aplikasi bernoulli pada saluran kovergen/divergen diffuser, sudden expansion fluida gas flowmeter :...
Post on 27-Dec-2015
232 Views
Preview:
TRANSCRIPT
APLIKASI BERNOULLI PADASaluran Kovergen/Divergen Diffuser, Sudden expansionFluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter
PERS.BERNOULLI
dm
dQu
dm
dWVgz
P other)(2
2
Steady
Fdm
dWVgz
P other
)(2
2
inin
sys
dmV
gzP
uV
gzumd )()(22
22
otheroutout dWdQdmV
gzP
u )(2
2
PERS.BERNOULLI
Fdm
dWVgz
P other
)(2
2
g
F
gdm
dW
g
Vz
g
P other
)(2
2
HEAD FORM OF BERNOULLI EQUATION
DIFFUSERCara untuk untuk memperlambat kecepatan aliran
FA
AVPP
22
11
21
12 12
Fdm
dWVgz
P other
)(2
2
V1,P1,A1V2,P2,A2
z1-z2
12
SUDDEN EXPANSIONSCara untuk untuk memperlambat kecepatan aliran
FV
PP 2
21
12
1 2P1,V1 P2,V2=0z1-z2
Fdm
dWVgz
P other
)(2
2
BERNOULLI UNTUK GAS
Fdm
dWVgz
P other
)(2
2
M
RTvP 1
11
1
VR,PRP1,V1 21
1
)(2
atmR PP
V
21
1
11 )(
2
atmR PP
MP
RTV
--------------------P1-Patm V (ft/s) Psia (Eq.5.17) --------------------------0.001 350.1 1110.3 1910.6 2671.0 3402.0 4675.0 679
)1()1(
2
2 11
21
T
T
kRkT
MV R
(Eq.5.17)
1
11
kk
RR
T
T
P
P
Patmosfir
MP
RTv
1
1
11
1
Eq.in Chap.8
-------------V(ft/s)(Eq.in Chap.8)--------- 35111191269344477714
BERNOULLI FOR FLUID FLOW MEASUREMENT
PITOT TUBE
FVPP
2
2112
)(
212 hhgPP atm
21 ghPP atm 2111 22 FghV
2111 2ghV
1 2
h1
h2
Fdm
dWVgz
P other
)(2
2
••
VENTURIMETER
V1,P1
V2,P2
1 2
Manometer
02
21
2212
VVPP
)(
21
21
22
122 1
2
AA
PPV
)(
21
21
22
212 1
2
AA
PPCV v
Fdm
dWVgz
P other
)(2
2
Venturi Flowmeter
The classical Venturi tube (also known as the Herschel Venturi tube) is used to determine flowrate through a pipe. Differential pressure is the pressure difference between the pressure measured at D and at d
D d Flow
ORIFICEMETER
21
Orifice plateCircular drilled hole
where, Co - Orifice coefficient
- Ratio of CS areas of upstream to that of down stream
Pa-Pb - Pressure gradient across the orifice meter
- Density of fluid
ORIFICEMETER
where, Co - Orifice coefficient
- Ratio of CS areas of upstream to that of down stream
Pa-Pb - Pressure gradient across the orifice meter
- Density of fluid
incompressible flow through an orifice
compressible flow through an orifice
Y is 1.0 for incompressible fluids and it can be calculated for compressible gases.[2]
For values of β less than 0.25, β4 approaches 0 and the last bracketed term in the above equation approaches 1. Thus, for the large majority of orifice plate installations:
Y = Expansion factor, dimensionless
r = P2 / P1
k = specific heat ratio (cp / cv), dimensionless
compressible flow through an orifice
compressible flow through an orifice
k = specific heat ratio (cp / cv), dimensionless
= mass flow rate at any section, kg/s
C = orifice flow coefficient, dimensionless
A2 = cross-sectional area of the orifice hole, m²
ρ1 = upstream real gas density, kg/m³
P1 = upstream gas pressure, Pa with dimensions of kg/(m·s²)
P2 = downstream pressure in the orifice hole, Pa with dimensions of kg/(m·s²)
M = the gas molecular mass, kg/kmol (also known as the molecular weight)
R = the Universal Gas Law Constant = 8.3145 J/(mol·K)
T1 = absolute upstream gas temperature, K
Z = the gas compressibility factor at P1 and T1, dimensionless
Sudden Contraction (Orifice Flowmeter)
Orifice flowmeters are used to determine a liquid or gas flowrate by measuring the differential pressure P1-P2 across the orifice plate
QCd A2
2( p1 p2)
(1 2 )
1/ 2
QCd A2
2( p1 p2)
(1 2 )
1/ 2
0.60.650.7
0.750.8
0.850.9
0.951
102 105 106 107
Re
Cd
Reynolds number based on orifice diameter Red
P1 P2
dD
Flow
103 104
1
2
3
2
Solid ball with diameter D0
Density B
Fluid with density F
z=0
Tansparent tapered tube with diameter D0+Bz
ROTAMETER
bawahtekananboyancyatastekanangravity FFFF 0
201
30
203
30 66
0 DPgDDPgD fb
1
2
3
2
Solid ball D0
Density B
F z=0
D0+Bz
ROTAMETER
Fdm
dWVgz
P other
)(2
2
2 2 2 2
2 1 2 21 2 2
1
( ) (1 )2 2 2f f
V V V AP P
A
2
1
02 3
f
fbgDV
zBDD .0
20
202 .
4DzBDA
201
30
203
30 66
0 DPgDDPgD fb
3 20 0 1 3( ) ( )
6 b fD g D P P
01 2( ) ( )
6 b f
Dg P P
3 2 jika P P
222
1
0A
jikaA
22
1 2 2f
VP P
Only one possible value that keep the ball steaduly suspended
1
2
3
2
Solid ball D0
Density B
F z=0
D0+Bz
ROTAMETER
2 2 2Q V A
2
1
02 3
f
fbgDV
zBDD .0
20
202 .
4DzBDA
For any rate the ball must move to that elevation in the tapered tube where
2
2 [ 2 ( . ]4
A Bz B z
2 2A Bz
2 2 2Q V Bz
2
. 0B z
The height z at which the ball stands, is linearly proportional to the volumetric flowrate Q
TEKANAN ABSOLUT NEGATIF ?
40ft
10ft1
2
3 1 2
3 1 32 ( ) 2(32.2)(10) 25.3 /V g h h ft s
)( 22
22
12 2zzg
VPP
214.7 21.6 6.9 / 47.6lbf in kPa
? negatif
Fdm
dWVgz
P other
)(2
2
Applying the equation between point 1 and 3
Applying the equation between point 1 and 2
This flow is physically impossible. It is unrealBecause the siphone can never lift water more than 34 ft (10.4 m) above the water surfaceIt will not flow at all
top related