ALIRAN ZA ZAT T CAIR CAI R RIIL
Ir. Suroso Dipl.HE, M.Eng Dr.. Eng. Alwafi Pujir Dr Pujiraharjo aharjo Jurusan Teknik Sipi Jurusan Sipill Universita Unive rsitas s Brawij Brawijaya aya
Efek Kekentalan pada Aliran Pada anggapan
ideal fluid (zat fluid (zat cair ideal) → tidak mempunyai mempunyai kekentalan sehingga tidak ada geseran antara cairan-dinding saluran.
Pada
real fluid (zat fluid (zat cair riil) → ada kekentalan sehingga geseran akan memegang peran penting dalam aliran.
Kekentalan
→ - menyebabkan menyebabkan gaya geser - kehilanga kehilangan n energi energi
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Hukum Newton tentang Kekentalan Tegangan
geser antara dua partikel zat cair yang berdampingan adalah sebanding dengan perbedaan kecepatan dari kedua partikel.
du dy
du dy
Aliran Laminer dan Turbulen Aliran
laminer : gerak cairan dalam lapis-lapis
Aliran
turbulen: partikel lapisan cairan bercampur dengan partikel cairan lapisan lainnya
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Osborne Reynolds - England (1842-1912) Reynolds
was a prolific writer who published almost 70 papers during his lifetime on a wide variety of science and engineering related topics.
He
is most well-known for the Reynolds number, which is the ratio between inertial and viscous forces in a fluid. This governs the transition from laminar to turbulent flow.
Osborne Reynolds - England (1842-1912)
Reynolds’ apparatus consisted of a long glass pipe through which water could flow at different rates, controlled by a valve at the pipe exit. The state of the flow was visualized by a streak of dye injected at the entrance to the pipe. The flow rate was monitored by measuring the rate at which the free surface of the tank fell during draining. The immersion of the pipe in the tank provided temperature control due to the large thermal mass of the fluid.
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Aliran Laminar dan Turbulen Percobaan
Reynolds
Re
u D
inertia force viscous force / dumping
Hasil Percobaan Reynolds Setelah
melakukan percobaan berulang kali, Reynolds menyimpulkan bahwa: aliran dipengaruhi oleh kecepatan aliran U , kekentalan , rapat massa , dan diameter pipa D.
Angka
Reynolds (Reynolds number): Re
Re
u
D u
uD
D
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Angka Reynolds
Re
Angka
Reynolds tidak berdimensi.
Dalam
sistem satuan SI:
= rapat massa
: kg/m3
D = diameter pipa
:m
u = kecepatan aliran : m/det = kekentalan dinamis: N.det/m2 = kg/m.det
/det = kekentalan kinematis: / = m2
Re
D u
kg m m m.det . . . 1 3 m 1 det k g
Klasifikasi Aliran Menurut Reynolds aliran digolongkan menjadi :
Aliran laminer : Re < 2000
Aliran transisi : 2000 < Re < 4000
Aliran turbulen: Re > 4000
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Sifat Fisik Aliran Aliran laminer Angka
Reynolds Re < 2000
Kecepatan rendah
Zat warna tidak tercampur dengan air
Partikel zat cair bergerak dalam garis lurus
Dapat dianalisis dengan matematika sederhana
Jarang terjadi dalam praktek di lapangan
Aliran transisi Angka
Reynolds 2000 < Re < 4000
Kecepatan sedang
Zat warna sedikit tercampur dengan air
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Aliran turbulen Angka
Reynolds Re > 4000 Kecepatan tinggi Zat warna tercampur dengan cepat Partikel aliran zat cair tidak teratur Rata-rata gerak adalah dalam arah aliran Tidak dapat dilihat dengan mata telanjang Perubahan/fluktuasi sulit dideteksi Analisisis matematika sulit → dilakukan ekspirimen/percobaan Sering terjadi dalam praktek di lapangan.
