Resources | Aerodynamics for Students

Part 1: Subsonic Flow (Isentropic Flow, γ=7/5)

Notation :

M = Local flow Mach number
P/P_O = Ratio of static pressure to total pressure
ρ/ρ_O = Ratio of local flow density to stagnation density
T/T_O = Ratio of static temperature to total temperature
β = sqrt(1-M²) = Compressibility factor
V/a^* = Local velocity / speed of sound at sonic point
q/P_O = Dynamic pressure / total pressure
A/A^* = Local flow area / flow area at sonic point

M	P/P_O	ρ/ρ_O	T/T_O	β	q/P_O	A/A^*	V/a^*
0.00	1.0000	1.0000	1.0000	1.0000	0.0000	------	0.0000
0.01	0.9999	1.0000	1.0000	0.9999	7.000 E-5	57.8738	0.0110
0.02	0.9997	0.9998	0.9999	0.9998	2.799 E-4	28.9421	0.0219
0.03	0.9994	0.9996	0.9998	0.9995	6.296 E-4	19.3005	0.0329
0.04	0.9989	0.9992	0.9997	0.9992	1.119 E-3	14.4815	0.0438
0.05	0.9983	0.9988	0.9995	0.9987	1.747 E-3	11.5914	0.0548
0.06	0.9975	0.9982	0.9993	0.9982	2.514 E-3	9.6659	0.0657
0.07	0.9966	0.9976	0.9990	0.9975	3.418 E-3	8.2915	0.0766
0.08	0.9955	0.9968	0.9987	0.9968	4.460 E-3	7.2616	0.0876
0.09	0.9944	0.9960	0.9984	0.9959	5.638 E-3	6.4613	0.0985
0.10	0.9930	0.9950	0.9980	0.9950	6.951 E-3	5.8218	0.1094
0.11	0.9916	0.9940	0.9976	0.9939	8.399 E-3	5.2992	0.1204
0.12	0.9900	0.9928	0.9971	0.9928	9.979 E-3	4.8643	0.1313
0.13	0.9883	0.9916	0.9966	0.9915	1.169 E-2	4.4969	0.1422
0.14	0.9864	0.9903	0.9961	0.9902	1.353 E-2	4.1824	0.1531
0.15	0.9844	0.9888	0.9955	0.9887	1.550 E-2	3.9103	0.1639
0.16	0.9823	0.9873	0.9949	0.9871	1.760 E-2	3.6727	0.1748
0.17	0.9800	0.9857	0.9943	0.9854	1.983 E-2	3.4635	0.1857
0.18	0.9776	0.9840	0.9936	0.9837	2.217 E-2	3.2779	0.1965
0.19	0.9751	0.9822	0.9928	0.9818	2.464 E-2	3.1123	0.2074
0.20	0.9725	0.9803	0.9921	0.9798	2.723 E-2	2.9635	0.2182
0.21	0.9697	0.9783	0.9913	0.9777	2.994 E-2	2.8293	0.2290
0.22	0.9668	0.9762	0.9904	0.9755	3.276 E-2	2.7076	0.2398
0.23	0.9638	0.9740	0.9895	0.9732	3.569 E-2	2.5968	0.2506
0.24	0.9607	0.9718	0.9886	0.9708	3.874 E-2	2.4956	0.2614
0.25	0.9575	0.9694	0.9877	0.9682	4.189 E-2	2.4027	0.2722
0.26	0.9541	0.9670	0.9867	0.9656	4.515 E-2	2.3173	0.2829
0.27	0.9506	0.9645	0.9856	0.9629	4.851 E-2	2.2385	0.2936
0.28	0.9470	0.9619	0.9846	0.9600	5.197 E-2	2.1656	0.3043
0.29	0.9433	0.9592	0.9835	0.9570	5.553 E-2	2.0979	0.3150
0.30	0.9395	0.9564	0.9823	0.9539	5.919 E-2	2.0351	0.3257
0.31	0.9355	0.9535	0.9811	0.9507	6.293 E-2	1.9765	0.3364
0.32	0.9315	0.9506	0.9799	0.9474	6.677 E-2	1.9219	0.3470
0.33	0.9274	0.9476	0.9787	0.9440	7.069 E-2	1.8707	0.3576
0.34	0.9231	0.9445	0.9774	0.9404	7.470 E-2	1.8229	0.3682
0.35	0.9188	0.9413	0.9761	0.9367	7.878 E-2	1.7780	0.3788
0.36	0.9143	0.9380	0.9747	0.9330	8.295 E-2	1.7358	0.3893
0.37	0.9098	0.9347	0.9733	0.9290	8.719 E-2	1.6961	0.3999
0.38	0.9052	0.9313	0.9719	0.9250	9.149 E-2	1.6587	0.4104
0.39	0.9004	0.9278	0.9705	0.9208	9.587 E-2	1.6234	0.4209
0.40	0.8956	0.9243	0.9690	0.9165	0.1003	1.5901	0.4313
0.41	0.8907	0.9207	0.9675	0.9121	0.1048	1.5587	0.4418
0.42	0.8857	0.9170	0.9659	0.9075	0.1094	1.5289	0.4522
0.43	0.8807	0.9132	0.9643	0.9028	0.1140	1.5007	0.4626
