A convergente−divergent nozzle is operating under off-design conditions, resulting in the presence of a shock wave in the diverging portion. A reservoir containing air at 400 kPa and 800 K supplies the nozzle, whose throat area is 0.2 m². The Mach number upstream of the shock is M1 = 2.44. The area

Question

A convergente−divergent nozzle is operating under off-design conditions, resulting in the presence of a shock wave in the diverging portion. A reservoir containing air at 400 kPa and 800 K supplies the nozzle, whose throat area is 0.2 m². The Mach number upstream of the shock is [latex]M_1[/latex] = 2.44. The area at the nozzle exit is 0.7 m². Find the area at the location of the shock and the exit temperature.

Accepted Answer

Figure 15.14 shows the profile of the nozzle, where sections 1 and 2 represent conditions across the shock. As a shock wave can exist only in a supersonic stream, we know that sonic conditions are reached at the throat, and the throat area equals the critical area A*. The values given are therefore:

[latex]p_0=400 \mathrm{kPa},T_0=800 K,A_{ ext{throat}}=A_1^*=0.2 \mathrm{m}^2,M_1=2.44,\quad ext{ and }\quad A_3=0.7 \mathrm{m}^2[/latex].

Note that A* is constant upstream of the shock because the flow isentropic there; this is why [latex]A_{ ext{throat}}=A_1{^{*}}[/latex].

The technique of solving this problem is to proceed downstream from the given stagnation conditions. For [latex]M_1=2.44[/latex], the isentropic table Table 15.1 gives:

[latex]A_1/A^{*}_{1}=2.5 ,[/latex] so that [latex]A_1=A_2=(2.5)(0.2)=0.5 m^2[/latex].

