قياس وتحكم نظري

אאאא

אאאאFFEE

٢٦٧٢٦٧

٢٦٧

אאאאFE

،،אא،אW

אא א א א אאאאאא،אאאאאאא

אאאא אאאאאאאWא

אאK

אאאאאאא א ،א אא

אאאאאא،אאא א ،א אא א א אא א א א א א א א

אא،אאאא،אK

א א ? אאאאFE ?? ?אא אאא אא

אK

אאאאאאא،א ،א א אא

Kאאאאא

؛ א אא אאK

אאאא

אאא

אאאאאאאאFFEE

א

א

א

١

٢٦٧ אא אאאאFE אא

א

- ١ -

אאW אאא١٠٠K٪

אאW

אאאאאאאאא،אא،אא،אאK

אW

אאאאאאאאאאאאKאאאאא

אאאאאאאאא،אא،א،אK

אאאW

אאW ♦ אאאK ♦ אK Kאא،א ♦

אאWD1, D2, D5

אאW אאWאאK

אאW٣


א

- ٢ -

١ J١אאאW J

אאאאאאאאאאאאאאK

אאאאאאK אאאאאאאא

،אאאאאאאאאאאאאא،

אאאאאא،אאא،KKאK

١ J٢אFInstrumentation SystemsE

אאאKאא،אאאאאא<

א،אאאאאאאאאאאאאאאK

אאאאאאאאK

א،א[א??אאK

١ J٣אאא

אאאא،א،אאא،אאK


א

- ٣ -

١ J٣ J١אFSensorWE J

אאאאאאאא אאאאאK

١ J٣ J٢אFTransducerEW

אאא،–א–אאF–KEאא

Wאא،א،אאאאK

١ J٤אW ١ J٤ J١אאFAccuracyE

אאאאtrue valueאK

١ J٤ J٢אאFValues and UncertaintyE

♦ אאFTrue ValueE

אאאFאactualEKאאאאאtoleranceאK

אאאאא،אאאאאאאK


א

- ٤ -

١ J٤ J٤אFSensitivityE אאאאאK

א١א

אאW J

١ J١؟אאאא ١ J٢؟אאא ١ J٣FWEאFKEאK

אא


א

٢

٢٦٧ אא אאאאFE א

- ٥ -


אאW אאאאאא

אK אW

אאאאאאאאאWאאאאא

אאאאU،אאאאאאאא

אאא،אאאאאאאאאאK

Wאאא

אאאאאאאW ♦ אאK ♦ אאK ♦ אK ♦ אאK

אאWD1, D2, D5

אאW אאWאאK

אאW٣K


- ٦ -

٢ J١אW אאKא،א

אFatmE،אאFmHgE،אאFmH2OEאFbarKEאW J

١FPaZE١L٢Z1.01972 x 10-5L٢ ١L٢Z0.73559 mHgZ0.980665FbarKE ١Z0.760 mHgZ10.3323 mH2OZ1.01325Z1.3323L٢

