marking schem: Function(s): 10 marks Sentinel loop: 5 marks Invalid input checks
ID: 3568323 • Letter: M
Question
marking schem:
Function(s): 10 marks
Sentinel loop: 5 marks
Invalid input checks: 5 marks
Calculation and output of required data, including calling function(s) as appropriate: 10 marks
Final Lab Test Sample
The diagram below depicts a row of blades in an air compressor.
http://sce.carleton.ca/courses/ecor-1606/f14/practicelabfinal2/samplabfinal2.pdf
Air Flow
flow entry angle (
?1)
blade entry angle (
? 1)
blade exit angle (
? 2)
flow exit angle (
?2)
Incidence (
i)
s
c
solidity (?) = c/s
The designer knows the flow entry angle (
?1), the desired flow exit angle (?2) and the
desired
incidence (i). He (or she) must select the solidity (?) of the row, the blade entry
angle (
?1), and the blade exit angle (? 2).
Important note:
Angles are in degrees throughout. All of the formulae assume degrees.
Choosing the blade entry angle is easy.
= -
i 1 1 a b
A suitable solidity value may be obtained by solving the equation below.
(0.187148 15.2599) ln(1/ ) 0.677212
(ln(1/ )) 0
33.5291 (0.469188 0.0020961 )
2
2
2 2 1
- - =
+ + - +
b s s
b b b
Write a
function, computeSolidity, that takes ?1 and ?2, and computes and returns ?.
There are a number of ways of solving the equation. You are to use a brute force
approach. No great accuracy is required (the choice of a solidity value is in any case
somewhat subjective) and the number of values that need be considered is therefore
limited. Have your function evaluate the left hand side of the equation for solidity values
ranging from 0.6 to 2.1 (in steps of 0.1) and have it select the value that comes closest to
satisfying the equation (i.e. that makes the left hand side closest to zero).
To assist you in debugging your code, the function in the sample executable prints out a
table showing the results of its calculations. Your function must do likewise. The
columns of the table must line up, solidity values must be displayed with one decimal
place, and computed values must be displayed with four decimal places.
Once the blade entry angle and the solidity have been determined, the blade exit angle
that will give the desired flow exit angle can be determined using the following equation.
0.5
2
0.5
2
2 1
2
1
500
1 0.23
1
500
0.23
??
?
??
?
??
?
??
?
- +
??
?
??
?
??
?
??
?
- +
=
s
b
s
b
b a
a
Write a
function, computeBladeExitAngle, that takes ?1, ?2, and ?, and computes and
returns
?2.
Your functions must correspond exactly to the specifications given.
Write a C++
program ("practice2.cpp") that repeatedly reads in design scenarios (flow
entry angle
?1, desired flow exit angle ?2, and desired incidence i), until -1 -1 -1 is
entered. For each set of values entered your program should either i) output an error
message (if the entered values are invalid -- see next paragraph) or ii) compute and output
values for the blade entry angle, the row solidity, and the blade exit angle.
The flow exit angle
?2 must be between -10 and 50 degrees, the incidence i must be
between -3 and 3 degrees, and the value of
1 2
2
36 0.45
b b
b
-
-
must be between 0.75 and 1.25. All of these ranges are inclusive of the specified values.
Be sure to consider the possibility that the values entered for
?1 and ?2 may be equal.
Note:
Your program must include and use the two required functions described above.
Test Run #1
Enter flow entry angle, flow exit angle, and incidence:
40 0 0
Solidity LHS Value
----------------------------
0.6 -14.4428
0.7 -11.9999
0.8 -9.9098
0.9 -8.0862
1.0 -6.4709
1.1 -5.0226
1.2 -3.7112
1.3 -2.5139
1.4 -1.4130
1.5 -0.3949
1.6 0.5517
1.7 1.4358
1.8 2.2647
1.9 3.0447
2.0 3.7811
2.1 4.4782
Leaving function. The chosen value is 1.5
Blade entry angle: 40.0
Soldidity: 1.5
Blade exit angle: -9.2
Enter flow entry angle, flow exit angle, and incidence:
10 10 0
Invalid values ignored.
Enter flow entry angle, flow exit angle, and incidence:
20 10 0
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
60 40 0
Solidity LHS Value
----------------------------
0.6 -8.4975
0.7 -7.2086
0.8 -6.1181
0.9 -5.1762
1.0 -4.3496
1.1 -3.6148
1.2 -2.9548
1.3 -2.3566
1.4 -1.8106
1.5 -1.3089
1.6 -0.8454
1.7 -0.4152
1.8 -0.0142
1.9 0.3611
2.0 0.7135
2.1 1.0454
Leaving function. The chosen value is 1.8
Blade entry angle: 60.0
Soldidity: 1.8
Blade exit angle: 34.0
Enter flow entry angle, flow exit angle, and incidence:
30 30 0
Invalid values ignored.
Enter flow entry angle, flow exit angle, and incidence:
-1 -1 -1
Press any key to continue . . .
Test Run #2
Enter flow entry angle, flow exit angle, and incidence:
33.1 0 0
Solidity LHS Value
----------------------------
0.6 -7.5428
0.7 -5.0999
0.8 -3.0098
0.9 -1.1862
1.0 0.4291
1.1 1.8774
1.2 3.1888
1.3 4.3861
1.4 5.4870
1.5 6.5051
1.6 7.4517
1.7 8.3358
1.8 9.1647
1.9 9.9447
2.0 10.6811
2.1 11.3782
Leaving function. The chosen value is 1.0
Blade entry angle: 33.1
Soldidity: 1.0
Blade exit angle: -9.9
Enter flow entry angle, flow exit angle, and incidence:
41.6 -9.999 1
Solidity LHS Value
----------------------------
0.6 -21.4805
0.7 -18.7492
0.8 -16.4092
0.9 -14.3652
1.0 -12.5527
1.1 -10.9261
1.2 -9.4519
1.3 -8.1047
1.4 -6.8652
1.5 -5.7180
1.6 -4.6506
1.7 -3.6531
1.8 -2.7172
1.9 -1.8360
2.0 -1.0037
2.1 -0.2153
Leaving function. The chosen value is 2.1
Blade entry angle: 40.6
Soldidity: 2.1
Blade exit angle: -18.6
Enter flow entry angle, flow exit angle, and incidence:
40 0 4
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
40 0 -4
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
41.6 -10.01 1
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
50 -9.999 0
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
46.7 -9.999 1
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
60 -9.999 1
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
31.4 10.9 2
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
40 0 -3.1
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
60 10 0
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
15 10 0
Invalid values ignored
Enter flow entry angle, flow exit angle, and incidence:
-1 -1 -1
Press any key to continue . . .
Lab Test Hints
The second function is very straightforward: given alpha1, beta1, and beta2, calculate alpha2 as per the
formula.
The first function involves finding a minimum. You are to use the given values of beta1 and beta2 and
find the value of the left hand side of the equation using:
1. sigma = 0.6
2. sigma = 0.7
Explanation / Answer
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