solving an equation for a variable that has changing varibles in it
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joshua payne
2022-10-9
im trying to solve for M1 based off a changing Pr
index1=1:304;
index2=697:1000;
index3=305:696;
figure
plot(t(index1),M(index1), 'b')
hold on
plot(t(index2),M(index2), 'b')
%plot(t(index3),M(index3), 'r')
M2=(((M1).^(2))+(2/(gamma-1)))./((((2*gamma)/(gamma-1)).*(M1).^2)-1)
pr=Po(index3)./P(index3)
eqn=((1+((gamma-1)/2).*(M2).^2)).^(gamma/(gamma-1)).*(((gamma+1).*(M1).^2)./(2+(gamma-1).*(M1).^2))==pr
superM=vpasolve(eqn,M, 'real')
plot(t(index3),superM, 'r')
im trying to get only real vaules for M1
8 个评论
joshua payne
2022-10-9
i just defined M1 in syms and i changed superM(eqn,M1,'real'), i mistakenly put M.
but now i get new errors
joshua payne
2022-10-9
clc
clear all
t=[0.00
1.20
2.40
3.60
4.80
6.01
7.21
8.41
9.61
10.81
12.01
13.21
14.41
15.62
16.82
18.02
19.22
20.42
21.62
22.82
24.02
25.23
26.43
27.63
28.83
30.03
31.23
32.43
33.63
34.83
36.04
37.24
38.44
39.64
40.84
42.04
43.24
44.44
45.65
46.85
48.05
49.25
50.45
51.65
52.85
54.05
55.26
56.46
57.66
58.86
60.06
61.26
62.46
63.66
64.86
66.07
67.27
68.47
69.67
70.87
72.07
73.27
74.47
75.68
76.88
78.08
79.28
80.48
81.68
82.88
84.08
85.29
86.49
87.69
88.89
90.09
91.29
92.49
93.69
94.89
96.10
97.30
98.50
99.70
100.90
102.10
103.30
104.50
105.71
106.91
108.11
109.31
110.51
111.71
112.91
114.11
115.32
116.52
117.72
118.92
120.12
121.32
122.52
123.72
124.92
126.13
127.33
128.53
129.73
130.93
132.13
133.33
134.53
135.74
136.94
138.14
139.34
140.54
141.74
142.94
144.14
145.35
146.55
147.75
148.95
150.15
151.35
152.55
153.75
154.95
156.16
157.36
158.56
159.76
160.96
162.16
163.36
164.56
165.77
166.97
168.17
169.37
170.57
171.77
172.97
174.17
175.38
176.58
177.78
178.98
180.18
181.38
182.58
183.78
184.98
186.19
187.39
188.59
189.79
190.99
192.19
193.39
194.59
195.80
197.00
198.20
199.40
200.60
201.80
203.00
204.20
205.41
206.61
207.81
209.01
210.21
211.41
212.61
213.81
215.02
216.22
217.42
218.62
219.82
221.02
222.22
223.42
224.62
225.83
227.03
228.23
229.43
230.63
231.83
233.03
234.23
235.44
236.64
237.84
239.04
240.24
241.44
242.64
243.84
245.05
246.25
247.45
248.65
249.85
251.05
252.25
253.45
254.65
255.86
257.06
258.26
259.46
260.66
261.86
263.06
264.26
265.47
266.67
267.87
269.07
270.27
271.47
272.67
273.87
275.08
276.28
277.48
278.68
279.88
281.08
282.28
283.48
284.68
285.89
287.09
288.29
289.49
290.69
291.89
293.09
294.29
295.50
296.70
297.90
299.10
300.30
301.50
302.70
303.90
305.11
306.31
307.51
308.71
309.91
311.11
312.31
313.51
314.71
315.92
317.12
318.32
319.52
320.72
321.92
323.12
324.32
325.53
326.73
327.93
329.13
330.33
331.53
332.73
333.93
335.14
336.34
337.54
338.74
339.94
341.14
342.34
343.54
344.74
345.95
347.15
348.35
349.55
350.75
351.95
353.15
354.35
355.56
356.76
357.96
359.16
360.36
361.56
362.76
363.96
365.17
366.37
367.57
368.77
369.97
371.17
372.37
373.57
374.77
375.98
377.18
378.38
379.58
380.78
381.98
383.18
384.38
385.59
386.79
387.99
389.19
390.39
391.59
392.79
393.99
395.20
396.40
397.60
398.80
400.00
401.20
402.40
403.60
404.80
406.01
407.21
408.41
409.61
410.81
412.01
413.21
