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ODDIY DIFFERENSIAL TENGLAMALAR YORDAMIDA TABIIY GAZNI
TOZLASHNI MATEMATIK MODULINI TUZISH
Xusanov Bazar
Samarqand davlat arxitektura-qurilish universiteti, dotsent
E-mail:
Annatatsiya:
Qazib olingan tabiiy gazni ishlab chiqarish jarayonida hosil bo’ladigan
tarkibida har xil qo’shimchalar, keraksiz qattiq, suyuq va gaz holatidagi aralashmalardan
tozalash natijasida qimmatbaho mahsulotlar ushlab qolinadi va ulardan sanoatda ko’plab
mahsulotlar ishlab chiqariladi.Bu aralashmalarni olish uchun skrubber apparatini ishlash
sxemasini oddiy differensial tenglamalar yordamida matametik moduli yaratilgan va uni
ishlash sxemasi ko’rsatilgan.
Kalit so’zlar:
Absorbsiya ,adsorbsiya, elektrostatik kuchlar, filterlash. skrubbber ,adsorber,
konsentratsiya ,differensial
tenglama , proparsionallik
koeffitsenti, umumiy yechim,
o’zgaruvchilari ajralgan, konussimon, xususiy yechim , aralashma konsentratsiyasi, matematik
model
Qazib olingan gazni ishlab chiqarish jarayonida hosil bo’ladigan tarkibida har xil
qo’shimchalar keraksiz qattiq, suyuq va gaz holidagi aralashmalardan tozalash natijasida
qimmatbaho mahsulotlar ushlab qolinadi va undan sanoatda ko’plab mahsulotlar ishlab
chiqiladi, keyin qayta ishlash natijasida yomon ta’sir qiladigan yoki apparatlarni yemiradigan
qo’shimchalar ajratiladi. Bu jarayonda tashqi havoga chiqadigan iflosliklar kamaytiriladi.
Buning natijasida ekologik muhit yuzaga keladi. Bu esa hozirgi zamonning asosiy
masalalaridan iborat. Gazlarni tozalashning bir nechta usullari mavjud bo’lib, ular
quyidagilardan iborat:
Absorbsiya – gazdagi qo’shimcha moddalarni suyuqliklar yordamida yuttirish;
Adsorbsiya – gazdagi qo’shimchalarni qattiq moddalar yordamida yuttirish;
Elektrostatik kuchlar ta’sirida qo’shimcha moddalarni cho’ktirish;
Suv bilan tozalash, filtrlash va hokozo.
Gazlarni tozalash uchun asosan quyidagi apparatlar yoki jihozlar mavjud bo’lib ular:
skrubber, adsorber va hokozo.
Biz qarayotgan hozirgi ishimizda skrubber gaz tozalash apparati bilan ishlab chiqarilgan
gazni tozalash jarayonlarini tavsiflovchi noma’lun funksiyalar va ularning hosilalarini o’zaro
bog’lovchi munosabat mavjud bo’lganda bu funksiyalarni topishga keltiriladigan masalalarni
qaraymiz. Bunday munosabatlar yoki bog’liqliklar oddiy differensial tenglamalarga keltiriladi
va ularning yechimlari topiladi. [1]
Yuqorida gazni tozalashda skrubber apparati qo’llaganimizda o’zgaruvchilar ajraladigan
birinchi tartibli differensial tenglamaga olib keladi. Biror gazli aralashmadan gazni tozalash
uchun uni skrubber (Skrubber – u yoki bu moddalarni yutuvchi har xil shakldagi idish) apparati
orqali o’tkazamiz. Ma’lum tayin rejimda uni yutqich deb ataymiz. Yutqichning yupqa qatlami
INTERNATIONAL JOURNAL OF SCIENTIFIC RESEARCHERS
ISSN: 3030-332X Impact factor: 8,293
Volume 11, issue 2, May 2025
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yutadigan gazsimon aralashma miqdori aralashma konsentrasiyasiga, shuningdek, qatlamning
ko’ndalang kesimi qalinligi va yuzasiga proporsional bo’ladi. Skrubber asosining radiusi
R
,
balandligi
H
bo’lgan konus shakliga ega bo’lsin. Gaz konus uchidan kiradi. Agar kelayotgan
gazda aralashma konsentratsiyasi
a
%, chiqib ketayotgan gazda esa
b
% bo’lsa, skrubberdagi
gazli aralashma konsentratsiyasi qatlamdan konus uchigacha bo’lgan masofaning funksiyasi
sifatida qarash mumkin bo’ladi. Buni topish uchun gazli aralashmani konsentratsiyasini
g
%
orqali, qatlamdan konus uchigacha bo’lgan masofani
h
orqali belgilab, birinchi tartibli
o’zgaruvchilari ajraladigan differensial tenglamaga keltiramiz. U holda bu jarayonni ushbu
differensial tenglama shaklida ifodalaymiz: [7]
2
r
k
dh
d
gp
g
=
.
(1.)
Bu yerda
k
- proporsionallik koeffitsiyenti,
g
- aralashma konsentratsiyasi,
r
- konusning
yupqa qatlami kesimining radiusi. Yupqa qatlam radiusi
r
ning konus o’lchamlari bilan
bog’liqligi
H
Rh
r
=
munosabat orqali topish mumkin bo’ladi. U holda (1.46) ifodani
quyidagicha yozamiz:
dh
h
H
R
k
d
2
2
2
gp
g
=
.
