Transcript
ALIRAN ZAT CAIR RIIL
Ir. Suroso Dipl.HE, M.EngDr. Eng. Alwafi Pujiraharjo
Jurusan Teknik SipilUniversitas Brawijaya
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Efek Kekentalan pada Aliran
Pada anggapan ideal fluid (zat cair ideal) →tidak mempunyai kekentalan sehingga tidak ada geseran antara cairan-dinding saluran.
Pada real fluid (zat cair riil) → ada kekentalan sehingga geseran akan memegang peran penting dalam aliran.
Kekentalan → - menyebabkan gaya geser
- kehilangan 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 dudy dy
τ τ µ∝ ⇒ =
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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.
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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 forceviscous force dumping
ρµ
= =
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Hasil Percobaan ReynoldsSetelah melakukan percobaan berulang kali, Reynolds menyimpulkan bahwa: aliran dipengaruhi oleh kecepatan aliran U, kekentalan µ, rapat massa ρ, dan diameter pipa D.
Angka Reynolds (Reynolds number): Re
Re u D u u D
D
ρµ µ υρ
= = =
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Angka Reynolds Re
Angka Reynolds tidak berdimensi.Dalam sistem satuan SI:ρ = rapat massa : kg/m3
D = diameter pipa : mu = kecepatan aliran : m/detµ = kekentalan dinamis: N.det/m2 = kg/m.detυ = kekentalan kinematis: µ /ρ = m2/det
3
.detRe . . . 11 det
D u kg m m mm kg
ρµ
= = =
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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 laminerAngka Reynolds Re < 2000Kecepatan rendahZat warna tidak tercampur dengan airPartikel zat cair bergerak dalam garis lurusDapat dianalisis dengan matematika sederhanaJarang terjadi dalam praktek di lapangan
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Aliran transisi
Angka Reynolds 2000 < Re < 4000Kecepatan sedangZat warna sedikit tercampur dengan air
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Aliran turbulen
Angka Reynolds Re > 4000Kecepatan tinggiZat warna tercampur dengan cepatPartikel aliran zat cair tidak teraturRata-rata gerak adalah dalam arah aliranTidak dapat dilihat dengan mata telanjangPerubahan/fluktuasi sulit dideteksiAnalisisis matematika sulit → dilakukan ekspirimen/percobaanSering terjadi dalam praktek di lapangan.
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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 Prandtl’s boundary layer, Physics Today, 2005, 58, no.12, 42-48).
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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
x
y ( )xδ( ) 0.99u y U=( ) 0.99u y U=
( ) 0.99u y U=
U is the free-stream velocity
δ(x) is the boundary layer thickness when u(y) ≈ 0.99U
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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:
Equating these gives the equation for the displacement thickness:
( )0
q U u dy and q δ* U∞
= − =∫
0
uδ* 1 dyU
∞ ⎛ ⎞= −⎜ ⎟⎝ ⎠∫
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Momentum Thickness
In the boundary layer, the fluid loses momentum, so imagining an equivalent layer of lost momentum:
Equating these gives the equation for the momentum thickness:
( ) 2m
0
m ρu U u dy and m ρU δ∞• •
= − =∫
∫∞
⎟⎠⎞
⎜⎝⎛ −=
0m dy
Uu1
Uuδ
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Laminar Boundary Layer Growth # 1
τ + dτ
τ
dy
x
yδ(x)
L
Boundary layer Inertia is of the same magnitude as Viscosity
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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 ∝ ρU/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 ∝ ρU2/L
b) Viscous force:
since U is the characteristic velocity and δ the characteristic length in the y direction
2
2 2
U UFy yµτ µ µ
δ∂ ∂
∝ ∝ ∝∂ ∂
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Laminar Boundary Layer Growth # 3
Comparing a) and b) gives:
So the boundary layer grows according to √L
Alternatively, dividing through by l, the non-dimensionalised boundary layer growth is given by:
δ 1
LL R∝
2
2 5 (Blasius)U U L LL U U
ρ µ µ µδ δδ ρ ρ
∝ ⇒ ∝ ⇒ =
Note the new Reynolds numbercharacteristic velocity and characteristic length
ρUL ULµ υLR = =
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Laminar Boundary Layer Growth # 4
Critical Reynolds number for flow along a surface is RL = R* = 3.2*105
Critical velocity (u*) = velocity when RL = 3.2*105
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Prandtl’s Boundary Layer Theory # 1
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Prandtl’s Boundary Layer Theory # 2Aliran laminer dengan kecepatan seragam U0setelah melalui pelat datar → distribusi kecepatan berubah dari 0 → U0 seperti gambar → ada lapis batas dengan tebal δ.
Didalam daerah turbulen sempurna aliran turbulen dipisahkan dari dinding batas oleh sub lapis laminer
* *
5. 35.L Tu u
υ υδ δ= =
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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
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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
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Flow at a pipe entry # 4
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Flow at a pipe entry # 5
In a pipe Reynold number is given by:
For open flow:
Considering a pipe as two boundary layers meeting, D = 2a = 2δ
Re u Dρµ
=
5 LUµδρ
=
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Flow at a pipe entry # 6
Hence, the mean velocity in the pipe is comparable to the free-stream velocity, U:
If RL is R* = 3.2*105 then Re = 5657
ρU µL ρULRe .10 10 10µ ρU µ LR= = =
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Posisi daerah laminer, transisi dan turbulen
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Pengaruh kekasaran pada sub lapis
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