TABLE 15.1 Isentropic Flow of a Perfect Gas (γ = 1.4)
M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*	M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*
0	1	1	1	∞	0.62	0.7716	0.831	0.9286	1.1656
0.02	0.9997	0.9998	0.9999	28.9421	0.64	0.7591	0.8213	0.9243	1.1451
0.04	0.9989	0.9992	0.9997	14.4815	0.66	0.7465	0.8115	0.9199	1.1265
0.06	0.9975	0.9982	0.9993	9.6659	0.68	0.7338	0.8016	0.9153	1.1097
0.08	0.9955	0.9968	0.9987	7.2616	0.7	0.7209	0.7916	0.9107	1.0944
0.1	0.993	0.995	0.998	5.8218	0.72	0.708	0.7814	0.9061	1.0806
0.12	0.99	0.9928	0.9971	4.8643	0.74	0.6951	0.7712	0.9013	1.0681
0.14	0.9864	0.9903	0.9961	4.1824	0.76	0.6821	0.7609	0.8964	1.057
0.16	0.9823	0.9873	0.9949	3.6727	0.78	0.669	0.7505	0.8915	1.0471
0.18	0.9776	0.984	0.9936	3.2779	0.8	0.656	0.74	0.8865	1.0382
0.2	0.9725	0.9803	0.9921	2.9635	0.82	0.643	0.7295	0.8815	1.0305
0.22	0.9668	0.9762	0.9904	2.7076	0.84	0.63	0.7189	0.8763	1.0237
0.24	0.9607	0.9718	0.9886	2.4956	0.86	0.617	0.7083	0.8711	1.0179
0.26	0.9541	0.967	0.9867	2.3173	0.88	0.6041	0.6977	0.8659	1.0129
0.28	0.947	0.9619	0.9846	2.1656	0.9	0.5913	0.687	0.8606	1.0089
0.3	0.9395	0.9564	0.9823	2.0351	0.92	0.5785	0.6764	0.8552	1.0056
0.32	0.9315	0.9506	0.9799	1.9219	0.94	0.5658	0.6658	0.8498	1.0031
0.34	0.9231	0.9445	0.9774	1.8229	0.96	0.5532	0.6551	0.8444	1.0014
0.36	0.9143	0.938	0.9747	1.7358	0.98	0.5407	0.6445	0.8389	1.0003
0.38	0.9052	0.9313	0.9719	1.6587	1	0.5283	0.6339	0.8333	1
0.4	0.8956	0.9243	0.969	1.5901	1.02	0.516	0.6234	0.8278	1.0003
0.42	0.8857	0.917	0.9659	1.5289	1.04	0.5039	0.6129	0.8222	1.0013
0.44	0.8755	0.9094	0.9627	1.474	1.06	0.4919	0.6024	0.8165	1.0029
0.46	0.865	0.9016	0.9594	1.4246	1.08	0.48	0.592	0.8108	1.0051
0.48	0.8541	0.8935	0.9559	1.3801	1.1	0.4684	0.5817	0.8052	1.0079
0.5	0.843	0.8852	0.9524	1.3398	1.12	0.4568	0.5714	0.7994	1.0113
0.52	0.8317	0.8766	0.9487	1.3034	1.14	0.4455	0.5612	0.7937	1.0153
0.54	0.8201	0.8679	0.9449	1.2703	1.16	0.4343	0.5511	0.7879	1.0198
0.56	0.8082	0.8589	0.941	1.2403	1.18	0.4232	0.5411	0.7822	1.0248
0.58	0.7962	0.8498	0.937	1.213	1.2	0.4124	0.5311	0.7764	1.0304
0.6	0.784	0.8405	0.9328	1.1882	1.22	0.4017	0.5213	0.7706	1.0366
TABLE 15.1 Isentropic Flow of a Perfect Gas (γ = 1.4)-cont'd
M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*	M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*
1.24	0.3912	0.5115	0.7648	1.0432	1.88	0.1539	0.2627	0.5859	1.5308
1.26	0.3809	0.5019	0.759	1.0504	1.9	0.1492	0.257	0.5807	1.5553
1.28	0.3708	0.4923	0.7532	1.0581	1.92	0.1447	0.2514	0.5756	1.5804
1.3	0.3609	0.4829	0.7474	1.0663	1.94	0.1403	0.2459	0.5705	1.6062
1.32	0.3512	0.4736	0.7416	1.075	1.96	0.136	0.2405	0.5655	1.6326
1.34	0.3417	0.4644	0.7358	1.0842	1.98	0.1318	0.2352	0.5605	1.6597
1.36	0.3323	0.4553	0.73	1.094	2	0.1278	0.23	0.5556	1.6875
1.38	0.3232	0.4463	0.7242	1.1042	2.02	0.1239	0.225	0.5506	1.716
1.4	0.3142	0.4374	0.7184	1.1149	2.04	0.1201	0.22	0.5458	1.7451
1.42	0.3055	0.4287	0.7126	1.1262	2.06	0.1164	0.2152	0.5409	1.775