(2)
Bu tenglama o’zgaruvchilari ajraladigan birinchi tartibli oddiy differensial tenglama. Uning
umumiy yechimini topish uchun o’zgaruvchilarini ajratamiz:
dh
h
H
R
k
d
2
2
2
p
g
g
=
.
(3)
(1.48) ni har ikkala tomonini kvadraturaga keltiramiz, u holda
C
dh
h
H
R
k
d
ln
2
2
2
+
=
p
g
g
.
Bundan
C
H
h
R
k
ln
3
ln
2
3
2
+
=
p
g
yoki
2
3
2
3
ln
ln
H
h
R
k
C
p
g
=
-
,
2
3
2
3
ln
H
h
R
k
C
p
g
=
.
2
3
2
3
H
h
R
k
Ce
p
g
=
.
(4)
Boshlang’ich shartlardan foydalanib, agar
0
=
h
bo’lsa,
a
g
=
bo’lgani
uchun
a
=
C
bo’ladi. Demak,
R
r
O
O
1
H
h
1-rasm
INTERNATIONAL JOURNAL OF SCIENTIFIC RESEARCHERS
ISSN: 3030-332X Impact factor: 8,293
Volume 11, issue 2, May 2025
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Index:
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2
3
2
3
H
h
R
k
e
p
a
g
=
(5)
H
h
=
bo’lganda
b
g
=
shartdan
k
- koeffitsiyentni aniqlaymiz
2
3
2
3
H
h
R
k
e
p
a
b
=
(6)
bo’ladi. Bu yerdan
k
qatnashgan ifodani aniqlash biz uchun qulay, shu sababli
2
2
3
2
1
3
H
H
h
R
k
e
=
a
b
p
(7)
bo’lganligidan, topilgan (7) ifodani (5) ga qo’ysak
3
3
H
h
=
a
b
a
g
(8)
ni hosil qilamiz. Bu topilgan
g
(1.) – differensial tenglamani berilgan boshlang’ich shartlardagi
xususiy yechimi bo’lib, gazdagi aralashma konsentratsiyasini ifodalaydi.
Xulosa .
Biz yuqorida
tabiiy gazni har xil chiqindilardan tozalash, uni iste’mol uchun
foydalanish usullarini ko’rib chiqdik, tozalshdan hosil bo’lgan chiqindilarni qayta ishlab
qimmatbaho mahsulotlar tayyorlanadi, yomon ta’sir qiluvchi apparatlarni yemuruvchi
qo’sshimchalkardan ajratiladi, bu jarayon tashqi havoga chiqadigan iflosliklarni kamaytiradi va
zamon talabiga asosan ekologik muhitni yuzaga keltiradi.
Adabiyotlar:
1. Cоколов В .А Геохимия газов земной коры и атмосферы. М .1966г
2. Husanov, B., & Mahfuza, T. (2022). GEODESICAL VIEWS IN THE MATHEMATICAL
WORKS OF ABU RAYHAN BERUNI. Central Asian Journal of Theoretical and Applied
Science, 3(6), 123-127. Retrieved from
3. https://www.cajotas.centralasianstudies.org/index.php/CAJOTAS/article/view/568
4. B., Khusanov, and Fatkhullayev F. "Existence of the Isolated Special Points Three-
dimensional Differential Systems of a Special Look." JournalNX, 2020, pp. 239-242.
5. Bazar, Khusanov, and Kulmirzaeva G. Abduganievna. "Singular Points Classification of
First Order Differential Equations System Not Solved for Derivatives." International
Journal on Integrated Education, vol. 4, no. 3, 2021, pp. 448-450,
doi:10.31149/ijie.v4i3.1533.
INTERNATIONAL JOURNAL OF SCIENTIFIC RESEARCHERS
ISSN: 3030-332X Impact factor: 8,293
Volume 11, issue 2, May 2025
https://wordlyknowledge.uz/index.php/IJSR
worldly knowledge
Index:
google scholar, research gate, research bib, zenodo, open aire.
https://scholar.google.com/scholar?hl=ru&as_sdt=0%2C5&q=wosjournals.com&btnG
https://www.researchgate.net/profile/Worldly-Knowledge
https://journalseeker.researchbib.com/view/issn/3030-332X
458
6. Husanov, B., Shodiyev, K., & Mehroj, V. (2024). FUNKSIYA EKSTRUMLARINI
IQTISODIY VA QURULISH MASALALARINI YECHISHGA TADBIQI. Gospodarka i
Innowacje., 44, 11-16
7. Husanov, B., Shodiyev, K., & Mehroj, V. (2024). TEKISLIKDA TO’G’RI CHIZIQ
TENGLAMALARINI IQTISODIY MASALARNI YECHISHGA TADBIQI. TA'LIM VA
RIVOJLANISH TAHLILI ONLAYN ILMIY JURNALI, 4(1), 11-14
8. B .Xusanov , Sh.Zikriyayev , Ya .Muxtarov “Oliy matematika “,Samarqand 2022y. 196 b
9.
Khusanov, B., Shodiev, K., & Vahobov, M. (2024, November). On exceptional directions
of a homogeneous polynomial system of the second degree. In American Institute of
Physics Conference Series (Vol. 3244, No. 1, p. 020039)