١Z105L٢Z1.01972L٢ אאא،אאאאאW J

אאZאאHאא אאאאאאאFאאאאEא

אאKאאא1.013 bar to 7000 barK

F٢ J١E אאFkPaEאא٩K

אW אאZ900 + 101.3 Z1001.3FkPaE

٢ J٢אא אאאאW J

٢ J٢ J١אא

אאKF٢ J١EאFEFAEאאFBEאאK


- ٧ -

אאFCEאאאK

אאאאאאאאאא

אאK

F٢ J١Eאא

٢ J٢ J٢FDiaphragmE אאF elastic-element pressure transducerKEF٢ J٢Eאא،אאאאK אאאאאאא

אאKאאאאFgauge pressureEFdifferential pressureKE

אאאאאאאאאK


- ٨ -

F٢ J٢Eאאא

٢ J٢ J٣FBourdon tubeE אאאאאאאאאK

אאאאKF٢ J٣KE،،

אאאאאK


- ٩ -

F٢ J٣Eאא

٢ J٢ J٤אאא

אא7000 barאאאאא

אאF83%،12.7%،3.9%KE


- ١٠ -

א٢א

אאW J ٢ J١אCK ٢ J٢אאאא7000 BarK

أجهزة قياس درجة الحرارة المستخدمة في دوائر التحكم األوتوماتيكي


אא

א

אא

א

٣

٢٦٧ אא אאאאFEאאאאאא

- ١١ -


אאW

אאאאאאאאK

אW

אאאאאאאאאאאאאאKאא

אאFאאEאאKאאאאא،،אאאאא،

אא،אאאאאאאאא

אאאא،אאאאאאאאאFאE

אFאEאאאאא،אא

אאאאאאK

אאאW אאאאאאאאW

♦ אאאK ♦ אאאK ♦ אאאK


- ١٢ -

אאWD1,D2, D5

אאW אאWאאK

אאW٣

٣ J١אאא

אאאאאK،אאאאאKאאאאאאאאאKאאאא،אאא

אא،אאאK אאא،W

♦ אאאWאאאא،אאאK ♦ אWאאא،אאא

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♦ אWאאאאאKאאאאאאאאאאאK

אאאאא،אאאאאאK


- ١٣ -

٣ J٢אא אאאאW

١K אFThermometersEאא600° CK ٢K אFPyrometersEאא600° CK

٣ J٢ J١אאאאFThermoelectric ThermometerE

FאאאEFThermocoupleE אאאאאאאאאאאאא

אKא אאאאאK

אF٣ J١E،אאאKאאאאFt2 > t1E،א

אאאאאאאאאאאאאאאאKאאאאאאאא

אאאKאא،אאFE،אאאא،אאFאאKE

F٣ J١EאאאTypical Thermocouples


- ١٤ -

٣ J٢ J١ J١אאאאFThermocouple materialsE אאאאאW

♦ K ♦ K ♦ אK ♦ אאאאאאK

אאאאאאאאאאW

♦ J٣٠٠١٠٠F–KE ♦ ١٣٠٠F–KE ♦ ٦٠٠١٨٠٠F–אE ♦ ١٣٠٠٢٩٠٠F–E ♦ ١٠٠٠١٦٠٠F–EאאFReduced

atmosphereKE ♦ ١٦٠٠٢١٠٠F–אEאאFOxidized

atmosphereKE


- ١٥ -

F٣ J١EאאאאאK אאChemical composition א

Ni Mn FeCuCr AL

95 2.5 0.5 2 אAlumel

90 10

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45

55

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F٣ J١Eאאא

F٣ J٢EאאאאאאK

אא אאF°E

אH א J אT אא٢٠٠ J٣٠٠٢٥٠ J٣٥٠J אא٦٠٠ J٤٠٠٧٥٠ J٥٠٠Eאאאא٧٠٠ J٤٥٠٨٠٠ J٥٠٠Kאאא ١٠٠٠ J٦٥٠١٢٠٠ J٨٥٠