1.44	0.2969	0.4201	0.7069	1.1379	2.08	0.1128	0.2104	0.5361	1.8056
1.46	0.2886	0.4116	0.7011	1.1501	2.1	0.1094	0.2058	0.5313	1.8369
1.48	0.2804	0.4032	0.6954	1.1629	2.12	0.106	0.2013	0.5266	1.869
1.5	0.2724	0.395	0.6897	1.1762	2.14	0.1027	0.1968	0.5219	1.9018
1.52	0.2646	0.3869	0.684	1.1899	2.16	0.0996	0.1925	0.5173	1.9354
1.54	0.257	0.3789	0.6783	1.2042	2.18	0.0965	0.1882	0.5127	1.9698
1.56	0.2496	0.371	0.6726	1.219	2.2	0.0935	0.1841	0.5081	2.005
1.58	0.2423	0.3633	0.667	1.2344	2.22	0.0906	0.18	0.5036	2.0409
1.6	0.2353	0.3557	0.6614	1.2502	2.24	0.0878	0.176	0.4991	2.0777
1.62	0.2284	0.3483	0.6558	1.2666	2.26	0.0851	0.1721	0.4947	2.1153
1.64	0.2217	0.3409	0.6502	1.2836	2.28	0.0825	0.1683	0.4903	2.1538
1.66	0.2151	0.3337	0.6447	1.301	2.3	0.08	0.1646	0.4859	2.1931
1.68	0.2088	0.3266	0.6392	1.319	2.32	0.0775	1.1609	0.4816	2.2333
1.7	0.2026	0.3197	0.6337	1.3376	2.34	0.0751	0.1574	0.4773	2.2744
1.72	0.1966	0.3129	0.6283	1.3567	2.36	0.0728	0.1539	0.4731	2.3164
1.74	0.1907	0.3062	0.6229	1.3764	2.38	0.0706	0.1505	0.4688	2.3593
1.76	0.185	0.2996	0.6175	1.3967	2.4	0.0684	0.1472	0.4647	2.4031
1.78	0.1794	0.2931	0.6121	1.4175	2.42	0.0663	0.1439	0.4606	2.4479
1.8	0.174	0.2868	0.6068	1.439	2.44	0.0643	0.1408	0.4565	2.4936
1.82	0.1688	0.2806	0.6015	1.461	2.46	0.0623	0.1377	0.4524	2.5403
1.84	0.1637	0.2745	0.5963	1.4836	2.48	0.0604	0.1346	0.4484	2.588
1.86	0.1587	0.2686	0.591	1.5069	2.5	0.0585	0.1317	0.4444	2.6367
TABLE 15.1 Isentropic Flow of a Perfect Gas (γ = 1.4)-cont'd
M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*	M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*
2.52	0.0567	0.1288	0.4405	2.6865	3.16	0.0215	0.0643	0.3337	4.9304
2.54	0.055	0.126	0.4366	2.7372	3.18	0.0208	0.063	0.3309	5.0248
2.56	0.0533	0.1232	0.4328	2.7891	3.2	0.0202	0.0617	0.3281	5.121
2.58	0.0517	0.1205	0.4289	2.842	3.22	0.0196	0.0604	0.3253	5.2189
2.6	0.0501	0.1179	0.4252	2.896	3.24	0.0191	0.0591	0.3226	5.3186
2.62	0.0486	0.1153	0.4214	2.9511	3.26	0.0185	0.0579	0.3199	5.4201
2.64	0.0471	0.1128	0.4177	3.0073	3.28	0.018	0.0567	0.3173	5.5234
2.66	0.0457	0.1103	0.4141	3.0647	3.3	0.0175	0.0555	0.3147	5.6286
2.68	0.0443	0.1079	0.4104	3.1233	3.32	0.017	0.0544	0.3121	5.7358
2.7	0.043	0.1056	0.4068	3.183	3.34	0.0165	0.0533	0.3095	5.8448
2.72	0.0417	0.1033	0.4033	3.244	3.36	0.016	0.0522	0.3069	5.9558
2.74	0.0404	0.101	0.3998	3.3061	3.38	0.0156	0.0511	0.3044	6.0687
2.76	0.0392	0.0989	0.3963	3.3695	3.4	0.0151	0.0501	0.3019	6.1837
2.78	0.038	0.0967	0.3928	3.4342	3.42	0.0147	0.0491	0.2995	6.3007
2.8	0.0368	0.0946	0.3894	3.5001	3.44	0.0143	0.0481	0.297	6.4198
2.82	0.0357	0.0926	0.386	3.5674	3.46	0.0139	0.0471	0.2946	6.5409
2.84	0.0347	0.0906	0.3827	3.6359	3.48	0.0135	0.0462	0.2922	6.6642
2.86	0.0336	0.0886	0.3794	3.7058	3.5	0.0131	0.0452	0.2899	6.7896
2.88	0.0326	0.0867	0.3761	3.7771	3.52	0.0127	0.0443	0.2875	6.9172
2.9	0.0317	0.0849	0.3729	3.8498	3.54	0.0124	0.0434	0.2852	7.0471
2.92	0.0307	0.0831	0.3696	3.9238	3.56	0.012	0.0426	0.2829	7.1791