414.41
415.62
416.82
418.02
419.22
420.42
421.62
422.82
424.02
425.23
426.43
427.63
428.83
430.03
431.23
432.43
433.63
434.83
436.04
437.24
438.44
439.64
440.84
442.04
443.24
444.44
445.65
446.85
448.05
449.25
450.45
451.65
452.85
454.05
455.26
456.46
457.66
458.86
460.06
461.26
462.46
463.66
464.86
466.07
467.27
468.47
469.67
470.87
472.07
473.27
474.47
475.68
476.88
478.08
479.28
480.48
481.68
482.88
484.08
485.29
486.49
487.69
488.89
490.09
491.29
492.49
493.69
494.89
496.10
497.30
498.50
499.70
500.90
502.10
503.30
504.50
505.71
506.91
508.11
509.31
510.51
511.71
512.91
514.11
515.32
516.52
517.72
518.92
520.12
521.32
522.52
523.72
524.92
526.13
527.33
528.53
529.73
530.93
532.13
533.33
534.53
535.74
536.94
538.14
539.34
540.54
541.74
542.94
544.14
545.35
546.55
547.75
548.95
550.15
551.35
552.55
553.75
554.95
556.16
557.36
558.56
559.76
560.96
562.16
563.36
564.56
565.77
566.97
568.17
569.37
570.57
571.77
572.97
574.17
575.38
576.58
577.78
578.98
580.18
581.38
582.58
583.78
584.98
586.19
587.39
588.59
589.79
590.99
592.19
593.39
594.59
595.80
597.00
598.20
599.40
600.60
601.80
603.00
604.20
605.41
606.61
607.81
609.01
610.21
611.41
612.61
613.81
615.02
616.22
617.42
618.62
619.82
621.02
622.22
623.42
624.62
625.83
627.03
628.23
629.43
630.63
631.83
633.03
634.23
635.44
636.64
637.84
639.04
640.24
641.44
642.64
643.84
645.05
646.25
647.45
648.65
649.85
651.05
652.25
653.45
654.65
655.86
657.06
658.26
659.46
660.66
661.86
663.06
664.26
665.47
666.67
667.87
669.07
670.27
671.47
672.67
673.87
675.08
676.28
677.48
678.68
679.88
681.08
682.28
683.48
684.68
685.89
687.09
688.29
689.49
690.69
691.89
693.09
694.29
695.50
696.70
697.90
699.10
700.30
701.50
702.70
703.90
705.11
706.31
707.51
708.71
709.91
711.11
712.31
713.51
714.71
715.92
717.12
718.32
719.52
720.72
721.92
723.12
724.32
725.53
726.73
727.93
729.13
730.33
731.53
732.73
733.93
735.14
736.34
737.54
738.74
739.94
741.14
742.34
743.54
744.74
745.95
747.15
748.35
749.55
750.75
751.95
753.15
754.35
755.56
756.76
757.96
759.16
760.36
761.56
762.76
763.96
765.17
766.37
767.57
768.77
769.97
771.17
772.37
773.57
774.77
775.98
777.18
778.38
779.58
780.78
781.98
783.18
784.38
785.59
786.79
787.99
789.19
790.39
791.59
792.79
793.99
795.20
796.40
797.60
798.80
800.00
801.20
802.40
803.60
804.80
806.01
807.21
808.41
809.61
810.81
812.01
813.21
814.41
815.62
816.82
818.02
819.22
820.42
821.62
822.82
824.02
825.23
826.43
827.63
828.83
830.03
831.23
832.43
833.63
834.83
836.04
837.24
838.44
839.64
840.84
842.04
843.24
844.44
845.65
846.85
848.05
849.25
850.45
851.65
852.85
854.05
855.26
856.46
857.66
858.86
860.06
861.26
862.46
863.66
864.86
866.07
867.27
868.47
869.67
870.87
872.07
873.27
874.47
875.68
876.88
878.08
879.28
880.48
881.68
882.88
884.08
885.29
886.49
887.69
888.89
890.09
891.29
892.49
893.69
894.89
896.10
897.30
898.50
899.70
900.90
902.10
903.30
904.50
905.71
906.91
908.11
909.31
910.51
911.71
912.91
914.11
915.32
916.52
917.72
918.92
920.12
921.32
922.52
923.72
924.92
926.13
927.33
928.53
929.73
930.93
932.13
933.33
934.53
935.74
936.94
938.14
939.34
940.54
941.74
942.94
944.14
945.35
946.55
947.75
948.95
950.15
951.35
952.55
