~
~
~
~
=
It can be shown that particles falling at thesr terminal s>eed
experience three types of flowina fluid: streamline or laminar Sow
where viscous forces predominate (10° & R, & 2.8!) antermediate Dow
where inertia forces predominate (2 © R. £500); asd turbulent fow
where inertia forces predominate (500 R, £105). Below a Reynolds
}
4
-
se see
:
.
:
:
The limiting diameter to which Eq {1} holds is:
ws
.
dts
36 yp?
{
: he
UAE. yy
oF spheres anc
.
number of 107* certaia corrections must be applied io the equaticas
°
because the particle diameter approaches the mean iree path of tne fluid
medium; the region above a Reynolds number of i1¢* is importance only
dos
in ballistics, These limiting cases will not be discussed bere.
2
.
.
.
.
Most empirical equations developed in pass experimental work
have been fer spheres dropped in various liquids. Some work has been
done on irregular-shaped particles and some done im wind tunneis. The
equations’ used to determine the failing rates for pazticlesin a Laud
medium follow,
:
:
:
t
:
For streamline motion, 1674 £R, € 2.0
.
Vs 2K
*
[AP fa
( 7
£-)
)
(a)
vt
(—+
ay
(% )
where
‘
3
.
.
Vv,
‘
ago
i
:
9
dad
=
a
.
Ks s
-
Ky)
:
.
gravity
= constant incorporating
P'
.
:
.
:
:
i
.
.
:
= 54.5 for spheres
° This equation
‘
mo
particle diameter in ¢m
36.0 for irregular-shaped particles.
——~—
i
ala
or irre galar-skaped particles.
.
ya
We
2
oats
;
5 s
2,
.
do
.
.
wy
sz)
= d- fat
0.4 for spheres
limiting diameter to which streamline mpotion applies
= 30.6 for spbkerés
= 19.0 for irregular-snaped particles.
Pp
a
= absolute viscosity of fluid in poises
=
for
o
=. 0.279 for irregular shapes
f= particle density in gm/em!
= fluid density in gm/cm?}
“o
ya grth
7
:
:
= terminal velocity in cm/sec
ff
=K
1
where
-
Vs
‘
:
oo
For Intermediate motion, 2.6 4 Re £ 500
& _~
” "
.
~
Hn
The parameters actively affecting a particie's falling speed
are: its woight; its drag coefficient; its density; as well as the fad
density and fluid viscosity.
.
ds
~ sr (A,)
~
”
°
54.4 pe?
d™
.
:
“
.
:
-UNCLASSIFIED
.
=
= 43.5 sia
7 LP. j
for spheres
.
A
.
.
a"
=
51
/
for. irregular~szaped Particles.
.
2
tas)
sf, 7-7?
For tarbulent motion, S20 6 Re S 10%
>
taken from Ref t, However, cerain consians have beet re-evaluated.
4
;
The limiting diameter ts wich the Eq (2) kels iss
:
>
af3
2
ab
Vy = Ky (>
}
x
.
oo
Ky
ar
= 34.6 for spheres
= 50.0 for irregular-siazped particles,
ee
°
-
These equatous were tacea from fel 1, Homeeer.
cersiz cunstaass Lawe smee re-evalvaed.
~5-
.
UNCLASSIFIED
ce Nema MMAR NB ae Me me Tk
ee
—-
Te Ye
Netter ee ee a nn ee
em ae ee
Te ee
-
tees