08 Aliran Zat cair Riil.pdf

ALIRAN ZAT CAIR RIIL

Ir. Suroso Dipl.HE, M.EngDr. Eng. Alwafi Pujiraharjo

Jurusan Teknik SipilUniversitas Brawijaya

Aliran Zat Cair Riil 2

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


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∝ ⇒ =


Aliran Laminer dan Turbulen

Aliran laminer : gerak cairan dalam lapis-lapis

Aliran turbulen: partikel lapisan cairan bercampur dengan partikel cairan lapisan lainnya


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.


Aliran Laminar dan Turbulen

Percobaan Reynolds

Re/

u D inertia forceviscous force dumping

ρµ

= =


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

= = =


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

= = =


Klasifikasi Aliran

Menurut Reynolds aliran digolongkan menjadi :

Aliran laminer : Re < 2000

Aliran transisi : 2000 < Re < 4000

Aliran turbulen: Re > 4000


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


Aliran transisi

Angka Reynolds 2000 < Re < 4000Kecepatan sedangZat warna sedikit tercampur dengan air


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


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


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


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


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

∞ ⎛ ⎞= −⎜ ⎟⎝ ⎠∫


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


Laminar Boundary Layer Growth # 1

τ + dτ

τ

dy

x

yδ(x)

L

Boundary layer Inertia is of the same magnitude as Viscosity



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∂ ∂

∝ ∝ ∝∂ ∂



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 = =



Critical Reynolds number for flow along a surface is RL = R* = 3.2*105

Critical velocity (u*) = velocity when RL = 3.2*105


Prandtl’s Boundary Layer Theory # 1


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= =


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





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





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

=



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= = =


Posisi daerah laminer, transisi dan turbulen


Pengaruh kekasaran pada sub lapis


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08 Aliran Zat cair Riil.pdf