953.75
954.95
956.16
957.36
958.56
959.76
960.96
962.16
963.36
964.56
965.77
966.97
968.17
969.37
970.57
971.77
972.97
974.17
975.38
976.58
977.78
978.98
980.18
981.38
982.58
983.78
984.98
986.19
987.39
988.59
989.79
990.99
992.19
993.39
994.59
995.80
997.00
998.20
999.40
1000.60
1001.80
1003.00
1004.20
1005.41
1006.61
1007.81
1009.01
1010.21
1011.41
1012.61
1013.81
1015.02
1016.22
1017.42
1018.62
1019.82
1021.02
1022.22
1023.42
1024.62
1025.83
1027.03
1028.23
1029.43
1030.63
1031.83
1033.03
1034.23
1035.44
1036.64
1037.84
1039.04
1040.24
1041.44
1042.64
1043.84
1045.05
1046.25
1047.45
1048.65
1049.85
1051.05
1052.25
1053.45
1054.65
1055.86
1057.06
1058.26
1059.46
1060.66
1061.86
1063.06
1064.26
1065.47
1066.67
1067.87
1069.07
1070.27
1071.47
1072.67
1073.87
1075.08
1076.28
1077.48
1078.68
1079.88
1081.08
1082.28
1083.48
1084.68
1085.89
1087.09
1088.29
1089.49
1090.69
1091.89
1093.09
1094.29
1095.50
1096.70
1097.90
1099.10
1100.30
1101.50
1102.70
1103.90
1105.11
1106.31
1107.51
1108.71
1109.91
1111.11
1112.31
1113.51
1114.71
1115.92
1117.12
1118.32
1119.52
1120.72
1121.92
1123.12
1124.32
1125.53
1126.73
1127.93
1129.13
1130.33
1131.53
1132.73
1133.93
1135.14
1136.34
1137.54
1138.74
1139.94
1141.14
1142.34
1143.54
1144.74
1145.95
1147.15
1148.35
1149.55
1150.75
1151.95
1153.15
1154.35
1155.56
1156.76
1157.96
1159.16
1160.36
1161.56
1162.76
1163.96
1165.17
1166.37
1167.57
1168.77
1169.97
1171.17
1172.37
1173.57
1174.77
1175.98
1177.18
1178.38
1179.58
1180.78
1181.98
1183.18
1184.38
1185.59
1186.79
1187.99
1189.19
1190.39
1191.59
1192.79
1193.99
1195.20
1196.40
1197.60
1198.80
1200.00];
P=[101000.00
100821.64
100643.29
100464.93
100286.57
100108.22
99929.86
99751.50
99573.15
99394.79
99216.43
99038.08
98859.72
98681.36
98503.01
98324.65
98146.29
97967.94
97789.58
97611.22
97432.87
97254.51
97076.15
96897.80
96719.44
96541.08
96362.73
96184.37
96006.01
95827.66
95649.30
95470.94
95292.59
95114.23
94935.87
94757.52
94579.16
94400.80
94222.44
94044.09
93865.73
93687.37
93509.02
93330.66
93152.30
92973.95
92795.59
92617.23
92438.88
92260.52
92082.16
91903.81
91725.45
91547.09
91368.74
91190.38
91012.02
90833.67
90655.31
90476.95
90298.60
90120.24
89941.88
89763.53
89585.17
89406.81
89228.46
89050.10
88871.74
88693.39
88515.03
88336.67
88158.32
87979.96
87801.60
87623.25
87444.89
87266.53
87088.18
86909.82
86731.46
86553.11
86374.75
86196.39
86018.04
85839.68
85661.32
85482.97
85304.61
85126.25
84947.90
84769.54
84591.18
84412.83
84234.47
84056.11
83877.76
83699.40
83521.04
83342.69
83164.33
82985.97
82807.62
82629.26
82450.90
82272.55
82094.19
81915.83
81737.47
81559.12
81380.76
81202.40
81024.05
80845.69
80667.33
80488.98
80310.62
80132.26
79953.91
79775.55
79597.19
79418.84
79240.48
79062.12
78883.77
78705.41
78527.05
78348.70
78170.34
77991.98
77813.63
77635.27
77456.91
77278.56
77100.20
76921.84
76743.49
76565.13
76386.77
76208.42
76030.06
75851.70
75673.35
75494.99
75316.63
75138.28
74959.92
74781.56
74603.21
74424.85
74246.49
74068.14
73889.78
73711.42
73533.07
73354.71
73176.35
72998.00
72819.64
72641.28
72462.93
72284.57
72106.21
71927.86
71749.50
71571.14
71392.79
71214.43
71036.07
70857.72
