Consider two different points on the surface of an airplane wing flying at 80 m/s. The pressure coefficient and flow velocity at point 1 are -1.5 and 110 m/s, respectively. The pressure coefficient at point 2 is -0.8. Assuming incompressible flow, calculate the flow velocity at point 2.
Consider two different points on the surface of an airplane wing flying at 80 m/s. The pressure coefficient and flow velocity at point 1 are -1.5 and 110 m/s, respectively. The pressure coefficient at point 2 is -0.8. Assuming incompressible flow, calculate the flow velocity at point 2.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:• Consider two different points on the surface of an airplane
wing flying at 80 m/s. The pressure coefficient and flow
velocity at point 1 are 1.5 and 110 m/s, respectively. The
pressure coefficient at point 2 is -0.8. Assuming
incompressible flow, calculate the flow velocity at point 2.
![Table B.2 Properties of the International Standard Atmosphere (ISA) between sea level and 20 km
geopotential altitude
9,000
9,500
Standard values at altitude
P (Pa)
8
Alt. (m)
T (K)
0
288.15 1 340.29
500 284.90 0.9887 338.37
1,000 281.65 0.9774 336.43
1,500 278.40 0.9662 334.49
2,000 275.15 0.9549 332.53
2,500 271.90 0.9436 330.56
3,000 268.65 0.9306 328.58
3,500 265.40 0.9210
326.58
4,000 262.15 0.9098 324.58
4,500 258.90 0.8985 322.56
255.65 0.8872 320.53
252.40 0.8759 318.48
249.15 0.8647 316.43
6,500
245.90 0.8534 314.36
7,000 242.65 0.8421 312.27
310.17
308.06
5,000
5,500
6,000
7,500 239.40 0.8308
8,000 236.15 0.8195
8,500
305.93
33,099
41,060 0.4052 0.5895 0.4812
38,251 0.3775 0.5566 0.4544
35,599 0.3513 0.5252
232.90 0.8083
0.3267
0.4951
229.65
0.7970 303.79
30,742 0.3040 0.4663
226.40 0.7857 301.63 28,523 0.2815 0.4389
0.4127
0.3877
10,000
0.3639
0.2655
0.2268
0.1851
223.15
0.7744
299.46 26,436 0.2609
10,500 219.90 0.7631 297.27 24,474 0.2415
11,000 216.65 0.7519 295.07 22,632 0.2234
12,000 216.65 0.7519 295.07 19,330 0.1908 0.3108
13,000 216.65 0.7519 295.07 16,510 0.1629
14,000 216.65 0.,7519 295.07 14,101 0.1392
15,000 216.65 0.7519 295.07 12,044 0.1189 0.1937 0.1581
16,000 216.65 0.7519 295.07 10,287 0.1015 0.1654 0.1350
17,000 216.65 0.7519 295.07 8,786 0.0867 0.1413 0.1153
18,000 216.65 0.7519 295.07 7,505 0.0741 0.1207 0.0985
19,000 216.65 0.7519 295.07 6,410 0.0633 0.1031 0.0842
20,000
216.65 0.7519 295.07 5,475 0.0540 0.0880 0.0718
0
a (m/s)
p (kg/m³) 0
μ/1₂
1
1
1.2250
1.1673 0.9529 0.9912
1.1117 0.9075 0.9823
1.0581 0.8638 0.9735
1.0065 0.8216 0.9645
0.9569 0.7811 0.9556
0.9091 0.7421 0.9465
0.8632 0.7055
101,325 1
95,461 0.9421
89,874 0.8870
84,556 0.8345
79,495
0.7846
74,682 0.7371
70,108 0.6919
65,764 0.6490
61,640 0.6083
57,728 0.5697
54,020 0.5331
50,506 0.4985 0.6971 0.5691 0.9006
47,181 0.4656 0.6597 0.5385
44,034 0.4346 0.6238 0.5092
0.9099
0.8191 0.6686
0.7768 0.6341
0.7361 0.6009
0.9375
0.9283
0.9191
0.2537
0.2167
P₁A₁V₁ = P₂A₂V₂
V
P₂+PZ=P₁+PZ
P/= P₁
V²
C₂T₁+2=C₂T₂+
0.8911 V₂ =
0.8818
0.8724
0.8628
0.4287 0.8532
0.4042 0.8436
0.3807 0.8339
0.3583 0.8241
0.8143
0.3369
0.3165
0.8044
0.2971
0.7944
p=pRT
a = √√YRT
V₁ =
Advanced Aircraft Design: Conceptual Design. Analysis and Optimization of Subsonic Civil Airplanes. First Edition. Egbert Torenbeck.
