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