Sאא

F١٠٪E ١٤٠٠ ١٦٠٠

R אאF١٣٪E

١٤٠٠ ١٦٠٠

B אא

F٣٠٪E אא

F٦٪E ١٥٠٠ ١٧٠٠

F٣ J٢Eאאאא


- ١٦ -

٣ J٢ J١ J٢אאאא ♦ אK ♦ אK ♦ אאאK ♦ אK ♦ אK

אאאאאאאאK

٣ J٢ J١ J٣אאא ♦ Fusually 50 µV/°C (28 µV/°F) or lessKE ♦ אאאא،אא

אא،אK

٣ J٢ J٢אאאא Resistance thermometer or resistance-temperature device (RTD)

אאאאא٥٥٠א٨٥٠،אאFResistance pyrometersKEא

אאאאאאאאאאאאאאאאאא

אאאKF٣ J٢EאאאאאK


- ١٧ -

F٣ J٢EאאResistance Temperature Detectors

אאאאאאאא

אאאאK

٣ J٢ J٢ J١אאW ♦ K ♦ אאאאK ♦ אאFHigher signal-to-noise ratioKE

٣ J٢ J٢ J٢אW

♦ K ♦ K ♦ אאK


- ١٨ -

٣ J٢ J٣אאאFאE Thermistor (Thermal Sensitive Resistor)

אאאאאא،،،،KאאF

NTCEאאאאאאKNTCאא

אאאאאKאאאאאKאFאאEF٣ J٣KE،

אKאאאאK

٣ J٢ J٣ J١אאאW

♦ אF≈± 0.02 ° CE،אאא،אאאאK

♦ ،אאאא،אאאאK

♦ אאאK ♦ אאאאK ♦ אK

٣ J٢ J٣ J٢אאW ♦ אאאKאאאאא

K ♦ אא– 100 – 150 ° CK ♦ אאאאאK


- ١٩ -

F٣ J٣EאאאאTypical Thermistors

٣ J٢ J٤אאאFThermal Radiation ThermometerE

אאאאKאאאאאאאאאאאF

Plank’s LawKE א٣א

אאW J

٣ J١21° CK ٣ J٢אFWEFKEK ٣ J٣א؟אא ٣ J٤אאאFWEFKEא

אאK ٣ J٥אאFWEFKEאאא

אFKEאאאאאK

אאאא

אאאאFE

א

א

٤

٢٦٧ אאא

אאאאFEאאא

- ٢٠ -


אאW

אאאאאאאK

אW אאאאאא

אאאאKאאאאאאWאא،

אאאאא،א،אאא،

אא،אאא،אא،אאא

אא،אאאאKאאאאאאא

אKאאאאאKאאא

אאאאאאKאאאא،א

א،אK

٢٦٧ אאא

אאאאFEאאא

- ٢١ -

אאאW אאאאאאא

אW ♦ אK ♦ אK ♦ K ♦ אאאK ♦ אאK

אאWD1,D2, D5 אאW

אאWאאK אאW٣

٤ J١אאFInstrumentation of FlowE אאאאאW

٤ J١ J١אאFאEDifferential Pressure Flowmeter ،א،ForificeE،FnozzleE،

FventuriEאF٤ J١E،אאאאKאא

،אאKאQF٣LE،W

Q = α A √(2g(pa-pb)/γ αWא

A WאF٢E gWאFL٢E γWאאFL٣E Fpa-pbWEאאFL٢E

٢٦٧ אאא

אאאאFEאאא

- ٢٢ -

F٤ J١E

٤ J١ J٢אאVariable Area Flowmeter (Rotameter)E

אאאא،אאאKאא،אא

אאK אאאrotameterF٤ J٢EאאKאאFfloatEא

אKאאאאאאאאא،אK

אאאא،אאאKאאאאFEאאא،

٢٦٧ אאא

אאאאFEאאא

- ٢٣ -

אאא،אKאאאKאא

،אאאK،אא،אא

אKאאאאאאאאאאאאKא

±3%א،א±0.2%K

אאאא،אאא،

٢٦٧ אאא

אאאאFEאאא

- ٢٤ -

אאאFאEאאאאKאאKאא

אאאK F٤ J٢Eאאאא

אאאאאFEאאאאאאCDK

∆p/(ρg) = u2

2/(2g) – u12/(2g) (1)

אאאFContinuity equationWE A1u1 = A2u2 (2)

W A1ZאK A2ZאאאאאאK

אF١EF٢EאאאW

אאא

∆p = Vf (ρf - ρ)g/Af

٢٦٧ אאא

אאאאFEאאא

- ٢٥ -

Vfאא،ρfאא،AfאאאKW

אCDאאF٤ J٣E،FReynolds Number -ReEאאאא

אאKW ♦ אאאאאאאא

אאKאאאאK ♦ אאאאאאאFא

אEאא،אאאאאאK

F٤ J٣Eאאאאאא

٢٦٧ אאא

אאאאFEאאא

- ٢٦ -

٤ J١ J٣אFPitot TupeE pitotאאאאאאK

אF٤ J٤E

F٤ J٤E

אאF٤ J٥EpitotאאK

٢٦٧ אאא

אאאאFEאאא

- ٢٧ -

F٤ J٥Eאא

٤ J١ J٤אאFElectromagnetic FlowmeterE

אאאאאKאאאFE،F٤ J٦KEא

אאאאאKאאאאאKא

אאא،אK

٢٦٧ אאא

אאאאFEאאא

- ٢٨ -

F٤ J٦Eאאאא

אאאK

flowmetersאאאאאKא،אאאאאF٤ J

٧KEאאאאFאאEK،א،אאא

אאאאK

F٤ J٧EאאאאאK

٤ J٢אFInstrumentation of Liquid LevelE ٤ J٢ J١אאאFFloat Liquid Level IndicatorE

٢٦٧ אאא

אאאאFEאאא

- ٢٩ -

אאאאאאKF٤ J٨EאאאאK

F٤ J٨Eאא

Liquid level sensors with a continuous output signal for process control signal data

