Download - kuliah-1-2-statika.ppt
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FLUIDMECHANICS
2005/2006
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04/22/23 Ir.Darmadi,MM 2
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I. KETENTUAN
• Lulus mata kuliah Mekanika Fluida• Disiplin waktu• Disiplin berpakaian• Disiplin etika belajar• KBM dua arah (interaktif)• Tugas : kerjasama, bukan sama-sama kerja.• Ujian : sama-sama kerja, bukan kerjasama.
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II. SKS
Bagi mahasiswa, satu kredit semester perkuliahan adalah beban kegiatan per minggu sbb:a.50 menit tatap muka terjadwal dengan tenaga pengajar.b.60 menit kegiatan akademik terstruktur, yaitu kegiatan yang tidak terjadwal, tetapi direncanakan oleh dosen, misalnya dalam bentuk membuat pekerjaan rumah atau menyelesaikan soal-soal.c.60 menit kegiatan akademik mandiri yaitu kegiatan yang harus dilakukan oleh mahasiswa secara mandiri, untuk mendalami, mempersiapkan atau tujuan lain suatu tugas akademik, misalnya membaca bahan acuan.Bagi tenaga pengajar, satu kredit semester perkuliahan adalah beban kegiatan per minggu sbb.a.50 menit acara tatap muka terjadwal dengan mahasiswa.b.60 menit acara pertemuan perencanaan dan evaluasi kegiatan akademik terstruktur.c.60 menit pengembangan mata kuliah.
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III. SISTEM PENILAIAN
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Lihat: Buku pedoman akademik FT UNSRI 2009/2010
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IV. PUSTAKA
• Chow V.T., 1988, Open Channel Hydraulics.• Graf, H.W, 2003, Fluvial Hydraulics. John Wiley and Sons, Inc.,
Ontario,Canada.• Sturn, W.T., 2001, Open Channel Hydraulics, McGraw- Hill Co.,
New York , N.Y.• Triatmodjo, B., 2003, Hidraulika II, Beta Offset, Yogyakarta.• Roberson, dkk., 1997, Hydraulic Engineering, John Wiley and
Sons, Inc., New York.• dll.
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1.1. INTRODUCTION• Mekanika fluida adalah bagian daripada mekanika
terapan (applied mechanics) yang mempelajaristatika dan dinamika dari cairan (fluida) dan gas.
• Fluida adalah benda yang tidak memberikanperlawanan terhadap perubahan bentuk geometris.Supaya bentuknya tetap fluida harus dibatasidengan dinding kedap, dan jika dinding ini diubahmaka bentuk geometri fluida akan berubahmenyesuaikan diri.
• Ketidak mampuan fluida mempertahankan bentukgeometrisnya disebabkan oleh lemahnya gayakohesi antar molekul.
• Berdasarkan kohesinya fluida dibagi menjadi bendagas dan benda cair (liquid).
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1.2. DIMENSIONS, UNITS AND PHYSICAL QUANTITIES(Symbol, units system –foot,metric,SI-)
– MASA (MASS)M, slug, gram, kilogram
– GAYA (FORCE)F, lbf, kgf, dyne, Newton (kgm/det2)
– KERAPATAN (MASS DENSITY)ρ, slug/ft3, gm/cc, kg/m3
– BERAT SPECIFIC (SPECIFIC WEIGHT)w = γ = ρg, lbf/ft3, dyne/cm3
– SPECIFIC GRAVITY (RELATIVE DENSITY)ρ fluida /ρ water, tidak berdimensi
– KEKENTALAN KINEMATIKµ, lbf.sec/ft2, dyne-sec/cm2, Newton sec/m2
– KEKENTALAN DINAMIKυ = µ/ρ , ft2/sec, cm2 /sec, m2/sec
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•••••••
PERENCANAAN/PERHITUNGANKONSTRUKSI
TANGKI AIRRESERVOIR BAWAH TANAHKOLAM RENANGTEBING SUNGAIPINTU AIRBENDUNGBENDUNGAN
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P O T E N TIALM I K R O H Y D R O in WEST JAVA
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SMALL WEIR ON IRRIGATIONCHANNEL
WEST JAVA
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P O T E N TIALM I K R O H Y D R O in WEST JAWA
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P O T E N TIALM I K R O H Y D R O in Yogyakarta
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RETAINING WALL
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SHEET PILE
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1.2.
4.5.
CHAPTER 2 : FLUID STATIC2.1. INTRODUCTION2.2. PRESSURE AT A POINT2.3. PRESSURE VARIATION2.4. FLUID AT REST
PRESSURE IN LIQUID AT RESTPRESSURE IN THE ATMOSPHERIC
3.
