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
Review FLUIDA STATIK
• TEKANAN P = F/A
• EFEK GRAVITASI PADA TEKANAN–P = P0 + ρgd
• GAYA BUOYANT F = ρ g V
05
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
Seseorang menginjak jari kakimu dengan gaya 500 N pada luasan 1.0 cm2. Berapa atmosfir tekanan tersebut .
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 −×=
=
TEKANAN
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,
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
0=F
EFEK GRAVITASI PADA TEKANAN FLUIDA
F = gaya dari atas + gaya dari bawah + gaya gravitasi = 0
0=∆∆∆−∆∆−∆∆ zyxgyxPyxP ba ρ
gz
PP ba ρ−=∆−
Tekanan atasPb
Tekanan bawah Pa
Za
Zb
Densitas=ρ
∆z
gdz
dP ρ−=
TEKANAN DENGAN KEDALAMAN
gdz
dP ρ−=
)( 122 1zzgPP −−=− ρ
Untuk gas RT
PM=ρg
RT
PM
dz
dP =
)(ln 121
2 zzRT
gM
P
P −−=
(gas ideal, isotermal)
Untuk cair
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
ρρ
Kerapatan air segar
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
ρρ
ρ
Density of sea water
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.
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
ρρ
ρ
==−=−
+==
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.
Using a u-tube manometer to measure gauge pressure of fluid density 700 kg/m3, and the manometric fluid is mercury, with a relative density of 13.6. What is the gauge pressure if: a). h1 = 0.4m and h2 = 0.9m? b) h1 stayed the same but h2 = -0.1m?
THE U-TUBE MANOMETER.
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 = ρgh
pa = ρgh
examples
water: h = pa/ρg =105/(103*9.8) ~10m
mercury: h = pa/ρg =105/(13.4*103*9.8) ~800mm
ARCHIMEDES’ PRINCIPLE
• Buoyant Force (FB) weight of fluid displaced
–FB = ρfluidVdisplaced g
–Fg = mg = ρobject Vobject g
–object sinks if ρobject > ρfluid
–object floats if ρobject < ρfluid
– object floats if ρfluid = ρobject
ARCHIMEDES EXAMPLE
A 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?
h
koin
ARCHIMEDES EXAMPLE
mg
Fb
Mg
Σ F = m a
Fb – Mg – mg = 0
ρ g Vdisp = (M+m) g
Vdisp = (M+m) / ρ
h A = (M+m) / ρ
h = (M + m)/ (ρ A)
= (51.2+9)/(1 x 4 x 4) = 3.76 cm
M = ρplastic Vcube = 0.8x4x4x4
= 51.2 g
h
koin
( )
( )
( )( ) 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
ρ
ρρ
ρ
Wadah segi 4 berdasar datar diisi dengan coal, massanya 3.0×105 kg. Panjang 20 m dan lebar 10m, mengambang diair. Berapa kedalaman wadah masuk ke dalam air.
w
FB
1. Go up, causing the water to spill out of the glass.
2. Go down.
3. Stay the same.
CORRECT
COBA PIKIRKAN
B = ρW g Vdisplaced
W = ρice g Vice → ρW g V
Must be same!
ice-cube
Sebuah balok es mengambang diatas segelas air, sampai permukaan air rata pada pinggiran.
Ketika es meleleh maka air di dalam akan :
COBA PIKIRKAN
Which 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
Weight of ship = Buoyant force =
Weight of displaced water16
Sepotong logam dilepaskan dibawah air water. Volume metal 50.0 cm3 dan SG 5.0. Hitung percepatan initialnya, saat v=0 tidak ada gaya drag.
w
FB
w
FB
mawFF B =−=∑
VgFB waterρ=
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 ==ρρ
ρwater = 1000 kg/m3 (at 4 °C).
2
objectobject
water m/s 8.710.5
11
..
11
ρ
ρ −=
−=
−=
−= g
GSg
V
Vga
KEDALAMAN OIL RESERVOIR
What the depth below the surface
of oil reservoir that produce oil
with relative density 0.8 and
wellhead pressure of 120 kN/m2?
ρ water = 1000 kg/m3, and p atmosphere = 101kN/m2.
DECANTER
• It is proposed to use a gravity decanter to separate a light petroleum oil (density 50.0 lbm/ft3) from water (density 62.3 lbm/ft3). Its desire to maintain a total depth of 30 in. in the vessel and to have exactly equal depth of oil and water. What should be the height , expressed in inch of the water discharge leg above the bottom of the vessel.
Example
An open tank contains water 5m deep.
It is sitting on an elevator.
Calculate the gauge pressure at the bottom of the tank
(a) when the elevator is standing still,
(b) when the elevator is accelerating upward at the rate of 5m/s2, and
(c) when the elevator is accelerating downward at the rate of 5 m/s2.
TEKANAN DALAM BENDA RIGID BERGERAK
Gerak rotasiCentripetal accelaration =(angular velocity)2.radius
rac2ω−=
rdr
dP 2ρω=
2
2( cos )c
c
d adPg
da dtρ θ=− +
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