2013 by Tighert Torenbeek. Published 2013 by John Wiley & Sons, Lad.
C₂ =
h = c₂T
e = c₂T
P₂
P₁
Poz
P₁
=
0.7944
0.7944 M
0.7944
2(P₁-P₂)
√P[1-(A₂/A₂)²)
2(Po-P)
P
2(Po-P)
Ps
YR
Y-1
-) =)"
Y/(-1)
17/(-1).
(y + 1)²M
[4YM-2(y-1)]
2 (P₂)(x-1)/y
0.7944
0.7944
Y-1
0.7944 dp = -pvdv
0.7944
0.7944 T₁=To [1 + x2 ¹ Mi ¹
0.7944
²16) *-₁]
Y-
2a Po-Pi
1-y+2yM
Y+1
PD P² + 1) - / - 1
-7/(Y-1)
P₁ = Po [(1 + ² = 1¹ M³ ] "
2
P₁ = Po [(1 + ² = ¹ M²³)]*
-1/(-1)
(4)
Re, =
8 =
C
C₁:
8 =
"
=
Ca
1 2
M² y+1
5.2x
PuVx
Hoo
√Rex
0.664
a=
q=
Re
1.328
REL
0.37x
Re2
ci-ci-c|_ci
0.0592
Re
0.074
a=dc₁/da
C₂
Cp=
900
4a
√M²-1
C₂
Coat
REAR
(¹
1
μ= arcsin
(+1)/(-1)
1+57.3a0/(ne,AR)
1
M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4612b8e-bd3c-4aa1-bedf-8b928188dc49%2F800a75b8-ae71-4e13-8888-b2b3545b3da6%2F8htolsc_processed.png&w=3840&q=75)
Transcribed Image Text:Table B.2 Properties of the International Standard Atmosphere (ISA) between sea level and 20 km
geopotential altitude
9,000
9,500
Standard values at altitude
P (Pa)
8
Alt. (m)
T (K)
0
288.15 1 340.29
500 284.90 0.9887 338.37
1,000 281.65 0.9774 336.43
1,500 278.40 0.9662 334.49
2,000 275.15 0.9549 332.53
2,500 271.90 0.9436 330.56
3,000 268.65 0.9306 328.58
3,500 265.40 0.9210
326.58
4,000 262.15 0.9098 324.58
4,500 258.90 0.8985 322.56
255.65 0.8872 320.53
252.40 0.8759 318.48
249.15 0.8647 316.43
6,500
245.90 0.8534 314.36
7,000 242.65 0.8421 312.27
310.17
308.06
5,000
5,500
6,000
7,500 239.40 0.8308
8,000 236.15 0.8195
8,500
305.93
33,099
41,060 0.4052 0.5895 0.4812
38,251 0.3775 0.5566 0.4544
35,599 0.3513 0.5252
232.90 0.8083
0.3267
0.4951
229.65
0.7970 303.79
30,742 0.3040 0.4663
226.40 0.7857 301.63 28,523 0.2815 0.4389
0.4127
0.3877
10,000
0.3639
0.2655
0.2268
0.1851
223.15
0.7744
299.46 26,436 0.2609
10,500 219.90 0.7631 297.27 24,474 0.2415
11,000 216.65 0.7519 295.07 22,632 0.2234
12,000 216.65 0.7519 295.07 19,330 0.1908 0.3108
13,000 216.65 0.7519 295.07 16,510 0.1629