2.94	0.0298	0.0813	0.3665	3.9993	3.58	0.0117	0.0417	0.2806	7.3135
2.96	0.0289	0.0796	0.3633	4.0763	3.6	0.0114	0.0409	0.2784	7.4501
2.98	0.0281	0.0779	0.3602	4.1547	3.62	0.0111	0.0401	0.2762	7.5891
3	0.0272	0.0762	0.3571	4.2346	3.64	0.0108	0.0393	0.274	7.7305
3.02	0.0264	0.0746	0.3541	4.316	3.66	0.0105	0.0385	0.2718	7.8742
3.04	0.0256	0.073	0.3511	4.399	3.68	0.0102	0.0378	0.2697	8.0204
3.06	0.0249	0.0715	0.3481	4.4835	3.7	0.0099	0.037	0.2675	8.1691
3.08	0.0242	0.07	0.3452	4.5696	3.72	0.0096	0.0363	0.2654	8.3202
3.1	0.0234	0.0685	0.3422	4.6573	3.74	0.0094	0.0356	0.2633	8.4739
3.12	0.0228	0.0671	0.3393	4.7467	3.76	0.0091	0.0349	0.2613	8.6302
3.14	0.0221	0.0657	0.3365	4.8377	3.78	0.0089	0.0342	0.2592	8.7891
TABLE 15.1 Isentropic Flow of a Perfect Gas (γ = 1.4)-cont'd
M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*	M	[latex]p/p_0[/latex]	[latex] ho/ ho_0[/latex]	[latex]T/T_0[/latex]	A/A*
3.8	0.0086	0.0335	0.2572	8.9506	4.42	0.0038	0.0187	0.2038	15.4724
3.82	0.0084	0.0329	0.2552	9.1148	4.44	0.0037	0.0184	0.2023	15.7388
3.84	0.0082	0.0323	0.2532	0.2817	4.46	0.0036	0.0181	0.2009	16.0092
3.86	0.008	0.0316	0.2513	9.4513	4.48	0.0035	0.0178	0.1994	16.2837
3.88	0.0077	0.031	0.2493	9.6237	4.5	0.0035	0.0174	0.198	16.5622
3.9	0.0075	0.0304	0.2474	9.799	4.52	0.0034	0.0171	0.1966	16.8449
3.92	0.0073	0.0299	0.2455	9.9771	4.54	0.0033	0.0168	0.1952	17.1317
3.94	0.0071	0.0293	0.2436	10.1581	4.56	0.0032	0.0165	0.1938	17.4228
3.96	0.0069	0.0287	0.2418	10.342	4.58	0.0031	0.0163	0.1925	17.7181
3.98	0.0068	0.0282	0.2399	10.5289	4.6	0.0031	0.016	0.1911	18.0178
4	0.0066	0.0277	0.2381	10.7188	4.62	0.003	0.0157	0.1898	18.3218
4.02	0.0064	0.0271	0.2363	10.9117	4.64	0.0029	0.0154	0.1885	18.6303
4.04	0.0062	0.0266	0.2345	11.1077	4.66	0.0028	0.0152	0.1872	18.9433
4.06	0.0061	0.0261	0.2327	11.3068	4.68	0.0028	0.0149	0.1859	19.2608
4.08	0.0059	0.0256	0.231	11.5091	4.7	0.0027	0.0146	0.1846	19.5828
4.1	0.0058	0.0252	0.2293	11.7147	4.72	0.0026	0.0144	0.1833	19.9095
4.12	0.0056	0.0247	0.2275	11.9234	4.74	0.0026	0.0141	0.182	20.2409
4.14	0.0055	0.0242	0.2258	12.1354	4.76	0.0025	0.0139	0.1808	20.577
4.16	0.0053	0.0238	0.2242	12.3508	4.78	0.0025	0.0137	0.1795	20.9179
4.18	0.0052	0.0234	0.2225	12.5695	4.8	0.0024	0.0134	0.1783	21.2637
4.2	0.0051	0.0229	0.2208	12.7916	4.82	0.0023	0.0132	0.1771	21.6144
4.22	0.0049	0.0225	0.2192	13.0172	4.84	0.0023	0.013	0.1759	21.97
4.24	0.0048	0.0221	0.2176	13.2463	4.86	0.0022	0.0128	0.1747	22.3306
4.26	0.0047	0.0217	0.216	13.4789	4.88	0.0022	0.0125	0.1735	22.6963
4.28	0.0046	0.0213	0.2144	13.7151	4.9	0.0021	0.0123	0.1724	23.0671
4.3	0.0044	0.0209	0.2129	13.9549	4.92	0.0021	0.0121	0.1712	23.4431
4.32	0.0043	0.0205	0.2113	14.1984	4.94	0.002	0.0119	0.17	23.8243
4.34	0.0042	0.0202	0.2098	14.4456	4.96	0.002	0.0117	0.1689	24.2109
4.36	0.0041	0.0198	0.2083	14.6965	4.98	0.0019	0.0115	0.1678	24.6027
4.38	0.004	0.0194	0.2067	14.9513	5	0.0019	0.0113	0.1667	25
4.4	0.0039	0.0191	0.2053	15.2099

