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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

otheroutoutdWdQdm

Vgz

Pu )(

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

DIFFUSER Cara untuk untuk memperlambat kecepatan aliran

FA

AVPP

2

2

1

1

2

112 1

2

Fdm

dWVgz

P other

)(2

2

V1,P1,A1 V2,P2,A2

z1-z2

1

2

SUDDEN EXPANSIONS Cara untuk untuk memperlambat kecepatan aliran

FV

PP 2

2

112

1 2

P1,V1 P2,V2=0 z1-z2

Fdm

dWVgz

P other

)(2

2

BERNOULLI UNTUK GAS

Fdm

dWVgz

P other

)(2

2

M

RTvP 111

1

VR,PR P1,V1 21

1

)(2

atmR PPV

21

1

11 )(

2

atmR PP

MP

RTV

-------------------- 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

)1()1(

2

2 11

2

1

T

T

kRkT

MV R

(Eq.5.17)

1

11

kk

RR

T

T

P

P

Patmosfir

MP

RTv

1

1

1

1

1

Eq.in Chap.8

------------- V(ft/s)

(Eq.in Chap.8)

---------

35

111

191

269

344

477

714

BERNOULLI FOR FLUID FLOW MEASUREMENT

PITOT TUBE

FVPP

2

2

112

)(

212 hhgPP atm

21 ghPP atm 2111 22 FghV

2111 2ghV

1 2

h1

h2

Fdm

dWVgz

P other

)(2

2

VENTURIMETER

Fdm

dWVgz

P other

)(2

2

bP

V1,P1

V2,P2

1 2

Manometer

1

2

1 2

( )

( )

a b

a f

b f

f

P P

P P gx

P P g x h gh

P P gh

21

2

1

2

2

122

1

2

AA

PPV

)(

21

2

1

2

2

212

1

2

AA

PPCV v

h

1 2

2 2 2

2 1

2

1

f

v

ghV C

A A

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

2 1

Orifice plate

Circular 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 less than 0.25, 4 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


k = specific heat ratio (cp / cv), dimensionless

= mass flow rate at any section, kg/s

C = orifice flow coefficient, dimensionless

A

2 = cross-sectional area of the orifice hole, m

1 = upstream real gas density, kg/m

P1 = upstream gas pressure, Pa with dimensions of kg/(ms)

P2 = downstream pressure in the orifice hole, Pa with dimensions of kg/(ms)

M = the gas molecular mass, kg/kmol (also known as the molecular weight)

R = the Universal Gas Law Constant = 8.3145 J/(molK)

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

Q Cd A22( p1 p2)

(1 2 )

1/ 2

0.6 0.65 0.7

0.75 0.8

0.85 0.9

0.95 1

102 105 106 107

Re

Cd

Reynolds number based on orifice diameter Red

P1 P2

d D

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

2

01

3

0

2

03

3

066

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 2

f f

V V V AP P

A

2

1

02

3

f

fbgDV

zBDD .0

202

02 .4

DzBDA

2

01

3

0

2

03

3

066

0 DPgDDPgD fb

3 2

0 0 1 3( ) ( )6

b fD g D P P

01 2( ) ( )

6b f

Dg P P

3 2 jika P P

2

2

2

1

0A

jikaA

2

21 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

202

02 .4

DzBDA

For any rate the ball must move to that

elevation in the tapered tube where

2

2 [ 2 ( . ]4

A Bz B z

22

A 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

10ft 1

2

3

1 2

3 1 32 ( ) 2(32.2)(10) 25.3 /V g h h ft s

)( 22

2

212

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 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

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