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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 du

dy dy

Aliran Laminer dan Turbulen

Aliran laminer : gerak cairan dalam lapis-lapis

Aliran turbulen: partikel lapisan cairan bercampurdengan 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 TurbulenPercobaan 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

Reu D u u D

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

= kekentalan kinematis: / = m2/det

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.det. . . 1

1 detRe

kg m m m

m g

D u

k

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 > 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.

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).

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

( ) 0.99u y U

U

U is the free-stream velocity

(x) is the boundary layer thickness when u(y) 0.99U

x

y ( )x( ) 0.99u y U

( ) 0.99u y U

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 dy

U

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

0

m dyU

u1

U

uδ

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Laminar Boundary Layer Growth # 1

Boundary layer Inertia is of the same magnitude as Viscosity

+ d

dy

x

y(x)

L

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:

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

2

2 2

U UF

y y

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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 ρUL UL

μ υLR

2

25 (Blasius)

U U L L

L U U

Note the new Reynolds numbercharacteristic velocity and characteristic length

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

* *

5. 35.L T

u u

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Flow at a pipe entry # 1

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

L

U D

δ

Flow at a pipe entry # 2

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Flow at a pipe entry # 3

Ditinjau pipa bulat diameter D. Aliran bisa laminar atauturbulen. 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:

For open flow:

Considering a pipe as two boundary layers meeting, D = 2a = 2

Reu D

5L

U

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 10

μ ρU μLR

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Posisi daerah laminer, transisi dan turbulen

Pengaruh kekasaran pada sub lapis