Moeller. Wiring manual. Automation and Power distribution

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Specifications, Formulae, Tables

Formulea

Moeller Wiring Manual 02/05

9-91

Electric power

Mechanical force between 2 parallel conductors

Mechanical force between 3 parallel conductors

Power Current consumption

Single-phase AC

Three-phase AC

2 conductors with currents I

and I

s = Support spacing clearance

[cm]

a = Support spacing clearance

[cm]

3 conductors with current I

PUI× W[]=

---

A[]=

PUIcosϕ×× W[]=

Ucosϕ×

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

A[]=

P3UIcosϕ××× W[]=

3Ucosϕ××

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

A[]=

0.2

×××

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

N[]=

0.808

N[]×=

0.865

N[]×=

0.865

N[]×=

Specifications, Formulae, Tables

Formulea

Moeller Wiring Manual 02/05

9-92

Voltage drop

Calculation of cross-section from voltage drop

Known power Known current

Single-phase AC

Three-phase AC

DC Single-phase AC Three-phase AC

Known power

Known current

Power loss

DC Single-phase AC

Three-phase AC

l = Single length of conductor [m];

A = Conductor cross section [mm

];

z = Conductivity (copper: z = 57; aluminium: z = 33; iron: z = 8.3 )

2 l× P×

z A× U×

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

V[]=

2 l× l×

z A×

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

V[]=

2 l× P×

z A× U×

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

V[]=

2 l× l×

z A×

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

cos×ϕ V[]=

l P×

z A× U×

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

V[]=

Δ 3

l l×

z A×

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

cos×ϕ V[]×=

2 l× P×

z u× U×

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

[]=

2 l× P×

z u× U×

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

[]=

l P×

z u× U×

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

[]=

2 l× l×

z u×

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

[]=

2 l× l×

z u×

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

cosϕ mm

[]×=

l l×

z u×

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

× cos×ϕmm

[]=

Verl

2 l× P× P×

z A× U× U×

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

W[]= P

Verl

2 l× P× P×

z A× U× U× cosϕ× cosϕ×

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

W[]=

Verl

l P× P×

z A× U× U× cosϕ× cosϕ×

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

W[]=

Ωmm

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

Specifications, Formulae, Tables

Formulea

Moeller Wiring Manual 02/05

9-93

Power of electric motors

Output Current consumption

Single-phase

Three-phase

= Rated mechanical power at the motor shaft

= Electrical power consumption

Efficiency

No. of poles Synchronous speed Full-load speed

2 3000 2800–2950

4 1500 1400–1470

6 1000 900–985

8 750 690–735

10 600 550–585

Synchronous speed = approx. no-load speed

Ul× h× W[]=

U h×

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

A[]=

Ul× cosϕ× h× W[]=

Ucosϕ× h×

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

A[]=

(1.73) U× l× cosϕ× h× W[]=

(1.73) U× cosϕ× h×

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

A[]=

-----

(100 %)×=

-----

W[]=

Moeller Wiring Manual 02/05

9-94

Specifications, Formulae, Tables

International Unit System

International Unit System (SI)