This is the nozzle’s cross-section area at the location of the shock. For [latex]M_1=2.44[/latex], the normal shock Table 15.2 gives:

TABLE 15.2 One-Dimensional Normal-Shock Relations (γ = 1.4)
[latex]M_1[/latex]	[latex]M_2[/latex]	[latex]p_2/p_1[/latex]	[latex]T_2/T_1[/latex]	[latex](p_0)_2/(p_0)_1[/latex]	[latex]M_1[/latex]	[latex]M_2[/latex]	[latex]p_2/p_1[/latex]	[latex]T_2/T_1[/latex]	[latex](p_0)_2/(p_0)_1[/latex]
1	1	1	1	1	1.62	0.663	2.895	1.402	0.888
1.02	0.98	1.047	1.013	1	1.64	0.657	2.971	1.416	0.88
1.04	0.962	1.095	1.026	1	1.66	0.651	3.048	1.43	0.872
1.06	0.944	1.144	1.039	1	1.68	0.646	3.126	1.444	0.864
1.08	0.928	1.194	1.052	0.999	1.7	0.641	3.205	1.458	0.856
1.1	0.912	1.245	1.065	0.999	1.72	0.635	3.285	1.473	0.847
1.12	0.896	1.297	1.078	0.998	1.74	0.631	3.366	1.487	0.839
1.14	0.882	1.35	1.09	0.997	1.76	0.626	3.447	1.502	0.83
1.16	0.868	1.403	1.103	0.996	1.78	0.621	3.53	1.517	0.821
1.18	0.855	1.458	1.115	0.995	1.8	0.617	3.613	1.532	0.813
1.2	0.842	1.513	1.128	0.993	1.82	0.612	3.698	1.547	0.804
1.22	0.83	1.57	1.14	0.991	1.84	0.608	3.783	1.562	0.795
1.24	0.818	1.627	1.153	0.988	1.86	0.604	3.869	1.577	0.786
1.26	0.807	1.686	1.166	0.986	1.88	0.6	3.957	1.592	0.777
1.28	0.796	1.745	1.178	0.983	1.9	0.596	4.045	1.608	0.767
1.3	0.786	1.805	1.191	0.979	1.92	0.592	4.134	1.624	0.758
1.32	0.776	1.866	1.204	0.976	1.94	0.588	4.224	1.639	0.749
1.34	0.766	1.928	1.216	0.972	1.96	0.584	4.315	1.655	0.74
1.36	0.757	1.991	1.229	0.968	1.98	0.581	4.407	1.671	0.73
1.38	0.748	2.055	1.242	0.963	2	0.577	4.5	1.688	0.721
1.4	0.74	2.12	1.255	0.958	2.02	0.574	4.594	1.704	0.711
1.42	0.731	2.186	1.268	0.953	2.04	0.571	4.689	1.72	0.702
1.44	0.723	2.253	1.281	0.948	2.06	0.567	4.784	1.737	0.693
1.46	0.716	2.32	1.294	0.942	2.08	0.564	4.881	1.754	0.683
1.48	0.708	2.389	1.307	0.936	2.1	0.561	4.978	1.77	0.674
1.5	0.701	2.458	1.32	0.93	2.12	0.558	5.077	1.787	0.665
1.52	0.694	2.529	1.334	0.923	2.14	0.555	5.176	1.805	0.656
1.54	0.687	2.6	1.347	0.917	2.16	0.553	5.277	1.822	0.646
1.56	0.681	2.673	1.361	0.91	2.18	0.55	5.378	1.837	0.637
1.58	0.675	2.746	1.374	0.903	2.2	0.547	5.48	1.857	0.628
1.6	0.668	2.82	1.388	0.895	2.22	0.544	5.583	1.875	0.619
TABLE 15.2 One-Dimensional Normal-Shock Relations (γ = 1.4)−cont'd
[latex]M_1[/latex]	[latex]M_2[/latex]	[latex]p_2/p_1[/latex]	[latex]T_2/T_1[/latex]	[latex](p_0)_2/(p_0)_1[/latex]	[latex]M_1[/latex]	[latex]M_2[/latex]	[latex]p_2/p_1[/latex]	[latex]T_2/T_1[/latex]	[latex](p_0)_2/(p_0)_1[/latex]
2.24	0.542	5.687	1.892	0.61	2.64	0.5	7.965	2.28	0.445
2.26	0.539	5.792	1.91	0.601	2.66	0.499	8.088	2.301	0.438
2.28	0.537	5.898	1.929	0.592	2.68	0.497	8.213	2.322	0.431
2.3	0.534	6.005	1.947	0.583	2.7	0.496	8.338	2.343	0.424
2.32	0.532	6.113	1.965	0.575	2.72	0.494	8.465	2.364	0.417
2.34	0.53	6.222	1.984	0.566	2.74	0.493	8.592	2.386	0.41
2.36	0.527	6.331	2.003	0.557	2.76	0.491	8.721	2.407	0.403
2.38	0.525	6.442	2.021	0.549	2.78	0.49	8.85	2.429	0.396
2.4	0.523	6.553	2.04	0.54	2.8	0.488	8.98	2.451	0.389
2.42	0.521	6.666	2.06	0.532	2.82	0.487	9.111	2.473	0.383
2.44	0.519	6.779	2.079	0.523	2.84	0.485	9.243	2.496	0.376
2.46	0.517	6.894	2.098	0.515	2.86	0.484	9.376	2.518	0.37
2.48	0.515	7.009	2.118	0.507	2.88	0.483	9.51	2.541	0.364
2.5	0.513	7.125	2.138	0.499	2.9	0.481	9.645	2.563	0.358
2.52	0.511	7.242	2.157	0.491	2.92	0.48	9.781	2.586	0.352
2.54	0.509	7.36	2.177	0.483	2.94	0.479	9.918	2.609	0.346
2.56	0.507	7.479	2.198	0.475	2.96	0.478	10.055	2.632	0.34
2.58	0.506	7.599	2.218	0.468	2.98	0.476	10.194	2.656	0.334
2.6	0.504	7.72	2.238	0.46	3	0.475	10.333	2.679	0.328
2.62	0.502	7.842	2.26	0.453

