APLIKASI BERNOULLI PADA
Saluran Kovergen/Divergen Diffuser,
Sudden expansion
Fluida gas
Flowmeter : Pitot tube, Orificemeter, Venturimeter,
Rotameter
PERS.BERNOULLI
Steady
2

V2 
P
V2
d m(u  gz  )  (u   gz  ) in dmin  (u  P  gz  V )out dmout  dQ  dWother
2  sys

2

2

 dWother 
V2
dQ 
(  gz  ) 
  u 


2
dm
dm 

P
 dWother
V2
(  gz  ) 
F

2
dm
P
PERS.BERNOULLI
 dWother
V2
(  gz  ) 
F

2
dm
P
HEAD FORM OF BERNOULLI EQUATION
 dWother F
P
V2
(
z )

g
2g
gdm
g
DIFFUSER
Cara untuk untuk memperlambat kecepatan aliran
2
1
z1-z2
V1,P1,A1
V2,P2,A2
 dWother
V2
(  gz  ) 
F

2
dm
P
V12 
A11 
1  2   F
P2  P1  
2  A2 
SUDDEN EXPANSIONS
Cara untuk untuk memperlambat kecepatan aliran
1
2
P1,V1
z1-z2
P2,V2=0
 dWother
V2
(  gz  ) 
F

2
dm
P
V12
P2  P1  
 F
2
BERNOULLI UNTUK GAS
Patmosfir
 dWother
V2
(  gz  ) 
F

2
dm
P
1
VR,PR
P1,V1
P1v1 
RT1
M
v1 
-------------------- ------------P1-Patm
V (ft/s)
Psia
(Eq.5.17)
-------------------------0.001
35
0.1
111
0.3
191
0.6
267
1.0
340
2.0
467
5.0
679
V(ft/s)
(Eq.in Chap.8)
--------35
111
191
269
344
477
714
1
1

RT1
P1M
 (P  P ) 
V1  2 R atm 



 2 RT1

V1  
( PR  Patm )
 P1M

12
MV12
2
T

( R  1)
2 RkT1 (k  1) T1
PR  TR 
 
P1  T1 
12
(Eq.5.17)
Eq.in Chap.8
k  k 1
BERNOULLI FOR FLUID FLOW MEASUREMENT
h1
1•
2
•
PITOT TUBE
P2  Patm  g h1  h2 
P1  Patm  gh2
 dWother
V2
(  gz  ) 
F

2
dm
P
h2
( P2  P1 ) V12

 F

2
V1  2 gh1  2 F 
12
V1  2gh1 
1 2
VENTURIMETER
1
V1,P1
2
V2,P2
 dWother
V2
(  gz  ) 
F

2
dm
P
Manometer
( P2  P1 ) V22  V12

0

2
 2 ( P2  P1 )  
V2  
2
2 
1

A
A
2
1


12
 2P1  P2  
V2  Cv 
2
2 

1

A
A
2
1 



12
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
1
2
Orifice plate
Circular drilled hole
where, C - Orifice coefficient
o
- Ratio of CS areas of upstream to that of down stream
P -P - Pressure gradient across the orifice meter
a
- Density of fluid
b
ORIFICEMETER
where, C - Orifice coefficient
o
- Ratio of CS areas of upstream to that of down stream
P -P - Pressure gradient across the orifice meter
a
- Density of fluid
b
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
A
= orifice flow coefficient, dimensionless
= cross-sectional area of the orifice hole, m²
2
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
R
= the Universal Gas Law Constant = 8.3145 J/(mol·K)
T1
= absolute upstream gas temperature, K
Z
(also known as the molecular weight)
= 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
2( p1  p2 )1/ 2

Q  Cd A2
2

  (1   ) 

1
0.95
0.9
0.85
Cd 0.8
0.75
0.7
0.65
0.6
102
103
P1
D
d
Flow
105
104
Re
Reynolds number based on orifice diameter Red
P2
106
107
ROTAMETER
Tansparent tapered tube
with diameter D0+Bz
Solid ball with
diameter D0
Density B
3
2
2
1
z=0
Fluid with density F
0  Fgravity  Ftekananatas  Fboyancy  Ftekananbawah
0

6
D  b g  P3D 
3
0
2
0

6
D03  f g  P1D02
ROTAMETER
0

6
D  b g  P3D 
3
0

6
2
0

6
D03  f g  P1D02
D  D0  B.z
D0+Bz
Solid ball D0
Density B
D ( b   f ) g   D ( P1  P3 )
3
0
2
0
3
2
jika P3  P2
2
1
D0
( b   f ) g  ( P1  P2 )
6
F
z=0
 dWother
V2
(  gz 
)
F

2
dm
P
A22
jika 2  0
A1
V22
P1  P2   f
2
 D0 g b   f
V2  
 3
f

V22 V12
V22
A22
P1  P2   f (  )   f
(1  2 )
2
2
2
A1




1
2
Only one possible value that keep the
ball steaduly suspended
A2 

4
D0  B.z 2  D02
ROTAMETER
D  D0  B.z
D0+Bz
For any rate the ball must move to that
elevation in the tapered tube where
Solid ball D0
Density B
3
 D0 g b   f
V2  
 3
f

Q2  V2 A2
Q2  V2

2
Bz




2
1
2
2
1
A2 

A2 
 B.z 
z=0
D0  B.z 2  D02
4

4
2
F
[ 2 Bz  ( B.z  ]
0
2
A2 
The height z at which the ball stands, is linearly proportional to
the volumetric flowrate Q

2
 Bz 
TEKANAN ABSOLUT NEGATIF ?
2
40ft
 dWother
V2
(  gz  ) 
F

2
dm
P
1
10ft
3
Applying the equation between point 1 and 3
V3  2 g  (h1  h3 ) 
12
 2(32.2)(10)  25.3 ft / s
Applying the equation between point 1 and 2
V22

P2  P1     g ( z2  z2 )
2

2
14.7  21.6  6.9lbf / in  47.6kPa
? negatif
This flow is physically impossible. It is unreal
Because the siphone can never lift water more than 34 ft (10.4 m)
above the water surface
It will not flow at all