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Table 341A. Skin Friction on Flat Plates

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 skin-friction 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( 1-5 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 boundary-layer thickness. The local skin-friction 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 skin-friction 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=7------10 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 :

Sea-level pressure po = 29.921 inHg

= 407.1 inH,O

= 2116.2 lb/ft'

Sea-level temperature t o = 59°F

Sea-level absolute temperature TO= 518.4"F abs

Sea-level 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=To--h

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



ft-sec



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 normal-shock flow. Isentropic flow is generally valid for a subsonic or

supersonic expanding flow and may be used for subsonic compression flow. Normal-shock

How is valid for supersonic compression flow when the deviation of the flow through the

shock is zero. Oblique-shock flow may be obtained from the normal-shock 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 normal-shock flow are:



'::a



But-cher. Marie A . , Compressilde flow tables for air, N.\C.\ TN No. 1592, August 1948.



(continued)

SMITHSONIAN PHYSICAL TABLES



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