Factors for conversion of old units into SI units

Basic parameters

Physical

parameters

Symbol SI basic unit Further related SI units

Length

l m (Metre) km, dm, cm, mm, mm,

nm, pm

Mass

m kg (Kilogram) Mg, g, mg, mg

Time

t s (Second) ks, ms, ms, ns

Electrical current

I A (Ampere) kA, mA, mA, nA, pA

Thermo-dynamic

temperature

T K (Kelvin) –

Amount of

substance

n mole (Mol) Gmol, Mmol, kmol,

mmol, mmol

Luminous intensity

cd (Candela) Mcd, kcd, mcd

Conversion factors

Parameter

Old unit SI unit exact Approximate

Force

1 kp

1 dyn

9.80665 N

1·10

-5

10 N

1·10

-5

Momentum of

force

1 mkp 9.80665 Nm 10 Nm

Pressure

1 at

1 Atm = 760 Torr

1 Torr

1 mWS

1 mmWS

0.980665 bar

1.01325 bar

1.3332 mbar

0.0980665 bar

0.0980665 mbar

9.80665 Pa

1 bar

1.01 bar

1.33 bar

0.1 bar

0.1 mbar

10 Pa

Tension

Energy 1 mkp

1 kcal

1 erg

9.80665 J

4.1868 kJ

1·10

-7

10 J

4.2 kJ

1·10

-7

----------

9.80665

----------

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-95

Power

1.163 W 1.16 W

1 PS 0.73549 kW 0.740 kW

Heat transfer

coefficient

dynamic viscosity

1 Poise

1 Poise 0.1

Kinetic viscosity 1 Stokes

Angle (flat) 1

1 gon

57.296 1 rad

63.662 gon 1 rad

Conversion factors

Parameter

Old unit SI unit exact Approximate

kcal

--------

4.1868

----

4.2

----

kcal

--------

kcal

h°C

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

4.1868

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

4.2

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

kcal

h°C

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

1.163

---------

1.16

---------

110

6–

kps

--------

⋅ 0 980665, 10

5–

------

⋅ 110

5–

------

⋅

0.1

------

0.1

------

Pa s⋅

110

4–

------

⋅ 110

4–

------

⋅

360

--------

pla

278, 10

3–

pla⋅

400

--------

pla

25 10

3–

pla⋅,

180

--------

rad

17 5 10

3–

rad⋅,

200

--------

rad

15 7, 10

3–

pla⋅

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-96

Conversion of SI units, coherences

Conversion of SI units and coherences

Parameter SI units

name

Symbol

Basic unit Conversion of SI units

Force Newton N

Force

momentum

Newton-

metre

Pressure Bar bar

Pascal Pa

Energy, heat Joule J 1 J = 1 Ws = 1 Nm

Power Watt W

Tension

Angle (flat) Grad

Gon

gon

360° = 1 pla = 2p rad

400 gon = 360°

Radian rad

Full circle pla 1 pla = 2p rad = 360°

Voltage Volt V

Resistor Ohm O

Conductivity Siemens S

Electric

charge

Coulomb C 1 · A · s

kg m⋅

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

⋅

kg m

⋅

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

⋅

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

1 bar 10

Pa 10

------

⋅

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

⋅

1 Pa 10

5–

bar=

kg m

⋅

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

⋅

kg m

⋅

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

⋅

W1=

Nm⋅

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

----------

⋅

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

----------

--------

----

kg m

⋅

A⋅

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

⋅

1 V 1=

----

⋅

kg m

⋅

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

⋅

1 Ω 1=

---

-----

⋅=⋅

⋅

kg m

⋅

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

⋅

1 M 1=

---

-----

⋅⋅

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-97

Decimal powers (parts and multiples of units)

Capacitance Farad F

Field strength

Flux Weber Wb

Flux density Tesla T

Inductance Henry H

Power Prefix Symbol Power Prefix Symbol

–18

Atto a10

–1

Deci d

–15

Femto f10Deca da

–12

Pico p10

Hecto h

–9

Nano n10

Kilo k

–6

Micro m10

Mega M

–3

Milli m10

Giga G

–2

Centi c10

Tera T

Conversion of SI units and coherences

Parameter SI units

name

Symbol

Basic unit Conversion of SI units

A⋅

kg m

⋅

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

⋅ 1 F 1=

---

⋅ 1

⋅

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

⋅=

----

kg m⋅

A⋅

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

⋅ 1

----

Am⋅

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

⋅=

kg m

⋅

A⋅

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

⋅

1 W

1= Vs 1

Ws⋅

-----------

⋅=⋅⋅

A⋅

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

⋅

1 T

------

Vs⋅

---------

⋅ 1

Ws⋅

-----------

⋅== =

kg m

⋅

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

⋅

1 H

------

Vs⋅

---------

⋅ 1

Ws⋅

-----------

⋅== =

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-98

Physical units

Mechanical force

Pressure

Obsolete units

SI unit: N (Newton) J/m

(Joule/m)

Previous unit: kp (kilopond)

dyn (Dyn)

