第九章 习题解答
9-1
???13.5?T?c，p0?p1?0?T0?T1?2cp?T1?21?T??p1?0?
?T1?1002?298 K， c1?100m/s，T0?293?2020?298?p0?0.1???293?3.5?0.106 MPa
3002?337.6 K， c1?300m/s，T0?293?2020?337.6?p0?0.1???0.164 MPa
293??5002?416.8 K， c1?500m/s，T0?293?2020?416.8?p0?0.1???0.343 MPa
293??10002?788 K， c1?1000m/s，T0?293?20203.53.5?788?p0?0.1???293?9-2
3.5?3.190 MPa
?p?T2?T1?2??p1???1??0.2??473???0.3?1.4?11.4?421.2 K
c2?2cp?T1?T2??2?1010?473?421.2??323.5 m/s
v2?RT2287?421.2??0.6044 m3/kg 6p20.2?10?21?0.6044mv??1.868?10?3 m2 c2323.5f2?工程热力学 41
9-3
pc??p1?0.528?2.5?1.32 MPa ? pB ∴p2?pB?1.5 MPa
?p??1.5?T2?T1?2??353??305.1 K ??2.5??p1?RT287?305.13v2?2??0.0584 m/kg 6p21.5?10c2?2cp?T1?T2??2?1010?353?305.1??311 m/s
??1?1.4?11.4f2c21?10?4?311??m??0.533 kg/s
v20.05849-4
pc??p1?0.528?2.5?1.32 MPa ? pB ∴p2?pc?1.32 MPa
?p??1.32?T2?T1?2??353??294.1 K ??2.5??p1?RT287?294.13v2?2??0.0639 m/kg 6p21.32?10??1?1.4?11.4c2?cc??RTc?1.4?287?294.1?343.8 m/s f2c21?10?4?343.8??m??0.538 kg/s
v20.06399-5
pc??p1?0.528?0.7?0.37MPa （1）p2?0.5 MPa ? pc，采用渐缩喷管
??1?1.4?11.4?p2??0.5?T2?T1???1220??1108 K ?p0.7???1?RT287?1108v2?2??0.636 m3/kg 6p20.5?10c2?2cp?T1?T2??2?1010?1220?1108??475.6 m/s
f2??20.5?0.636mv??6.68?10?4 m2 c2475.642
工程热力学
（2）p2?0.12 MPa ? pc，采用渐缩渐扩喷管
?p??0.12?T2?T1?2??1220??737 K ??0.7??p1?RT287?737v2?2??1.763 m3/kg 6p20.12?10c2?2cp?T1?T2??2?1010?1220?737??987.8 m/s
??1?1.4?11.4f2??20.5?1.763mv??8.92?10?4 m2 c2987.8RT1287?373??0.714 m3/kg 6p10.15?10f1c10.1?100??14.01 kg/s v10.714f2c20.1?171.4??1.223 m3/kg ?m14.019-6
（1）v1???m（2）v2?p2v20.14?106?1.223T2???596.8 K
R287（3）9-7
?p?T2?T1?Q??H?mc ?14.01?1.01??596.8?373??3167 kW
pc??p1?0.528?0.5?0.264 MPa?p2，采用渐缩渐扩喷管
?p??0.1?（1）T2?T1?2??600??379 K ?p0.5???1?RT287?379v2?2??1.088 m3/kg 6p20.1?10c2?2cp?T1?T2??2?1010?600?379??668.1 m/s
??1?1.4?11.4f2??21.5?1.088mv??0.00244 m2 c2668.143
工程热力学
（2）T2??T1??n?T1?T2??600?0.95?600?379??390 K
v2??RT2?287?3903??1.119 m/kg 6p20.1?10c2??2cp?T1?T2???2?1010?600?390??651.3 m/s
f2???2?1.5?1.119mv??0.00258 m2 c2?651.39-8 由题意得：T1?300 K，p1?784.6kPa
p2??p1?0.528?784.6?414.3 kPa
?p??0.4143?T2?T1?2??300???249.96 K ?p0.7846???1?c2?2cp?T1?T2??2000??300?249.96??316.4m/s RT2287?249.963??0.1732 m/kg 6p20.4143?1011f2??d2??3.14?0.032?7.07?10?4 m2
44f2c27.07?10?4?316.4??m??1.292 kg/s
v20.1732??mRT?1.292?287?300?3600?4083.5 m3/h Vp98070??11.36?1cp??1000?264.7 J/kg?K 9-9 R??1.36v2???1?1.4?11.4????0.535 ???????1??1.36?1?（1）pc??p1?0.535?1?0.535 MPa
1.36?1?pc?Tc?T1???1000?0.5351.36?847.4 K
?p1?RT264.7?847.43vc?c??0.4193 m/kg 6pc0.535?10?2????1?2?1.361.36?1??1?cc??RTc?1.36?264.7?847.4?552.3 m/s
?mv5?0.4193fmin?c??0.00380 m2
cc552.3工程热力学
44
?p??0.1?（2）T2?T1?2??1000???543.6 K ?p1???1?T2??T1??n?T1?T2??1000?0.95?1000?543.6??566.4 K
v2??RT2?264.7?566.43??1.50 m/kg 6p20.1?10?2?5?1.50mv??0.00805 m2 c2?931.21f2?fmin?0.398 m ?tg5??1?1.36?11.36c2??2cp?T1?T2???2?1000?1000?566.4??931.2 m/s
f2??（3）取顶锥角??10?，渐扩部分长度l：
l?d2?dmin2tg????2c9-10 由M?得：
a2cp?T0?T1??RT1?T1?p1?p0???T0??2000??350?T1?1.4?287?T11.41.4?1?0.6?T1?326.4 K
???1?326.4??0.65????350??0.51 MPa
c1?2cp?T0?T1??2000??350?326.4??217.3 m/s
pc??p0?0.528?0.65?0.3432MPa > 0.28MPa ∴p2?0.3432 MPa
T2?T0???1??350?0.5281.4?11.4?291.6 K
c2?2cp?T0?T2??2000??350?291.62??341.7m/s
??∵mf1c1f2c2RTRT?，又：v1?1，v2?2 v1v2p1p2f1c1T2p12.6?10?3?217.3?291.6?0.51f2???2.195?10?3 m2
p2T1c20.3432?326.4?341.7工程热力学
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