 --------------------------------------------------------5
Conclusion---------------------------------------------------------------------------7
References/sources of information--------------------------------------------7
Engineering Mathematics 1 (4HX502)
Individual Student Portfolio
Semester 1 2013-14
Student name: Aras Ibrahim
Student no: 100303438
Programme Title: Engineering Mathematics 1
Programme Code: 4HX502
Portfolio Contents:
Assessor to complete column below
Activity sheets and solutions:
1 Algebraic methods
2 Geometry, trigonometry and vector applications
3 Calculus
Overall Score
4* 3* 2* 1* F*
Assessors name: Date:
Portfolio Activity Sheet 1
Algebraic Methods
1. Two variables, Q water flow rate in m3/s and H metres, the depth of flow of water over a weir, are believed to be related by a function of the form Q = kHn An investigation is carried out and a set of observations obtained:
Q
0.07
0.13
0.15
0.40
0.47
0.61
1.03
1.73
2.15
3.15
H
0.30
0.38
0.41
0.65
0.72
0.89
1.10
1.20
1.40
i. Plot a graph of logQ (vertical) against logH (horizontal)
Log Q
-1.15
-0.89
-0.82
-0.40
-0.33
-0.21
0.01
0.24
0.33
0.50
Log H
-0.52
-0.42
-0.39
-0.19
-0.14
-0.05
0.04
0.08
ii. Determine the values of the constants k and n
logk=0.13 N=0.5-0.20.15-0.03
k=100.13 N=2.5
k=1.35
iii. State the function relating Q and H
Q=1.35H2.5
iv. Use this function to find the expected flow rate when H = 0.5m
Q=1.35(0.5)2.5 = 0.239… when H = 0.5
v. Use this function to find the expected depth of flow when Q = 0.75m3/s
H=(0.751.35)(12.5) = 0.790… when Q = 0.75
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2. A piece of construction plant is purchased at a price of £51200. Previous plant records indicate that after 2 years plant has a value of 50% of its new cost.
Assuming exponential decay:
i. Determine a function that represents the value (V) of construction plant as a function of its age in years (Y).
v=51200ekY 25600=51200e2k
0.5=e2k
ln0.5=2k
k=ln(0.5)2
v=51200e...
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