Mekanika Fluida 2
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Transcript of Mekanika Fluida 2
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Sasaran
FLUIDA STATIKHYDROSTATICS PRINCIPLES
Dapat menghitung distribusi tekanan dan gaya pada benda yang terendam dalam fluida.
Dapat menghitung cara menghitung tekanan menggunakan differential manometry.
Dapat a menggunakan manometer untuk mengukur tekanan
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Review FLUIDA STATIK
• TEKANAN DALAM BEJANA P = F/A
• EFEK GRAVITASI PADA TEKANAN–P = P0 + rgd
• GAYA BUOYANT F = r g V
05
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TEKANAN DALAM BEJANA
Tekanan timbul karena adanya tabrakan antara partikel fluida dengan dinding bejana (molecules “bouncing” )
Ada perubahan momentum (impulse), jika partikel menabrak dinding, balik arah menjauhi dinding wadah. Jadi pasti ada gaya bekerja pada partikel dan dinding,
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TEKANANGaya per satuan luas, dimana gaya tegak lurus luasan.
p=A m2
Nm-2
(Pa)
NF
Tekanan absolut adalah tekanan relatif terhadap vakum
Tekanan gauge, yaitu tekanan relatif terhadap atmosfir ( p-pa)
patmosfir= 1.013X105 Nm-2Pa (Pascal)
1 psi = 6895 Pa
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Seseorang menginjak jari kakimu dengan gaya 500 N pada luasan 1.0 cm2. Hitunglah tekanan dalam satuan atmosfir.
atm 49
Pa 10013.1
atm 1
N/m 1
Pa 1N/m 100.5
m 101.0
N 500
5226
24-av
A
FP
242
2 m 100.1cm 100
m 1cm 0.1 luasan
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Pascal’s PrinciplePerubahan tekanan pada semua titik dalam fluida diteruskan keseluruhan fluida. Ini berguna untuk sistim pengangkat hidrolik.
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Gaya force F1 bekerja pada piston A1.
Gaya ditransmisikan ke piston A2.
F2
11
22
2
2
1
1
A
A
A
F
A
F
2point at 1point at
FF
PP
F2
1 500 N
10 5000 N
100 50,000 N
12 AA
Assume F1 = 500 N
A1A2
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EFEK GRAVITASI PADA TEKANAN FLUIDA
dgPP
dgPP
dgPP
gAdAPAP
wAPAPF
12
12
12
12
12
or
0A cylinder of fluid
P1A
P2A
w
d
dgPP atm
Jika ujung atas kolom fluida terletak pada permukaan fluida maka P1=Patm jika wadah terbuka
P
Atm
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0F
EFEK GRAVITASI PADA TEKANAN FLUIDA
F = gaya dari atas + gaya dari bawah + gaya gravitasi = 0
0 zyxgyxPyxP ba
gz
PP ba
Tekanan atasPb
Tekanan bawah Pa
Za
Zb
Densitas=
Dz
gdz
dP
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TEKANAN DENGAN KEDALAMAN
gdz
dP
)( 122 1zzgPP
Untuk gas RT
PM
gRT
PM
dz
dP
)(ln 121
2 zzRT
gM
P
P
(gas ideal, isotermal)
Untuk cair
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Tekanan pada permukaan air danau adalah 105 kPa. Hitung tekanan pada kedalaman 35.0 m dibawah
permukaan air.
atm 3.4kPa 343
m 35m/s 8.9kg/m 1000
23
atm
atm
dgPPP
dgPP
Kerapatan air segar
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Tekanan di permukaan planet Venus adalah 95 atm. How far below the surface of the ocean on Earth do you need to be to experience the same pressure?
m 950
N/m 109.5m/s 8.9kg/m 1025
N/m 109.5atm 94
atm 1atm 95
2623
26
atm
d
d
dg
dg
dgPP
Density of sea water
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PENGUKURAN TEKANAN
A manometer is a U-shaped tube that is partially filled with liquid.
Both ends of the tube are open to the atmosphere.