٢٦٧ אאא

אאאאFEאאא

- ٣٠ -

٤ J٢ J٢אאFUltra sonicE אאאLא

אF٤ J٩E،אאאאאאאאא

KאאאאאאKאא

אאאאאאאK

٢٦٧ אאא

אאאאFEאאא

- ٣١ -

F٤ J٩Eאאאאאא

FUltrasonic TransducersE

٤ J٢ J٣א אאא–אFmicrowaveE

אF٤ J١٠KEF٤ J١١Eאאאאא،אאאאK

אאאאאאא،א،אאK

٢٦٧ אאא

אאאאFEאאא

- ٣٢ -

F٤ J١٠EאאאאאFmicrowaveEאא

F٤ J١١Eאאאאאאא

٢٦٧ אאא

אאאאFEאאא

- ٣٣ -

א٤א

אאאאK ٤ J١אאאK ٤ J٢אאאK ٤ J٣אאאאאK ٤ J٤؟אאאאאאאא

אאאאאא

אאאאFE

א

א

א

٥

٢٦٧ אא אאאאFEאאא

- ٣٤ -


אאW אאאאאאאאאא،

אא،KKKKKאK אאאאאאאK

אW אאאאאאאאK

אאא Kאא א א א א א א אא א K א

EאFאאאאאK

אאאW • אאW • אאאאK • אאאאאאK • אK • אאאK • אאאאאK

אאWD1, D2, D5

אאW

אאWאאK אאW٢


- ٣٥ -

٥ J١אאא אאא،אאאא

אא،אאאאא،אאאאאאאא

אאאאאאאאKאאאאאא

F،،،،KE

٥ J٢אא אא،،

אאאאאאאKאאאאאאאK

א،אאאאאאא،א،אאאK

٥ J٣אאאא Basic Concepts for Automatic Control Systems

٥ J٣ J١אא Block Diagram

אאאאא א א א א Kא

אאאאאאא،א F٥ J١ KEא א א א א א

אאאאאאאאאאF٥ J٢KE


- ٣٦ -

Block

Input Output

F٥ J١Eאא

Control Element

x y=dx/dt

d/dt

F٥ J٢E Jאא Jאאאאא

אאאאאאSumming Point א H – אא אאאא

א א ،א אא אF٥ J٣KE

x

y

+

+x+y x-y x+y+xx x

x

y y

+

-

+

+

F٥ J٣Eא

אאא

אTake off PointאאKF٥ J٤KE


- ٣٧ -

x

x

x

x

x

x

x

Take off point

Takeoff

point

F٥ J٤E

٥ J٣ J٢אאאא Block Diagram of Feed Back Control Systems אאאאאאאא

אKאאאאF٥ J٥KE, אאאאאא،אאא

אאא، אאא א אF J E א

אאאאK אאאאאK

١ Jאא Set Point

א אא אאאאK

٢ Jא Control Point אאאא

٣ JאאOffset אא א א אא

א. ٤ Jאא Deviation

אאאאאאFKE ٥ JאאFאאEPlant


- ٣٨ -

אKאאאאאאאK

٦ JאController אא،א

٧ Jאא Feedback Element אאאאאאאא

אאK ٨ JאאFאאE Reference Input

אאאאאK

٩ Jאא Controlled Outputאאאא אאאאK

١٠ Jאאאא Primary Feedback Signal אאאאאא،

אאK ١١ JאFאE Control Signal

،אאאאאאFאאEאאK

١٢ JאאManipulated Variable אאאאK

١٣ JאDistrurbance א א אא

אאFא،אאאאא،אאEאאא אא K

אאKאאאm אF٦ J٥E


- ٣٩ -

Controlledvariable

Disturbance

R

B

G1 G2

H

Feed backelement

PlantControlelement CME=R-B+

-

ForwardPath

BackwardPath

F٥ J٥E

W plant: א א KControl elemewntא KDisturbanceאKcontrolled variableאאאKK feed back

elementאאKKforward pathאאKBack ward pathאאKK

١٤ JאאForward Path

אאFEEאאFCE ١٥ Jאא Backward Path

אאאאאאא ١٦ JאאFאEFeedback

א א Fא Eא א א אאאאאא

אאאאK ١٧ Jאאא Servo-mechanisim


- ٤٠ -

אא א א א א א Servomechanisim אאאא

אאK

٥ J٤אאא Diagram Algebra and Transfer Functions א א א א Wא J

א Jא JאאאאאאאאאF٥ J٥EאאאאK

٥ J٥אאאאא

Control SystemאאW J ١ J אא Process ٢ J אMeasurements ٣ J א Comparison ٤ J אא Controller ٥ J אא Final Control Element אאKW ١ JאאProcess

