Table 341A. Skin Friction on Flat Plates
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344
T A B L E 341A.SKIN
.o
F R I C T I O N ON F L A T P L A T E S (FIGS. 11, 12) (continued)
I0
.006
.OO 4
.oo 2
CF
.oo I
.OOO 6
.ooo 4
.0002*,
.s
1.0
T h e local skinfriction coefficient2
5.O
2.0
29
10
may be approximated by a power function of the
@'.I
Reynolds number based on the momentum thickness, Re =
layer is laminar
1
[2.5 log,
0=
When the boundary
Re
When the boundary layer is turbulent
70 The momentum thickness
9
 0.2205
TO
29
2q
20x10~
2.5( 15 d70/29)
s:
+ 5.51 '
( 1 $)dy,
where ZI is the local velocity inside the boundary layer, V the local velocity outside the
boundary layer, and 6 the boundarylayer thickness. The local skinfriction coefficient is
plotted against Reynolds number for the case of a turbulent boundary layer.
(CO?ZtiWCd)
SMITHSONIAN PHYSICAL TABLES
345
T A B L E 3 4 1 A . 4 K I N FRICTION ON F L A T PLATES (FIGS. 11, 12) (concluded)
.0032
I
z
w .002 8
9
L
L
$ .0024
z
0
ua .0020
I
LL
z.0016
Y
cn
I
4.0012
s
'
0008
203
FIG. 12.The
I
500
I
I
I
I
I
1000 2000
5000 l0,OOO 20,000
REYNOLDS NUMBER R e
I
50,000 IO0,OOO
local skinfriction coefficient on a flat plate plotted against the Reynolds
number for a turbulent boundary layer.
T A B L E 342.STAN
DARD ATMOSPHERE
Standard atmospheric values are given up to altitudes of 65,000 feet, and quantities
that have been found to be of use in the interpretation of airspeed and related factors are
included (Table 343). These quantities are the pressure p in pounds per square foot, the
pressure p in inches of water, the speed of sound a, the coefficient of viscosity q , and the
kinematic viscosity Y . The values for the coefficient of viscosity q and the kinematic viscosity Y are not standard values since a standardization of air viscosity has not been agreed
upon as yet. The values listed for q and Y are believed to be sufficiently accurate, however,
to be useful in calculations requiring viscosity of air. The coefficietit of viscosity q was computed from the formula
2.318 Ta12
q=710 T + 2 1 6
The kinematic viscosity of air Y was obtained from the definition Y = 3 The quantity
P
l/VT is given to facilitate the computation of the true airspeed V from the equivalent
airspeed V e .
1
v=VY,
VO
The speed of sound in miles per hour is computed from a=33.42VT where T is the
temperature in degrees Fahrenheit absolute. A value of y = 1.4 was assumed to hold
throughout the temperature range.
The values of the standard atmosphere are based upon the following values :
Sealevel pressure po = 29.921 inHg
= 407.1 inH,O
= 2116.2 lb/ft'
Sealevel temperature t o = 59°F
Sealevel absolute temperature TO= 518.4"F abs
Sealevel density po = 0.002378 slug/ft"
Gravity g = 32.1740 ft/sec2
Temperature gradient dT  0.00356617"F/ft
dh The altitude of the lower limit of the isothermal atmosphere = 35,332 i r
Specific weight of mercury at 32°F = 848.7149 lb/ftn
Specific weight of water at 59°F = 62.3724 Ib/ft8

