216
1 - r a s m . K om b i n at s i y a l a sh g an p l u g rot o r i b i l an i r g ‘i ti l ga n tu p r oq
bo‘lakchalari uchish trayektoriyasi
B un d a
d a l a
y u z as i n i ng
t e ki sl a ng a nl i gi
t up r oq
bo ‘ l ak c h al a r i ni ng
yo yi
l i s h
yo ‘l a k c h as i g a
b o g ‘l i q
bo ‘ l ad i
v a
i rg ‘ i t i l i s h
u z oq l i g i
L g a
t up r oq
z a r r a c h a l ar ni n g
p a rus l i l i gi ,h a vo
m u hi t i ni n g
h ol a t i
k ab i
fi zi k
om i l l a r
t a ʻs i r
ko‘rsatadi.
T ad q i q o t n a ti j al a ri v a u l a rn i n g m u h ok am a s i .
M u hi t da
h a r a k at l a n
a y o t g a n
m
k
m as s al i
za r r a c h ag a
i k ki t a
ku c h
t a ’ s i r
qi l adi ( 2 r as m ):
og‘irlik
kuchi
G
k
= m
k
g v a
z a r r a c h an i ng
h a r a k at
yo ‘ n al i s h i g a
q a r am a
q a rs
h i
t om on g a
y un a l i b ,
t r a y ek t o r i y a si g a
t o ‘g ‘ ri
c hi zi ql i
u ri nm a
ko ‘ ri ni s h i d a
m u hi t
q a r s h i l i gi
R
v
.
H a v o
m uh i t i ni ng
qa r s hi l i k
k u chi
z a r ra c h a ni n g
k es i m y
uz a s i g a
v a
u
n i ng
h a r ak a t
t e zl i gi
k v ad r at i g a
t o‘ g ‘ ri
p ro po r s i on a l
[3 ]
y a ’ ni :
2
к
c
в
F
в
V
F
g
k
P
=
, (1)
b u nd a :
V
k
–
u ch a y ot ga n
za r r a c h a
t e z l i gi ,
m / s ;
v
–
m u hi t d ag i
h a vo ni n g
zi c hl i gi ,
kg / m
3
;
g – e rk i n
t us hi s h
t ez l a ni s h i , m / s
2
;
F
c
–
z a r r a ch a ni ng
k es i m y
u z as i ,
m
2
;
k
F
–
z a r r a c h a
f o rm a s i ni ng
y u z as i
bo ‘ yi ch a
k a r s hi l i k
k o ef f i t s i ye n t i .
T u p ro q
b o ‘l a k ch a l ar i ni ng
h a r ak a t i ni
bi t t a
t e ki s l i k d a
d e b
q ab ul
qi l am
i z . Z a r r a ch a
h a r a k at i ni ng
d i ff e r e ns i al
t e n g l a m as i
q u yi d ag i c h a
b o ‘l a di :
,
"
;
"
ву
к
вх
P
G
my
P
mx
+
−
=
−
=
(2)
bunda:
Rvx va
Rvu– koordinatalar o‘qida havoning
qarshilik kuchi proyeksiyalari;
x” va
u” – vertikal va gorrizontal yo‘nalishlarda zarrachaning tezlanishi.
217
2 - r a s m .
Z a r ra c h an i n g h a v od a u ch i b k e t ay o tga n vaq t i d a u n ga ta ’ s i r e t u v
c h i k u ch l a r s x em as i
Og‘irlik
kuchi
G va
muhit
qarshilik
kuchi
P
v
n i
j o yi ga
q o ‘y i b
q u
y i d agi
i fo d a g a
eg a
b o ‘l am i z:
,
sin
"
;
cos
"
2
2
i
к
c
в
F
i
к
c
в
F
V
F
mg
k
g
y
V
F
mg
k
x
+
−
=
−
=
(3)
b u nd a
α
i
–
tezlik
vektorining
OX
o‘qiga
nisbatan
og‘ish
burchagi.
k
F
,
v
, F
s
,
m va
g l a r n i
d oi m i yl i gi ni
h i s obg a
ol s ak
mg
F
k
c
в
F
i f o d as i ni
k
n
–
p a r u s l i l i k
k o e f fi t s i ye n t
i d e b
q a b ul
qi l a m i z.
B un d a:
.
sin
"
;
cos
"
2
2
i
к
п
i
к
п
V
k
g
y
V
k
x
+
−
=
−
=
(4)
U s hb u
t e n gl am a ni
s o dd a l as ht i r i s h
u c hu n
α
i
= 0
d eb
q ab u l
qi l am i z.
B un i n g
s ab a bi
b i ri n c h i d a n
r ot or ni n g
i sh c hi
o r g an l a r
i t up r o q
z a r r al a ri ni
s
h u dg o rl a n ay ot g an
da l a
y u z asi g a ni sb a t a n
u n ch a
k a t t a
bo‘ l m ag a n
b a l an dl i
k
h
n
=
1 3 -1 5 s m d a i r g ‘i t a di , i kk i n c hi d an A . A. K uk i b ny m a ʻl um ot l a ri g a ko ‘ r a
αi burchagi keltirilayotgan sharoit uchun 7 -90 dan oshmaydi [4].
cos90 = 0.9877 bo‘lganligi uchun uni 1 ga teng deb qabul qilamiz.
