AEE 3162-01 Fa 2021 Nozzle Design Term Project Guidelines
Note, this is only a sample calculation. You should do a similar calculation for your term project conditions.
Y
Y
To find the co-ordinates of the unknown point from known , for the three points.
0
0
x
x
Assuming the coordinates of points 1 and 2 in the rectangular Cartesian system as x1, y1 and x2, y2, respectively (as calculated from the previous step) the coordinates of point 3, x3, y3 can be calculated, assuming straight line segments between points, as follows.
Slope of line 1-3, m- = (y3 – y1)/(x3 –x1) = tan[0.5(1+3) – 0.5 (1+3)]
And for line 2-3, m+ = (y3-y2) / (x3-x2) = tan[0.5(+3) + 0.5 (2+3)]
Solving, x3 = [(y1 – y2) + x2m+ – x1 m-]/(m+ – m-)
and, y3 = [m+y1 – m-y2 +( x2-x1)(m- – m+)]/(m+ -m-)…………….PLEASE VERIFY THESE Equations
More details……..and correlation to Example 11.1 from text book
I explained in the class about Unit Processes. There are three types of unit processes, 1) a point near the surface or boundary, 2) a point interior in the flow, 3) a point near the oblique shock.
In the example 11.2 (in the book) we come across all the two types of Unit Processes except the oblique shock (sonic line instead). The initial line is a like a boundary point, where some angles are known. The example I wrote is for a general internal point. The points 1 and 2 are known points from the boundary conditions or previous calculations (from the Table that you create). So, for the construction you start from the sonic throat line. Take the half height of the throat as, say 1 unit (cm or inch). Your x, y coordinate starts from there. X axis is the axis of the nozzle. Y coordinate is vertical height of different points. For e.g., for the sonic line the x, y are 0,1, i.e., point a in Figure 11.8
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