'SAiken William S. Jr. Standard nomenclature far airsneeds with tables and charts for use in
Warfield, Calvin N., Tentative tables for the propcalculation'of airspeed NACA Ren. No. 837 1947.
erties of the upper atmosphere, NACA T N ' N o . 1200, January 1947.
(continued)
SMITHSONIAN PHYSICAL TABLES
346
T A B L E 342.STANDARD
ATMOSPHERE (concluded)
U p to the lower limit of the isothermal atmosphere (67°F corresponding to 35,332 ft)
the temperature is assumed to decrease linearly according to the equation
dT
T=Toh
dh
Further, the atmosphere is assumed to be a dry perfect gas that obeys the laws of Charles
and Boyle, so that the mass density corresponding to the pressure and temperature is
p=po
P To
Po
T
The pressure and altitude are related by
h = log.Po T m
P a To
The harmonic mean temperature T , is given by
Po
P
where Taui,TaUz,
. . . are the average temperatures for the altitude increments Ahi, Ahz, . . .
The NACA Special Subcommittee on the Upper Atmosphere, at a meeting on June 24,
1946, resolved that a tentative extension of the standard atmosphere from 65,000 to 100,000
feet be based upon a constant composition of the atmosphere and an isothermal temperature which are the same as standard conditions a t 65,000 feet. This tentative extended
isothermal region (Table 344) ends at 32 kilometers (approximately 105,000 ft). It is
possible that as results of higher altitude temperature soundings become available and the
standard atmosphere is extended to very high altitudes the present recommendations may
be modified.
The Subcommittee also recommended that the values of temperature given in the following table be considered as maximum and minimum values occurring for the given altitudes
with the variations between the specified points to be linear :

Temperature ("C abs)
Altitude
(km)
20
25
45
Minimum
Maximum
180
250
250
380

200
A tentative extension of the standard atmosphere computed from the equations using
the recommended isothermal temperature and constant gravity altitudes from 65,000 to
100,000 feet are included in the table. Calculations have been made by assuming that
the acceleration of gravity varies inversely as the square of the distance from the center
of the earth. Up to 100,000 feet this assumption does not greatly affect the tabulated values.
SMITHSONIAN PHYSICAL TABLES
OF THE S T A N D A R D A T M O S P H E R E *
T A B L E 343.PROPERTIES
AltiPressure, p
tude, h ,
ft
Ib/ft*
inHpO inHg
n 2116
Density
Density ratio
a=
slu:S/fta
f
1

Temperature,
T
V T "F nhs
518.4
1.030 511.2
1.061 504.1
1.094 497.0
s
Coefficient
of
~ viscosity,
d
sound,
7
Kinematic
viscosity,
Y
mi/hr
ftsec
ft2/sec
760.9
755.7
750.4
745.1
3.725X10'
3.685. .
3.644
3.602
1.566)<10'
1.644
1.725
1.812
4,000 1828
6,000 1696
407.1
378.5
351.6
326.2
29.92
27.82
25.84
23.98
.002242 .9428
.002112 .8881
.001988 .8358
1572
1455
1346
1243
302.4
279.9
258.9
239.1
22.22
20.58
19.03
17.57
.001869
.001756
.001648
.001545
.7859
,7384
.6931
,6499
1.128
1.164
1.201
1.240
489.9
482.7
475.6
468.5
739.7
734.3
728.8
723.4
3.561
3.519
3.476
3.434
1.905
2.004
2.109
2.223
16,000 1146
220.6
18.000 1056
203.2
20.000 972.1 187.0
22;000 893.3 171.9
16.21
14.94
13.75
12.63
.001448
.001355
.001267
,001183
.6088
.5698
.5327
.4974
1.282
1.325
1.370
1.418
461.3
454.2
447.1
439.9
718.7
712.2
706.6
701.1
3.391
3.348
3.305
3.261
2.342
2.471
2.608
2.756
,001103
.001028
BOO957
.000889
.4640
.4323
.4023
.3740
1.468
1.521
1.577
1.635
432.8
425.7
418.5
411.4
695.3
689.5
683.7
677.9
3.217
3.173
3.128
3.083
2.916
3.086
3.268
3.468
2,000
1968
8,000
10,000
12,000
14,000
157.7 11.59
144.5 10.62
132.2 9.720
120.8 8.880
347
24,000
26,000
28.000
30,000
819.8
751.2
687.4
628.0
32,000
34,000
35,332
36,000
572.9 110.2
521.7 100.4
489.8 94.24
474.4 91.31
8.101
7.377
6.926
6.711
.000826
.000765
.OW727
.O00705
,3472
.3218
.3058
,2963
1.697
1.763
1.808
1.837
404.3
397.2
392.4
392.4
672.0
666.0
662.0
662.0
3.038
2.992
2.962
2.962
3.678
3.911
4.073
4.204
38.000
40.000
42.000
44;OOO
431.1
391.9
356.2
323.7
82.97
75.44
68.56
62.29
6.098
5.544
5.038
4.578
.000MO
,000582
.000529
.000480
2692
.2448
.2225
2021
1.927
2.021
2.120
2.224
392.4
392.4
392.4
392.4
662.0 2.962
662.0 2.962
662.0 2.962
662.0 2.962
4.625
5.089
5.599
6.161
46.000
48,000
50,000
52,000
294.2
267.4
243.1
220.9
56.63
51.46
46.78
42.52
4.162
3.782
3.438
3.124
.000437
,000397
.000361
.000328
.1838
.1670
.1518
.1379
2.333
2.447
2.567
2.692
392.4
392.4
392.4
392.4
662.0
662.0
452.0
662.0
2.962
2.962
2.962
2.962
6.773
7.459
8.206
9.028
54,000
56,000
58,000
60,000
200.8
182.5
165.9
150.8
38.64
35.12
31.92
29.01
2.840
2.581
2.346
2.132
.000298
.000271
.000246
.000224
1.1254
.1140
.lo36
.09415
2.824
2.962
3.107
3.259
392.4
392.4
392.4
392.4
662.0
662.0
662.0
662.0
2.962
2.962
2.962
2.962
9.933
10.93
12.02
13.23
62,000
64,000
65,000
137.1
124.6
118.7
26.37 1.938 .000203 .08557 3.419 392.4 662.0 2.962
23.96 1.761 .000185 ,07777 3.586 392.4 662.0 2.962
22.85 1.679 .000176 .07414 3.672 392.4 662.0 2.962
14.56
16.02
16.80
For metric values see Table 628.
T A B L E 344.PROPERTIES
OF T H E T E N T A T I V E S T A N D A R D  A T M O S P H E R E
EXTENSION
Altitude
h
ft
Pressiire, p
Density,
slu:/ft3
Density
ratio.
1