70679.36
70501.00
70322.65
70144.29
69965.93
69787.58
69609.22
69430.86
69252.51
69074.15
68895.79
68717.43
68539.08
68360.72
68182.36
68004.01
67825.65
67647.29
67468.94
67290.58
67112.22
66933.87
66755.51
66577.15
66398.80
66220.44
66042.08
65863.73
65685.37
65507.01
65328.66
65150.30
64971.94
64793.59
64615.23
64436.87
64258.52
64080.16
63901.80
63723.45
63545.09
63366.73
63188.38
63010.02
62831.66
62653.31
62474.95
62296.59
62118.24
61939.88
61761.52
61583.17
61404.81
61226.45
61048.10
60869.74
60691.38
60513.03
60334.67
60156.31
59977.96
59799.60
59621.24
59442.89
59264.53
59086.17
58907.82
58729.46
58551.10
58372.75
58194.39
58016.03
57837.68
57659.32
57480.96
57302.61
57124.25
56945.89
56767.54
56589.18
56410.82
56232.46
56054.11
55875.75
55697.39
55519.04
55340.68
55162.32
54983.97
54805.61
54627.25
54448.90
54270.54
54092.18
53913.83
53735.47
53557.11
53378.76
53200.40
53022.04
52843.69
52665.33
52486.97
52308.62
52130.26
51951.90
51773.55
51595.19
51416.83
51238.48
51060.12
50881.76
50703.41
50525.05
50346.69
50168.34
49989.98
49811.62
49633.27
49454.91
49276.55
49098.20
48919.84
48741.48
48563.13
48384.77
48206.41
48028.06
47849.70
47671.34
47492.99
47314.63
47136.27
46957.92
46779.56
46601.20
46422.85
46244.49
46066.13
45887.78
45709.42
45531.06
45352.71
45174.35
44995.99
44817.64
44639.28
44460.92
44282.57
44104.21
43925.85
43747.49
43569.14
43390.78
43212.42
43034.07
42855.71
42677.35
42499.00
42320.64
42142.28
41963.93
41785.57
41607.21
41428.86
41250.50
41072.14
40893.79
40715.43
40537.07
40358.72
40180.36
40002.00
39823.65
39645.29
39466.93
39288.58
39110.22
38931.86
38753.51
38575.15
38396.79
38218.44
38040.08
37861.72
37683.37
37505.01
37326.65
37148.30
36969.94
36791.58
36613.23
36434.87
36256.51
36078.16
35899.80
35721.44
35543.09
35364.73
35186.37
35008.02
34829.66
34651.30
34472.95
34294.59
34116.23
33937.88
33759.52
33581.16
33402.81
33224.45
33046.09
32867.74
32689.38
32511.02
32332.67
32154.31
31975.95
31797.60
31619.24
31440.88
31262.53
31084.17
30905.81
30727.45
30549.10
30370.74
30192.38
30014.03
29835.67
29657.31
29478.96
29300.60
29122.24
28943.89
28765.53
28587.17
28408.82
28230.46
28052.10
27873.75
27695.39
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101034.72];
gamma=1.4;
M=((((Po./P).^((gamma-1)./gamma)-1)*2)/(gamma-1)).^(1/2);
Msonic=find(abs(M-1)<.005)
values=M(305)
values=M(696)
Po1=P.*(1+((gamma-1)/2).*M.^2);
M2=(((M.^2)+(2/(gamma-1)))/(((2*gamma)/(gamma-1))-1));
%Po2=
index1=1:304;
index2=697:1000;
index3=305:696;
figure
plot(t(index1),M(index1), 'b')
hold on
plot(t(index2),M(index2), 'b')
%plot(t(index3),M(index3), 'r')
%M2=((((M1).^(2))+(2/(gamma-1)))./((((2*gamma)/(gamma-1)).*(M1).^2)-1))
pr=Po(index3)./P(index3)
syms M1
eqn=((1+((gamma-1)/2).*(((((M1).^(2))+(2/(gamma-1)))./((((2*gamma)/(gamma-1)).*(M1).^2)-1))).^2)).^(gamma/(gamma-1)).*(((gamma+1).*(M1).^2)./(2+(gamma-1).*(M1).^2))==pr
superM=vpasolve(eqn,M1, 'real')
plot(t(index3),superM, 'r')
hold off
Ghazwan
2022-10-9
Please, re-post your quesiton after you put the data in an excel spreadsheet as it is diffcult to read it. Thanks!
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