The designer knows the flow entry angle (%u03B21), the desired flow exit angle (
ID: 3537529 • Letter: T
Question
The designer knows the flow entry angle (%u03B21), the desired flow exit angle (%u03B22) and the
desired incidence (i). He (or she) must select the solidity (%u03C3) of the row, the blade entry
angle (%u03B11), and the blade exit angle (%u03B1 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 that, given %u03B21 and %u03B22, computes and returns %u03C3. 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
%uF8F7%uF8F8
%uF8F6
%uF8EC%uF8ED
%uF8EB
%uF8F7%uF8F8
%uF8F6
%uF8EC%uF8ED
%uF8EB - +
%uF8F7%uF8F8
%uF8F6
%uF8EC%uF8ED
%uF8EB
%uF8F7%uF8F8
%uF8F6
%uF8EC%uF8ED
%uF8EB - +
=
s
b
s
b
b a
a
Write a function that, given %u03B11, %u03B22 and %u03C3, computes and returns %u03B12.
Write a C++ program that repeatedly reads in design scenarios (flow entry angle %u03B21,
desired flow exit angle %u03B22, 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 %u03B22 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 %u03B21 and %u03B22 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 . . .
Explanation / Answer
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