Efek Kekentalan pada Aliran

ALIRAN ZAT CAIR RIIL

Ir. Suroso Dipl.HE, M.Eng Dr. Eng. Alwafi Pujiraharjo Jurusan Teknik Sipil Universitas Brawijaya

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 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 

uD 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



 Du uD   

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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  = kekentalan kinematis:  / = m2/det

Re 

 D u kg m m m.det  3. . . 1  m 1 det kg

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 Prandtl’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: 

u  δ*   1   dy U 0

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 2δ m

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  Inertia is of the same magnitude as Viscosity

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:

  2U U F   2  2 y y 

since U is the characteristic velocity and  the characteristic length in the y direction

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Laminar Boundary Layer Growth # 3  Comparing a) and b) gives: U 2 L



U 2





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 1  L RL

Note the new Reynolds number characteristic velocity and ρUL UL RL   characteristic length μ υ

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

Prandtl’s Boundary Layer Theory # 2  Aliran laminer dengan kecepatan seragam U0 setelah melalui pelat datar → distribusi kecepatan berubah dari 0 → U0 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 

u D 

 For 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 

ρU μL ρUL .10  10  10 RL μ ρU μ

 If 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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