APLIKASI BERNOULLI PADASaluran Kovergen/Divergen Diffuser, Sudden expansionFluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter
PERS.BERNOULLI
dmdQu
dmdWVgzP other)(
2
2
Steady
FdmdWVgzP other
)(
2
2
ininsys
dmVgzPuVgzumd )()(22
22
otheroutout dWdQdmVgzPu )(2
2
PERS.BERNOULLI
FdmdWVgzP other
)(
2
2
gF
gdmdW
gVz
gP other
)(
2
2
HEAD FORM OF BERNOULLI EQUATION
DIFFUSERCara untuk untuk memperlambat kecepatan aliran
FAAVPP
2
2
11
21
12 12
FdmdWVgzP other
)(
2
2
V1,P1,A1V2,P2,A2
z1-z2
12
SUDDEN EXPANSIONSCara untuk untuk memperlambat kecepatan aliran
FVPP 2
21
12
1 2P1,V1 P2,V2=0z1-z2
FdmdWVgzP other
)(
2
2
BERNOULLI UNTUK GAS
FdmdWVgzP other
)(
2
2
MRTvP 1
11
1
VR,PRP1,V1 21
1)(2
atmR PPV
21
1
11 )(2
atmR PP
MPRTV
--------------------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(
22 11
21
TT
kRkTMV R
(Eq.5.17)
1
11
kk
RR
TT
PP
Patmosfir
MPRTv1
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
FdmdWVgzP other
)(
2
2
••
VENTURIMETER
V1,P1
V2,P2
1 2
Manometer
02
21
2212
VVPP
)(
21
21
22
122 1
2
AAPPV )(
21
21
22
212 1
2
AAPPCV v
FdmdWVgzP 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 A22( 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
23
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
23
2
Solid ball D0
Density B
F z=0
D0+Bz
ROTAMETER
FdmdWVgzP other
)(
2
2
2 2 2 2
2 1 2 21 2 2
1
( ) (1 )2 2 2f fV V V AP P
A
21
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 fD g P P
3 2 jika P P
222
1
0AjikaA
22
1 2 2fVP P
Only one possible value that keep the ball steaduly suspended
1
23
2
Solid ball D0
Density B
F z=0
D0+Bz
ROTAMETER
2 2 2Q V A
21
02 3
f
fbgDV
zBDD .0
20
202 .
4DzBDA
For any rate the ball must move to that elevation in the tapered tube where
22 [ 2 ( . ]
4A Bz B z
2 2A Bz
2 2 2
Q 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 2zzgVPP
214.7 21.6 6.9 / 47.6lbf in kPa
? negatif
FdmdWVgzP 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