Aliran Turbulen
Simulasi aliran turbulen yang keluar dari ujung akhir pipa
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Boundary Layer
The idea of the boundary layer dates back at least to the time of Prandtl (1904, see the article: Ludwig Pran dtl’s boundary layer, Physics Today , 2005, 58, no.12, 4248).
Boundary Layer There
are three main definitions of boundary layer thickness:
1. 99% thickness
2. Displacement thickness
3. Momentum thickness
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99% Thickness U
u ( y ) 0.99U
u ( y ) 0.99U
u ( y ) 0.99U
( x)
y x
U is the free-stream velocity
( x) is the boundary layer thickness when u( y) 0.99U
Displacement Thickness #1
There is a reduction in the flow rate due to the presence of the boundary layer
This is equivalent to having a theoretical boundary layer with zero flow
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Displacement Thickness # 2 The
areas under each curve are defined as being equal:
q
U u dy
and q δ* U
0
Equating
these gives the equation for the displacement thickness:
0
δ* 1
u dy U
Momentum Thickness In
the boundary layer, the fluid loses momentum, so imagining an equivalent layer of lost momentum:
m ρu U u dy
and
m ρU 2 δm
0
Equating
these gives the equation for the momentum thickness:
δm
0
u u 1 dy U U
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Laminar Boundary Layer Growth # 1 + d ( x)
y
dy
x L
Boundary layer Viscosity
Inertia is of the same magnitude as
Laminar Boundary Layer Growth # 2 a) Inertia Force: a particle entering the boundary layer will be slowed from a velocity U to near zero in time, t. giving force FI U/t. But u = x/t t L/U where U is the characteristic velocity and L the characteristic length in the x direction. Hence FI U2/L b) Viscous force:
U 2U F 2 2 y y
since U is the characteristic velocity and characteristic length in the y direction
the
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Laminar Boundary Layer Growth # 3 Comparing
U L
2
U
2
a) and b) gives:
L U
5
L U
(Blasius)
So the boundary layer grows according to L Alternatively,
dividing through by L, the nondimensionalised boundary layer growth is given by:
δ
L
1
R L
Note the new Reynolds number characteristic velocity and ρUL UL R L characteristic length μ υ
Laminar Boundary Layer Growth # 4
Critical Reynolds number for flow along a surface is R L = R* = 3.2*105
Critical velocity (u*) = velocity when RL = 3.2*105
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Prandtl’s Boundary Layer Theory # 1
Prandtl’s Boundary Layer Theory # 2 Aliran
laminer dengan kecepatan seragam U 0 setelah melalui pelat datar → distribusi kecepatan berubah dari 0 → U 0 seperti gambar → ada lapis batas dengan tebal .
Didalam
daerah turbulen sempurna aliran turbulen dipisahkan dari dinding batas oleh sub lapis laminer
L
5. u*
T
35. u*
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Flow at a pipe entry # 1
U
D δ L
If the boundary layer meet while the flow is still laminar the flow in the pipe will be laminar
If the boundary layer goes turbulent before they meet, then the flow in the pipe will be turbulent
Flow at a pipe entry # 2
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Flow at a pipe entry # 3
Ditinjau pipa bulat diameter D. Aliran bisa laminar atau turbulen. Dalam salah satu kasus, profil terjadi ke hilir sepanjang beberapa kali diameter disebut entry length L. L/D adalah fungsi dari Re.
Lh
Flow at a pipe entry # 4
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Flow at a pipe entry # 5 In
a pipe Reynold number is given by:
Re For
u D
open flow: 5
L U
Considering
a pipe as two boundary layers meeting, D = 2a = 2
Flow at a pipe entry # 6 Hence,
the mean velocity in the pipe is comparable to the free-stream velocity, U:
Re
If
ρU μ
.10
μL ρU
10
ρUL μ
10 RL
RL is R* = 3.2*105 then Re = 5657
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Posisi daerah laminer, transisi dan turbulen
Pengaruh kekasaran pada sub lapis
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