6.7.
MANOMETERFORCE ON PLANE AREASFORCE ON CURVED SURFACESBUOYANCYSTABILITY
2.5. LINEARLY ACCELERATION CONTAINER2.6. ROTATING CONTAINER
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2.1. INTRODUCTION
• Fluid Static adalah ilmu yangmempelajari fluida dengan kondisitidak ada pergerakan antar partikel darifluida tersebut.
• Kondisi ini bisa diartikan, jika tidak adapergerakan antara partikel maka tidakakan timbul gaya geser (shear stress)sehingga Tegangan yang ada hanyalahnormal stress dan tekanan (pressure).
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Ada 3 situasi mengenai fluida diam yangakan dipelajari lebih lanjut yaitu :
• 1.Air yang menekan bangunan misalnya pintuair, bendung, bendungan (dam)
• 2.Cairan yang terletak pada suatu tempat, yangmana tempat (wadah) tsb mengalamipergerakan linier (linear acceleration)
• 3.Cairan yang terletak di silinder yang berputar
(rotating cylinder)
Pada ketiga kondisi tersebut cairan/fluidadalam keadaan keseimbangan statis (staticequilibrium).
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A. Fluida Statis
1. TekananDefinisi tekanan sebagai gaya normal ( tegak lurus ) yang bekerja pada suatu
bidang dibagi dengan luas bidang tersebut.
Rumus tekanan : (7 – 1)
– Aplikasi Tekanan dalam Keseharian Untuk dapat meluncur diatas kolam es beku pemain ski menggunakan sepatu
luncur. Sepatu luncur memiliki pisau pada bagian bawahnya. Pisau ini memberi tekanan yang besar pada lantai es beku, hingga es yang berada tepat dibawah pisau mencair, tetapi di kiri – kanannya tidak. Cairan tepat dibawah pisau berfungsi sebagai pelumas, sedang es beku di kiri dan kanan pisau tetap mencengkeram pisau, sehingga sepatu luncur beserta pemain dapat meluncur diatas kolam beku. Seperti diketahui, bagian es yang mencair segera membeku setelah tekanan pisau hilang karena pemain berpindah. Jika pemain ski menggunakan sepatu luncur es, pisau memberi tekanan besar pada lapisan salju, sehingga lapisan salju mencair dan pemain ski justru tidak dapat meluncur diatas salju. Pemain ski justru harus menggunakan sepatu ski yang memiliki luas bidang cukup besar. Ini agar tekanan yang diberikan pemain ski yang berdiri pada sepatu ski tidak membuat salju mencair, sehingga pemain ski dapat meluncur di atas salju.
AFp
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3
APLIKASI DALAM DUNIA NYATA2. BIDANG PENGAIRAN
04/22/23 Ir.Darmadi,MM 20
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TEKANAN
AFP
Gaya tegak lurus bidang
Luas permukaan bidang
Apakah gaya pada seluruh permukaan sama ?
Tekanan pada sebuah titik :
AFP
A 0lim
dAdF
Satuan tekanan (dalam SI) : pascal (Pa)
2mN1Pa1
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PRESSURE BELOW FREE SURFACE
• dp/dz = - ρ gz
free surfaceair
liquidh
z= -h
p = 0 gage
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2.4.1. PRESSURE IN LIQUIDAT REST
• Fluid at rest means that no acceleration:dp ρ g dzp ρ g dzp ρ g dzp -ρ g z constpρ gz const
• Expressed that the pressure increaseswith depth
• (p/ ρ g) +(z) = piezometric head• p = ρ g h dan apabila p = 0 maka h = 0
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p
hρ
g
Dengan demikian maka dapat dinyatakan sebagai berikut :
p ρ g z atau p ρ g h (2.6)
dimana :
= tekanan pada kedalaman h dari permukaaan ( N/m2 )
= jarak vertikal (-z) diukur dari permukaan cairan ( m )
= kerapatan cairan ( kg/m3 )
= gaya gravitasi ( m/det2 )Fluida Statik 12
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Tangki-tangki pada gambar di bawah ini mempunyai luas dasaryang sama, demikian pula dengan kedalaman cairannya.
h
Luas A
h
Luas A
h
Luas A
h
Luas A
Gambar 2.3.Tekanan hidrostatik pada dasar tangki-tangki yangberbeda-beda bentuk tetapi luas dasarnya sama
Fluida Statik 13
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h
2.4.4.FORCE ON PLANE AREAS
α X
h y sinαγ hdA
y
C.P.
