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