APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter :...

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APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter

Transcript of APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter :...

Page 1: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

APLIKASI BERNOULLI PADASaluran Kovergen/Divergen Diffuser, Sudden expansionFluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter

Page 2: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida 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

Page 3: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

PERS.BERNOULLI

Fdm

dWVgz

P other

)(2

2

g

F

gdm

dW

g

Vz

g

P other

)(2

2

HEAD FORM OF BERNOULLI EQUATION

Page 4: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 5: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 6: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 7: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

••

Page 8: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 9: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 10: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 11: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 12: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

incompressible flow through an orifice

Page 13: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 14: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

compressible flow through an orifice

Page 15: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 16: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 17: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 18: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 19: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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

Page 20: APLIKASI BERNOULLI PADA Saluran Kovergen/Divergen Diffuser, Sudden expansion Fluida gas Flowmeter : Pitot tube, Orificemeter, Venturimeter, Rotameter.

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