Y
dy
C
dA
yp
y
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2.4.4.FORCE ON PLANE AREAS
• MAGNITUDE of the FORCE on a PLANEAREAS :
• PRESSURE ACT AT THE CENTROID multipliedby THE AREA
• GENERAL :• Force does not act at the centroid
except on a horizontal area for which y =center of pressure (C.P.) and thecentroid coincide
• FORCE (f)• Pressure Prism acting on the area
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FORMULA AND TERMINOLOGION PLANE AREAS
• C = centroid• CP = Center of Pressure
• y, y , xp, yp,
• p = ρ gh
• F = p *A
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FORCE ON PLANE AREAS WITHTOP EDGE FREE SURFACE
H
H’/3H’
H/3
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X
R h1
P2
P1 H yp
AP1
Y
A
yR
P2
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2.4.5.FORCE ON CURVEDSURFACES
F2 F2
F1
Fw
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2.4.6. BUOYANCY
THE LAW OF BUOYANCY (ARCHIMEDESPRINCIPLE) :
• BUOYANCY FORCE ON AN OBJECTEQUAL TO THE WEIGHT OFDISPLACED LIQUID
TO PROVE THE LAW OF BUOYANCY :• CONSIDER THE SUBMERGED BODY
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h1F1
Volume
h2
W + Fw
F2
FREE BODY DIAGRAM
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w
FB
FORCES ON FLOATING OBJECT
W = FB
FB = buoyant force
W = weight of floating object= ρg * Volume submerged body
CG = γ Volume
•W act through its center ofgravity of liquids
•Center of Gravity must lie onthe same vertical line as thecentroid of the liquid volume
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HYDROMETER
• Hydrometer :Instrument used to measure the specificgravity (S) of liquids operates on theprinciple of buoyancy.
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2.4.7.STABILITY
w w FB
w
G
C
FB
C
C
FB
G
FB
C
G
w
C GG
FB w
UNSTABLE NEUTRAL STABLE
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––––
W
GC
FB
G = Center of GravityC = Centroid (Center of Buoyancy)W = Weight of BodyFB = Buoyancy Force
• Jika letak G diatas C maka benda dalam keadaanmengapung
• Jika letak G coincide dengan C maka dalamkeadaan melayang
• Jika letak G dibawah C maka benda dalam keadaantenggelam
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METACENTRUM
Mw
G
CC
G
x C’ GM
WFB
(a) Equilibrium Position
FB
(b) Rotated Position
GM = Metacentric Height
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METACENTRUM
• GM yaitu jarak dari C terhadap titikperpotongan dari gaya apung dengantitik metacentrum M sebelum rotasi dansesudah rotasi.
• Benda berada dalam keadaan stabilmeskipun letak G diatas C, jika tinggimetacentric GM positive.
• Benda dalam keadaan tidak stabil jikaletak titik M dibawah G.
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F
P
2.5. LINEARLY ACCELERATING CONTAINERS(without VERTICAL ACCELERATION)
α
F P1 P2
W =mgF = m ax
P sin α = F = m axP cos α = W = m g
α
W m = massag = gravitasiax = percepatan linier
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EQUILIBRIUM CONDITION
P sin αmax ax
P cos αmg g
tan α = ax
g
P1=TEKANAN HIDROSTATIS PADA BAGIAN BELAKANG TANGKIP2= TEKANAN HIDROSTATIS PADA BAGIAN MUKA TANGKIax = PERCEPATAN LINIER/HORISONTALα = SUDUT PERMUKAAN CAIRAN DENGAN BIDANG HORISONTAL
TEKANAN YANG TERJADI PADA TANGKI :P =P1 – P2P = m ax
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LINEARLY ACCELERATING CONTAINERS
dp ∂p∂x
dx ∂p∂y
dy ∂p∂z
dz
dp −ρ a x dx −ρ a y dy −ρ ( a z g ) dzdp −ρ a x dx −ρ ( g a z ) dzp 2 −p1 −ρ a x ( x 2 −x1 ) −ρ ( g a z )( z 2 −z1 )
az
1ax
z1-z2 αx2-x1
2
z1 −z2
x2 −x1tan α = ax
g az
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GAYA2 YANG BEKERJA
Fy
α
θ
F
Fx
P W
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r
∂p ∂p∂r ∂r
d θ 2
2
2.6. ROTATING CONTAINERS
• NEWTON SECOND LAW :
∑F r ma
−drrd θ dz −prd θ dz −( dr ) 2 d θ dz
2 pdrdz prd θ dz −ρ drrd θ dzr ω2
∂p∂r
= ρ r ω
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