\/a
Coefficient
Tern Speed
of
perof
viscosity, Kinematic
ature, sound,
sl:xs
viscosity,
"F%s
mia/hr
65,000 118.7 22.85 1.679 .000176 ,07414 3.672 392.4 662.0
70,000 93.53 17.99 1.322 .000139 ,05839 4.138 392.4 662.0
75,000 73.66 14.17 1.042 .000109 ,04599 4.663 392.4 662.0
80,000 58.01 11.16 .8202 .0000861 .03621 5.255 392.4 662.0
85.000 45.68 8.789 ,6460 .OW0678 .02852 5.921 392.4 662.0
90:OOO 35.97 6.921 .5086 .0000534 .02246 6.672 392.4 662.0
95,000 28.33 5.451 .4006 .0000421 .01769 7.519 392.4 662.0
100,000 22.31 4.293 .3156 .0000331 ,01394 8.472 392.4 662.0
SMITHSONIAN PHYSICAL T A B L E S
f=
ft'ysec
2.962)<10~'16.80X10~4
2.962
21.33
2.962
27.09
2.962
34.39
2.962
43.67
2.962
55.45
2.962
70.41
2.%2
89.41
348
T A B L E 345.COMPRESSIBLE
F L O W TABLES FOR AIR'*
I n high speed research, use is frequently made of the theoretical relationships existing
between the Mach number and various flow parameters. Two types of flow are tabulated :
isentropic flow and normalshock flow. Isentropic flow is generally valid for a subsonic or
supersonic expanding flow and may be used for subsonic compression flow. Normalshock
How is valid for supersonic compression flow when the deviation of the flow through the
shock is zero. Obliqueshock flow may be obtained from the normalshock flow by superimposing a velocity tangential to the shock.
The assumption that air is a perfect gas with a value of y of 1.400 is valid for the conditions usually encountered in the subsonic and lower supersonic regions for normal stagnation conditions. For Mach numbers greater than about 4.0 or for unusual stagnation
conditions, however, the behavior of air will depart appreciably from that of a perfect gas
if the liquefaction condition is approached, and caution should be used in applying the
results in the table at the higher Mach numbers.
The formulas for isentropic flow are:
and the formulas for normalshock flow are:
'::a
Butcher. Marie A . , Compressilde flow tables for air, N.\C.\ TN No. 1592, August 1948.
(continued)
SMITHSONIAN PHYSICAL TABLES