אאא אאאFאא Jא–אא–אאKKKKKKאE

٢ JאMeasuring System

אאאאאKFEW J • אאא • א


- ٤١ -

א א א א א אאא אאא–אא–אא–א J

KKKKאK אאSensorאאאאא

אKאאאאאאW J • א • אא

אאאאאFEאאא אאא

אK

אTransmittersW א א Sensors א א Transducers

Transmitters K

٣ JאComparison Element אאאאאK

٤ JאController אControl lawאאאא

א א א א K אאאKאא

אComparatorK ٥ JאאFinal Control Devices and Actuators

אאאאאאKאK


- ٤٢ -

٥ J٦ אאא

אאאאאאאאאאFאKEא

אW

F١EאאאW

אאאאאאF٥ J٦KEאTi(t)אאאא

אאT(t) KאאKאאאאאאאאאא

אאאFאאאאEאאאאאאאאKאאאאאא

אK אאאאאא

אKא،אאאאאאאאאאא

אKאאאאT(t)אאאאאאאFאKE

א

אאאאא،אאאאאFאEאאKאאאאא

אאאאאאאאאאK

אאאאאאאא


- ٤٣ -

אאאאאאא

אאאאאאאאK

T

Heat Exchanger

T(t) C

Heated ProcessStream

Steam

Process Stream

Ti(t)

F٥ J٦Eא

W steam Kheat exchangerאK Process stream אK Heated process streamאאK

אאאאאא

F٥ J٧KEאאאא،אאאא

אאאאFE،KKKKKKKאKאאאאFאEK

אאאW J

• אWאאאK • אWאאאאK


- ٤٤ -

• אWאאאאK

אאFEאאאאאאKאאא،אFKE

T

TT

Ti(t) C

TC

Transmitter

Steam

Sensor

Final Control Element

F٥ J٧Eאא

Wsensor אK TransmitterאK Final control elementאאKsteam


- ٤٥ -

F٢WEאF٥ J٨E

אאאאאFhEאאKאא

אאאאאאK

F٥ J٨E

אW

אאאאאאW

١ J אאאWhFאE ٢ J אאW Fi FאאאאE ٣ J אאWFoFאאאE

Kאאאאאאאאא

Fi

Fo

h


- ٤٦ -

W؟אא

F٣WEF٥ J٩E

אאאKאאFTstEאאFFstKEאאאאאאאFToEK

אאאאFFiEאאאKWsteam K Condensate אK

Fi

Fo

h


- ٤٧ -

F٥ J٩E

אW

אאאאאאW

٤ J אאאW ToFאאאאE ٥ J אאW Fi FאאאאE ٦ J אאWFstFאאאE


אאאאK

W؟אא


- ٤٨ -

٥ J٧אFאEאא א א א אא א א

אאOpen Loopא Closed LoopKאאאאאאא

אא Kאא אאאא אאא א א א

אאאאKאאאאאא،אאאאא

אאא،אאאאאאאאאא K

א א א Kא אא אאאאאאKא

אאאאאאאאאאאא

אKאאאאFאEאאאK


- ٤٩ -

א٥א

٥ J١אאאאאאאאא؟ ٥ J٢؟א ٥ J٣؟אאאאא ٥ J٤אא–א Jא–אא

אאאאאאאא


אא

א

א

٦

٢٦٧ אא אאאאFE אאאא

- ٥٠ -


Wאא


אאK

אW אאאאאאאאא

אאKאאKאאאK

אאאW אאW

♦ אאאK ♦ אאא ♦ K ♦ אא

אאWD1, D2, D5

אאW אאWאאK

אאW ٤ K


- ٥١ -

٦ J١אאאא • אאאאאאאאא

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١ J אא) ( Proportional control action ٢ J אא) ( Integral control action ٣ J אא) ( Derivative control action ٤ J אאאא) ( PID Controller

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- ٥٢ -

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אאאאK ٥ J אאאאאW

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- ٦١ -

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- ٧٣ -

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- ٧٦ -

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- ٨٠ -

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- ٨١ -

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- ٨٢ -


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- ٨٣ -

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- ٨٤ -

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٧ J٤אאא Eccentric PlugValves ؟

٧ J٥אאאאLined Butterfly Valve ؟

٧ J٦אאאאאValve Selection؟

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٧ J٨؟אאאאאאא

٧ J٩אאאאא

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٧ J١١אאא؟א


- ٨٥ -

אאא١

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١ J٢אאאא،א،אאא،אא،א،K

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FEאאא،אK

אאא٢

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אאא٣ ٣ J١294.16 KK

٣ J٢FEא600° CK

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٣ J٣אאאK

٣ J٤FKE

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- ٨٦ -

אאא٤

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٤ J٢אאK

٤ J٣אK

٤ J٤אאאאאאאא،א

אא،אאאאאאאK

٢٦٧ אא

אאאאFE

אא 1. Internet Sites.