[latex]M_2=0.519,\quad ext{and}\quad p_{02}/p_{01}=0.523[/latex].

There is no loss of stagnation pressure up to section 1, so [latex]p_{01}=p_0[/latex], which implies:

[latex]p_{02}=0.523 p_0=0.523(400)=209.2 \mathrm{kPa}[/latex]

The value of A* changes across a shock wave. The ratio [latex]A_2/A_2{^*}[/latex] can be found from the isentropic table (Table 15.1) corresponding to a Mach number of [latex]M_2=0.519[/latex]. (Note that [latex]A_2{^*}[/latex] simply denotes the area that would be reached if the flow from state 2 were accelerated isentropically to sonic conditions.) For [latex]M_2=0.519[/latex], Table 15.1 gives:

[latex]A_2 / A_2^*=1.3, ext{ which leads to }A_2^*=A_2/1.3=0.5/1.3=0.3846 \mathrm{m}^2[/latex],

The flow from section 2 to section 3 is isentropic, during which A* remains constant, so:

[latex]A_3 / A_3^*=A_3 / A_2^*=0.7 / 0.3846=1.82[/latex].

Now find the conditions at the nozzle exit from the isentropic table (Table 15.1). However, the value of A/A* = 1.82 may be found either in the supersonic or the subsonic branch of the table. Since the flow downstream of a normal shock can only be subsonic, use the subsonic branch. For A/A* = 1.82, Table 15.1 gives:

[latex]T_3 / T_{03}=0.977[/latex].

The stagnation temperature remains constant in an adiabatic process, so that [latex]T_{03}=T_0[/latex]. Thus:

[latex]T_3=0.977(800)=782 K[/latex].

Question 15.5: A convergente−divergent nozzle is operating under off-design...

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