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Cylinder of gas
A container of gas is connected to one end of the U-tube
C
B’B
A d
gdP
gdPPPP
gdPPP
BCB
CBB
gauge
atm
'
B'B PP
atmc PP
Point A is the original location of the top of the fluid before the gas cylinder is connected.
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Measuring pressure Manometers
h
p1 p2=pa
liquiddensity
x y
z
p1 = px
px = py
pz= p2 = pa
(negligible pressure change in a gas)
(since they are at the same height)
py - pz = gh
p1 - pa = gh
So a manometer measures gauge pressure.
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Measuring Pressure Barometers
A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid.
p1 = 0vacuum
h
p2 = pa
p2 - p1 = gh
pa = gh
examples
water: h = pa/g =105/(103*9.8) ~10m
mercury: h = pa/g =105/(13.4*103*9.8) ~800mm
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Atmospheric pressure is equivalent to a column of mercury 76.0 cm tall.
gdP
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Archimedes’ Principle
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ARCHIMEDES’ PRINCIPLE • Buoyant Force (FB)
–weight of fluid displaced–FB = fluidVdisplaced g
–Fg = mg = object Vobject g
–object sinks if object > fluid
–object floats if object < fluid
• If object floats…–FB = Fg
–Therefore: fluid g Vdispl. = object g Vobject
–Therefore: Vdispl./Vobject = object / fluid
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ARCHIMEDES EXAMPLEA cube of plastic 4.0 cm on a side with density =
0.8 g/cm3 is floating in the water. When a 9 gram coin is placed on the block, how much sinks below water surface?
mg
Fb
Mg
S F = m a
Fb – Mg – mg = 0
g Vdisp = (M+m) g
Vdisp = (M+m) /
h A = (M+m) /
h = (M + m)/ ( A)
= (51.2+9)/(1 x 4 x 4) = 3.76 cm
M = ρplastic Vcube = 0.8x4x4x4
= 51.2 g
h
koin
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Sebuah balok es mengambang diatas segelas air, sampai permukaan air rata pada pinggiran. Ketika es meleleh maka air di dalam akan :
1. Go up, causing the water to spill out of the glass.
2. Go down.
3. Stay the same. CORRECT
COBA PIKIRKAN
B = W g Vdisplaced
W = ice g Vice W g VMust be same!
ice-cube
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COBA PIKIRKANWhich weighs more:
1. A large bathtub filled to the brim with water.
2. A large bathtub filled to the brim with water with a battle-ship floating in it.
3. They will weigh the same.
Tub of water
Tub of water + ship
Overflowed water
CO
RREC
T
Weight of ship = Buoyant force =
Weight of displaced water16
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Sepotong logam dilepaskan dibawah air water. Volume metal 50.0 cm3 dan SG 5.0. Hitung percepatan initialnya. Saat v=0 tidah ada gaya drag.
w
FB
mawFF B VgFB water
FB adalah berat fluida yang dipindahkan oleh benda
1
ρ
ρ
ρ
ρ
objectobject
water
objectobject
water
V
Vgg
V
Vga
gm
F
m
w
m
Fa BB
0.5gravity specificwater
object
water = 1000 kg/m3 (at 4 °C).
2
objectobject
water m/s 8.710.5
11
..
11
ρ
ρ
g
GSg
V
Vga
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m 5.1m 10*m 20kg/m 1000
kg 100.3
0
3
5
A
md
mAd
mV
gmgVgm
wF
wFF
w
b
bw
bww
bwww
B
B
Wadah segi 4 berdasar datar diisi dengan coal, massanya 3.0105 kg. Panjang 20 m dan lebar 10m, mengambang diair. Berapa kedalaman wadah masuk ke dalam air.
w
FB
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DECANTERS GRAVITY
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TEKANAN DALAM BENDA RIGID BERGERAK
)(2
2
dt
zdg
dz
dP
Gerak lurus
Gerak rotasi
Centripetal accelaration =(angular velocity)2.radius
rac2
rdr
dP 2
)cos(2
2
dt
adg
da
dP
Searah dengan gravitasi
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DECANTERS
Centrifugal
Aout
BoutrA
rB
ri
R
pA=pB=patm