2. Medlock, R. S. and Furness, R. A. “Mass flow measurement – a state of

the art review”, Measurement and Control, 23, 100-13, 1990.

3. Morris, A. S. : “Principles of measurement and instrumentation”, Prentice Hall, 1993.

4. Perry, R. H., Green, D. W., Maloney, J., O. : “Perry’s chemical

engineers’ handbook”, McGraw-Hill Boo; Company, 1992.

5. Quinn, T. J. “Temperature”, 2nd ed. Academic press, New York, 1990.

6. Spitzer, D. W. “Flow measurement”, Instrumentation Society of America, Research Triangle Park, NC, 1991.

7. Tilford, C. R. “Pressure and vacuum measurement”, In Physical methods

of chemistry, 2nd ed., Vol. 6, pp. 106-73, John Wiley and Sons, New York, 1992.

8. “Process/Industrial Instruments and Controls Handbook” Douglas M.

Considine, 4 th Edition, Mc-Graw Hill Inc.

9. “Process Control Systems-Applications, Design and Tuning”, 3 rd Edition, Mc-Graw Hill International, F.G. Shinsky, 1988.

10. “Principles and practice of Automatic Process Control”, Carlos, A.

Smith, and Armando, B. Corripo, 1985, Jhon Wiley and Sons.

11. “Programmable Logic Controllers”, Priciples and Applications , Second Editions, John W. Webb, 1992.

٢٦٧ א

אאאאFE

א ١ J١אאאW J K K K K K K K K K K K K K K K K K J٢ J ١ J٢אFInstrumentation SystemsE K K K K K K K K J٢ J ١ J٣אאא K K K K K K K K K K K K J٢ J ١ J٤אW K K K K K K K K K K K K K K K K K K K K K J٣ J

אא١ K K K K K K K K K K K K K K K K K K K K K K K J٤ J ٢ J١אW K K K K K K K K K K K K K K K K K K K K K K K K J٦ J ٢ J٢אא K K K K K K K K K K K K K K K K K K K K J٦ J

א٢א K K K K K K K K K K K K K K K K K K K K K K J١٠ J ٣ J١אאא K K K K K K K K K K K K K K K K K K K K J١٢ J ٣ J٢אא K K K K K K K K K K K K K K K J١٣ J ٣ J٤אאאא K K K K K K K K K K J١٦ J ٣ J٥אאאFאE K K K K K K K K K K K K K J١٨ J ٣ J٦אאאFThermal Radiation ThermometerE K K J١٩ J

א٣א K K K K K K K K K K K K K K K K K K K K K K J١٩ J ٤ J١אאFInstrumentation of FlowE K K K K K J٢١ J ٤ J٢אFInstrumentation of Liquid LevelE K K J٢٨ J

אא٤ K K K K K K K K K K K K K K K K K K K K K K J٣٣ J ٥ J١אאאא K K K K K K K K K K K K K J٣٥ J ٥ J٢אאאא K K K K K K K K K K K K K K J٣٥ J ٥ J٣אאא Diagram Algebra and Transfer Functions J٤٠ J ٥ J٤אאאאא K K K K K K K K K K K K K K J٤٠ J

אא٥ K K K K K K K K K K K K K K K K K K K K K K J٤٩ J ٦ J١אאאא K K K K K K K K K K K K K K K K K K K K٤٧ ٦ J٢אאא K K K K K K K K K >אאK٥٤

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אא٨ K K K K K K K K K K K K K K K K K K K K K K J٨٤ J אאא١ K K K K K K K K K K K K K K K K K K K K K K٧٥ אאא٢ K K K K K K K K K K K >אאK٧٥ אאא٣ K K K K K K K K K K K >אאK٧٥ אאא٤ K K K K K K K K K K K >אאK٧٥

אא K K K K K K K K K K K K K K K K K K K K K K K K K K J٥٣ J

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