0.44	0.8755	0.9094	0.9627	0.8980	0.1186	1.4740	0.4729
0.45	0.8703	0.9055	0.9611	0.8930	0.1234	1.4487	0.4833
0.46	0.8650	0.9016	0.9594	0.8879	0.1281	1.4246	0.4936
0.47	0.8596	0.8976	0.9577	0.8827	0.1329	1.4018	0.5038
0.48	0.8541	0.8935	0.9559	0.8773	0.1378	1.3801	0.5141
0.49	0.8486	0.8894	0.9542	0.8717	0.1426	1.3595	0.5243
0.50	0.8430	0.8852	0.9524	0.8660	0.1475	1.3398	0.5345
0.51	0.8374	0.8809	0.9506	0.8602	0.1525	1.3212	0.5447
0.52	0.8317	0.8766	0.9487	0.8542	0.1574	1.3034	0.5548
0.53	0.8259	0.8723	0.9468	0.8480	0.1624	1.2865	0.5649
0.54	0.8201	0.8679	0.9449	0.8417	0.1674	1.2703	0.5750
0.55	0.8142	0.8634	0.9430	0.8352	0.1724	1.2549	0.5851
0.56	0.8082	0.8589	0.9410	0.8285	0.1774	1.2403	0.5951
0.57	0.8022	0.8544	0.9390	0.8216	0.1825	1.2263	0.6051
0.58	0.7962	0.8498	0.9370	0.8146	0.1875	1.2130	0.6150
0.59	0.7901	0.8451	0.9349	0.8074	0.1925	1.2003	0.6249
0.60	0.7840	0.8405	0.9328	0.8000	0.1976	1.1882	0.6348
0.61	0.7778	0.8357	0.9307	0.7924	0.2026	1.1767	0.6447
0.62	0.7716	0.8310	0.9286	0.7846	0.2076	1.1656	0.6545
0.63	0.7654	0.8262	0.9265	0.7766	0.2127	1.1552	0.6643
0.64	0.7591	0.8213	0.9243	0.7684	0.2177	1.1451	0.6740
0.65	0.7528	0.8164	0.9221	0.7599	0.2226	1.1356	0.6837
0.66	0.7465	0.8115	0.9199	0.7513	0.2276	1.1265	0.6934
0.67	0.7401	0.8066	0.9176	0.7424	0.2326	1.1179	0.7031
0.68	0.7338	0.8016	0.9153	0.7332	0.2375	1.1097	0.7127
0.69	0.7274	0.7966	0.9131	0.7238	0.2424	1.1018	0.7223
0.70	0.7209	0.7916	0.9107	0.7141	0.2473	1.0944	0.7318
0.71	0.7145	0.7865	0.9084	0.7042	0.2521	1.0873	0.7413
0.72	0.7080	0.7814	0.9061	0.6940	0.2569	1.0806	0.7508
0.73	0.7016	0.7763	0.9037	0.6834	0.2617	1.0742	0.7602
0.74	0.6951	0.7712	0.9013	0.6726	0.2664	1.0681	0.7696
0.75	0.6886	0.7660	0.8989	0.6614	0.2711	1.0624	0.7789
0.76	0.6821	0.7609	0.8964	0.6499	0.2758	1.0570	0.7883
0.77	0.6756	0.7557	0.8940	0.6380	0.2804	1.0519	0.7975
0.78	0.6691	0.7505	0.8915	0.6258	0.2849	1.0471	0.8068
0.79	0.6625	0.7452	0.8890	0.6131	0.2894	1.0425	0.8160
0.80	0.6560	0.7400	0.8865	0.6000	0.2939	1.0382	0.8251
0.81	0.6495	0.7347	0.8840	0.5864	0.2983	1.0342	0.8343
0.82	0.6430	0.7295	0.8815	0.5724	0.3026	1.0305	0.8433
0.83	0.6365	0.7242	0.8789	0.5578	0.3069	1.0270	0.8524
0.84	0.6300	0.7189	0.8763	0.5426	0.3112	1.0237	0.8614
0.85	0.6235	0.7136	0.8737	0.5268	0.3153	1.0207	0.8704
0.86	0.6170	0.7083	0.8711	0.5103	0.3195	1.0179	0.8793
0.87	0.6106	0.7030	0.8685	0.4931	0.3235	1.0153	0.8882
0.88	0.6041	0.6977	0.8659	0.4750	0.3275	1.0129	0.8970
0.89	0.5977	0.6924	0.8632	0.4560	0.3314	1.0108	0.9058
0.90	0.5913	0.6870	0.8606	0.4359	0.3352	1.0089	0.9146
0.91	0.5849	0.6817	0.8579	0.4146	0.3390	1.0071	0.9233
0.92	0.5785	0.6764	0.8552	0.3919	0.3427	1.0056	0.9320
0.93	0.5721	0.6711	0.8525	0.3676	0.3464	1.0043	0.9407
0.94	0.5658	0.6658	0.8498	0.3412	0.3499	1.0031	0.9493
0.95	0.5595	0.6604	0.8471	0.3122	0.3534	1.0021	0.9578
0.96	0.5532	0.6551	0.8444	0.2800	0.3569	1.0014	0.9663
0.97	0.5469	0.6498	0.8416	0.2431	0.3602	1.0008	0.9748
0.98	0.5407	0.6445	0.8389	0.1990	0.3635	1.0003	0.9833
0.99	0.5345	0.6392	0.8361	0.1411	0.3667	1.0001	0.9916