14,000 216.65 0.,7519 295.07 14,101 0.1392
15,000 216.65 0.7519 295.07 12,044 0.1189 0.1937 0.1581
16,000 216.65 0.7519 295.07 10,287 0.1015 0.1654 0.1350
17,000 216.65 0.7519 295.07 8,786 0.0867 0.1413 0.1153
18,000 216.65 0.7519 295.07 7,505 0.0741 0.1207 0.0985
19,000 216.65 0.7519 295.07 6,410 0.0633 0.1031 0.0842
20,000
216.65 0.7519 295.07 5,475 0.0540 0.0880 0.0718
0
a (m/s)
p (kg/m³) 0
μ/1₂
1
1
1.2250
1.1673 0.9529 0.9912
1.1117 0.9075 0.9823
1.0581 0.8638 0.9735
1.0065 0.8216 0.9645
0.9569 0.7811 0.9556
0.9091 0.7421 0.9465
0.8632 0.7055
101,325 1
95,461 0.9421
89,874 0.8870
84,556 0.8345
79,495
0.7846
74,682 0.7371
70,108 0.6919
65,764 0.6490
61,640 0.6083
57,728 0.5697
54,020 0.5331
50,506 0.4985 0.6971 0.5691 0.9006
47,181 0.4656 0.6597 0.5385
44,034 0.4346 0.6238 0.5092
0.9099
0.8191 0.6686
0.7768 0.6341
0.7361 0.6009
0.9375
0.9283
0.9191
0.2537
0.2167
P₁A₁V₁ = P₂A₂V₂
V
P₂+PZ=P₁+PZ
P/= P₁
V²
C₂T₁+2=C₂T₂+
0.8911 V₂ =
0.8818
0.8724
0.8628
0.4287 0.8532
0.4042 0.8436
0.3807 0.8339
0.3583 0.8241
0.8143
0.3369
0.3165
0.8044
0.2971
0.7944
p=pRT
a = √√YRT
V₁ =
Advanced Aircraft Design: Conceptual Design. Analysis and Optimization of Subsonic Civil Airplanes. First Edition. Egbert Torenbeck.
2013 by Tighert Torenbeek. Published 2013 by John Wiley & Sons, Lad.
C₂ =
h = c₂T
e = c₂T
P₂
P₁
Poz
P₁
=
0.7944
0.7944 M
0.7944
2(P₁-P₂)
√P[1-(A₂/A₂)²)
2(Po-P)
P
2(Po-P)
Ps
YR
Y-1
-) =)"
Y/(-1)
17/(-1).
(y + 1)²M
[4YM-2(y-1)]
2 (P₂)(x-1)/y
0.7944
0.7944
Y-1
0.7944 dp = -pvdv
0.7944
0.7944 T₁=To [1 + x2 ¹ Mi ¹
0.7944
²16) *-₁]
Y-
2a Po-Pi
1-y+2yM
Y+1
PD P² + 1) - / - 1
-7/(Y-1)
P₁ = Po [(1 + ² = 1¹ M³ ] "
2
P₁ = Po [(1 + ² = ¹ M²³)]*
-1/(-1)
(4)
Re, =
8 =
C
C₁:
8 =
"
=
Ca
1 2
M² y+1
5.2x
PuVx
Hoo
√Rex
0.664
a=
q=
Re
1.328
REL
0.37x
Re2
ci-ci-c|_ci
0.0592
Re
0.074
a=dc₁/da
C₂
Cp=
900
4a
√M²-1
C₂
Coat
REAR
(¹
1
μ= arcsin
(+1)/(-1)
1+57.3a0/(ne,AR)
1
M
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