Table 340B. Forces on Nonrotating Circular Cylinders
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341
T A B L E 340B.-FORCES
O N N O N R O T A T I N G C I R C U L A R C Y L I N D E R S (FIG 7)
(concluded)
The variation of CII with aspect ratio for Reynolds number of 80,000 is as follows.
Aspect ratio
L
d
1
.63
CO
2
.69
3
5
10
20
40
00
.75
.75
.83
.92
1.00
1.20
If the axis of the cylinder is inclined to the wind direction, the force remains approximately at right angles to the axis of the cylinder, its magnitude falling off approximately
as the square of the sine of the angle of the axis to the wind.
T A B L E 340C.-FORCES
ON S P H E R E S (FIGS. 8-10)"'
For spheres, the linear dimension I is taken as the diameter of the sphere d and the area
A as sd". For values of Reynolds number between 80,000 and 400,000 at low values of
4
Mach number the value of the drag coefficient CO depends in large measure on the turbulence of the air stream. As the Reynolds number is increased in this range the drag
coefficient of the sphere and the pressure coefficient at the rear of the sphere decreaserapidly. The pressure coefficient is equal to the ratio of the difference between free stream
stagnation pressure and local static pressure to the dynamic pressure q. The Reynolds
number a t which the pressure coefficient a t the rear of the sphere is 1.22 is defined as the
critical Reynolds number, RcT.This value of pressure coefficient corresponds very nearly
to C D = .3. The value of R,, represented by point d in the figure is considered to be
typical of turbulence-free air.
FIG. 8.-The
drag coefficient C D on spheres as a function of the Reynolds number.
Vdp
Drag, D = C D AR~ = -9
Sphere tests in wind tunnels indicate different values of R,, for different sphere sizes.
Correlation of the data may be obtained if values of
";
- (+)*= ( K ) are
plotted as a
function of Rcr. The value V g is the root-mean-square of the fluctuation velocity in the
direction of the relative wind, 'I the velocity of the relative wind, d the sphere diameter,
and L is the scale of the turbulence as defined in the reference. The figure shows a correlation ( K ) obtained with two sizes of spheres and several values of L.
133 Allen, H. S. The motion of a sphere in a viscous fluid
Phil. Mag., vol. 50 p. 323, 1900.
Wieselherger C. Further information o n the laws of fiuid resisiance NACA T N No.' 121, Decemher
1922.
Miilikah C. B., and Klein A. I-., The effect of turbulence Aircraft Eng., vol. 5, p. 169. 1933.
Platt, Robert C., kurhulence factor; of NACA wind tunnels as dedrmined by sphere tests NACA Re
No. 558 1936.
Dryden, Hugh L., Schuhauer, C. B. Mock, W. C.. Jr., and Skranktad, H.
Measudments of intensity and scale of wind-tunnel turdulence and their relation to the critical Reynolds number of spheres NACA Rep. No. 581, 1937.
Ferri, Antonio, The influence of Reynolds
numbers at high Mach nAmbers, Atti di Guidonia, n. 67/69, Mar. 10. 1942.
2;
SMITHSONIAN PHYSICAL TABLES
(contimed)
342
TABLE 340C.-FORCES
O N SPHERES (FIGS. 8-10) (concluded)
.I 0
.O8
.O 6
K
.04
.o 2
0
FIG.9.-The
1.0
1.2
value of
1.4
1.6
1.8
2.0
2.2
CRITICAL REYNOLDS NUMEER,R,,
7
- (f)&= K
2.4
2.6 2.8X105
plotted as a function of the critical Reynolds
number, Rcr.
A t Mach numbers greater than about 0.3 the drag coeflicient C Ddepends on the values of
both Reynolds number and Mach number.
.7
.6
.5
A
CD
.3
.2
.I
0
FIG.10.-The
2
3
4
5
6
REYNOLDS NUMBER
7
8x1
5
R
drag coefficient for a sphere as a function of the Reynolds number for
several Mach numbers.
SMITHSONIAN PHYSICAL TABLES
T A B L E 341.-FORCES
O N M I S C E L L A N E O U S BODIES
343
The values of the drag coefficients in this table are based on the area of the projection
of the body on a plane normal to the wind direction. Where this projection is a circle, the
diameter is used as the linear dimension 1 in the Reynolds number. Where the projection
is rectangular, the shortest side of the rectangle is taken as 1.
Reynolds
number
CD
Body
Streamline bodies of revolution. ...........................
.05- .06
1.56
Rectangular prism 1 X 1 x 5 normal to 1 X 5 face.. ........
Rectangular prism 1 x 1 x 5 , long axis perpendicular to
.92
the relative wind and 1 X 5 face at 45". ..................
..............................................
Cone, angle 60", point to wind, solid.. .....................
Cone, angle 30", point to wind, solid .......................
Hemispherical cup, open back. ............................
Hemispherical cup, open front .............................
Sphero-conic body, cone 20" point forward.. ...............
Sphero-conic body, cone 20" point to rear ..................
Cylinder 120 cni long, spherical ends with
axis parallel to the relative wind.. .......................
Automobile
T A B L E 341A.-SKIN
3,000,000
180,000
254,000
[about
300,000
]
.78
.51
.34
.41
1.40
.16
.09
270,000
100,000
100,000
135,000
135,000
.19
100,000
F R I C T I O N O N F L A T P L A T E S (FIGS. 11, 12)
If the flat plate is in a uniform stream of fluid and the flow is parallel to the plate the skin
VLP
The skin
friction coefficient, Cf, is dependent mainly on the Reynolds number, R = -.
t)
D
friction coefficient CI = Awhere Dr is the friction drag per unit width of one side of the
qL
plate, q the dynamic pressure (see Table 339), and L the length from the leading edge
of the plate.
For laminar flow
1.328
c f ==
(Blasius)
VR
For turbulent flow
(Schlichting)
The Reynolds number for transition from laminar to turbulent flow depends on the
roughness of the plate and the turbulence of the airstream.
The figure shows the variation of the skin friction ( C f ) with R for laminar and turbulent flow.
1% Tetervin, Neal, A method for the rapid estimation of turbulent boundary-layer thickness for calculating profile drag, NACA ACR No. L4C14, July 1944
(cmi tinrced)
SMITHSONIAN PHYSICAL TABLES
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