U n d a
za r r a c h an i
OX o ‘q i g a
n i s b at a n
p r o y ek s i y as i ni n g
ha r a k a t
t en gl
a m a s i
q uyi d a gi
ko ‘r i ni s h d a
bo ‘l a di :
.
"
2
к
п
V
k
x
−
=
(5)
In t e g r a l l as h d an
a v va l
o ‘ z g ar u v ch i l a rn i n g
j o yl a ri ni
al m a s ht i r am i z
.
2
к
п
кx
V
k
dt
dV
−
=
(6)
O‘zgaruvchilarni
ajratib
tenglamani
integrallaymiz:
.
1
1
C
t
k
V
п
кx
+
=
(7)
218
t=0
va
V
k
=V
a
b o s h l an g ‘i c h
s h ar t l a r g a
as o s an
i nt e gr a l l a s h
d o i m i ys i n i
a n i ql ay m i z :
,
1
1
а
V
C =
(8)
b u nd a
V
a
t u p r oq
za r r a c h a s i ni ng
r ot o rd a n
u ch i b
c hi qi s h da g i
b o s h l an g ‘i c h
t e z l i gi ,
m / s . S
1
n i
t e ngl a m ag a
q o ‘y i b
q uy i d a gi
i fo d an i
ol a m i z:
.
1
1
"
а
п
кx
V
t
k
х
V
+
=
=
(9)
T u p ro q
z ar r a c h al a ri n i ng
i r g ‘i t i l i s h
u zoq l i gi ni a ni ql as h
u ch u n
o ‘ z g ar
u v c hi l a r ni
ol di n d an
a j r a t i b
y u qo ri d a gi
t en gl a m ani
i nt e gr a l l ay m i z:
.
1
а
п
V
t
k
dt
dх
+
=
(10)
2
ln
1
ln
1
C
V
t
k
k
х
а
п
п
−
+
=
. (11)
t =
0
va
x =
0
b o ‘ l g a n d a:
а
п
V
k
C
1
ln
1
ln
2
=
. (12)
S
2
n i
yu qo r i d a g
i t en g l am ag a
q o ‘y i b
qu y i d a gi ni
ol am i z:
(
)
1
ln
1
+
=
t
V
k
k
х
а
п
п
. (13)
V a q t
t n i
t o pi s h
u c h un
o ‘ zg a r uv c hi l a r n i
aj r at i b
z a r r a c ha n i ng
h a ra k
a t
t en gl a m as i n i
OY
o ‘ qi d ag i
p r oy e ks i y a s i ni
i n t eg r a l l aym i z:
y
´
= - gt+C
3
(14)
t = 0 va
y
´
= 0 b o ‘l g an d a
C
3
= 0
b o ‘l a di .
B un d a:
y
´
= - gt(15)
Natijada:
4
2
2
C
gt
y
+
−
=
(16)
t = 0, y = h, S
4
= h
n
bo‘lganda:
п
h
gt
y
+
−
=
2
2
(17)
B u
t en gl a m ad a n
y=0.b o ‘l g a nd a
z a r r a c h a
d a l a
y u z as i g a
b or i b
t us hg a n
m om e nt d ag i
v aq t n i
t op a m i z ,
bu n da
2
2
gt
h
п
=
v a
z a r r a c h an i n g
u chi s h
v aqt i :
g
h
t
п
2
=
(18)
.
ln
1
ln
1
2
C
V
t
k
k
x
а
n
n
−
+
=
(19)
219
T e n gl a m ag a
t – v aq t n i q o ‘y i b ko m b i na t s i y al a s h g an pl ug k o rp u s i ni n g
rotori bilan irg‘itilayotgan tuproq bo‘lakchalarini
maksimal uchish
u z o ql i gi ni ani ql o v ch i qu yi d ag i t e ng l am a s i ni k el t i ri b c hi q a r a m i z:
,
1
2
ln
1
max
+
=
g
h
V
k
k
x
п
а
n
n
(20)
b u nd a
k
n
–paruslilik
koeffitsiyenti;
V
a
– zarrachalarni irg‘itilishini boshlang‘ich
t e z l i gi , m / s ; h p = H p - a s h – rot o r t i s h i ni d a l a yu za s i d a n j o yl a s h i s h
b a l an dl i g i , m ; H p – r ot o r t i s hi ni eg a t t u bi d a n j o yl as hi s h b al a n dl i gi , m ;
a s h – s h ud go r l as h c h u qu r l i gi , m .
( 2 0 )t e ng l am a
t a hl i l i n i ng
k o ‘ rs a t i s hi c h a, z a r r a c h a l ar ni n g i r g‘i t i l i s h
b a l an dl i g i va t e zl i g i o rt i s h i h am d a ro t or ni n g i s h c hi e l em e nt l a ri
irg‘itayotgan palaxsaning paruslilik koeffitsiyenti kamayishi bilan uchish
u z o ql i gi o rt a r e k a n.