1 N = 1 J/m = 1 kg m/s

= 0.102 kp = 10

dyn

1 J/m = 1 N = 1 kg m/s

= 0.102 kp = 10

dyn

1 kg m/s

= 1 N = 1 J/m = 0.102 kp = 10

dyn

1 kp = 9.81 N = 9.81 J/m = 9.81 kg m/s

= 0.981 10

dyn

1 dyn = 10

–5

N= 10

–5

J/m = 10

–5

kg m/s

= 1.02 10

–5

SI unit: Pa (Pascal) bar (Bar)

unit:

at = kp/cm

= 10 m Ws

Torr = mm Hg

atm

1 Pa = 1 N/m

= 10

–5

bar

1 Pa = 10

–5

bar = 10.2 · 10

–6

at = 9.87 · 10

–6

at = 7.5 · 10

–3

Torr

1 bar = 10

Pa = 1.02 at = 0.987 at = 750 Torr

1 at = 98.1 · 10

Pa = 0.981 bar = 0.968 at = 736 Torr

1 atm = 101.3 · 10

Pa = 1.013 bar = 1.033 at = 760 Torr

1 Torr = 133.3 Pa = 1.333 · 10

–3

bar = 1.359· 10

–3

at = 1.316 · 10

–3

atm

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-99

Work

Power

SI unit: J (Joule)

Nm (Newtonmeter)

SI unit:

(as before)

Ws (Wattsecond)

kWh (Kilowatthour)

Previous unit: kcal (Kilocalorie) = cal · 10

–3

1 Ws = 1 J = 1 Nm 10

erg

1 Ws = 278 · 10

–9

kWh = 1 Nm = 1 J = 0.102 kpm = 0.239 cal

1 kWh = 3.6 · 10

Ws = 3.6 · 10

Nm = 3.6 · 10

J = 367 · 10

kpm = 860 kcal

1 Nm = 1 Ws = 278 · 10

–9

kWh = 1 J = 0.102 kpm = 0.239 cal

1 J = 1 Ws = 278 · 10

–9

kWh = 1 Nm = 0.102 kpm = 0.239 cal

1 kpm = 9.81 Ws = 272· 10

–6

kWh = 9.81 Nm = 9.81 J = 2.34 cal

1 kcal = 4.19 · 10

Ws = 1.16 · 10

–3

kWh = 4.19 · 10

Nm = 4.19 · 10

J = 427 kpm

SI unit: Nm/s (Newtonmetre/s)

J/s (Joule/s)

SI unit:

(as before)

W (Watt)

kW (Kilowatt)

Previous unit: kcal/s (Kilocalorie/sec.) = cal/s · 10

kcal/h (Kilocalorie/hour.) = cal/h · 10

kpm/s (Kilopondmetre/Sec.)

PS (metric horsepower)

1 W = 1 J/s = 1 Nm/s

1 W = 10

–3

kW = 0.102 kpm/s = 1.36 ·10

–3

PS = 860 cal/h = 0.239 cal/s

1 kW = 10

W = 102 kpm/s = 1.36 PS = 860 ·10

cal/h = 239 cal/s

1 kpm/s = 9.81 W = 9.81· 10

–3

kW = 13.3 ·10

–3

PS = 8.43·10

cal/h = 2.34 cal/s

1 PS = 736 W = 0.736 kW = 75 kpm/s = 632 · 10

cal/h = 176 cal/s

1 kcal/h = 1.16 W = 1.16 · 10

–3

= 119 · 10

–3

kpm/s

= 1.58 ·10

–3

PS = 277.8 · 10

–3

cal/s

1 cal/s = 4.19 W = 4.19· 10

–3

kW = 0.427 kpm/s = 5.69 · 10

–3

PS = 3.6 kcal/h

Specifications, Formulae, Tables

International Unit System

Moeller Wiring Manual 02/05

9-100

Magnetic field strength

Magnetic flux density

SI unit:

Previous unit: Oe = (Oerstedt)

= 0.01256 Oe

= 12.56 Oe

1 Oe

----

Ampere

Metre

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

----

0= 001

-----

1000=

----

79= 6

----

, 0= 0796

-----

SI unit Wb (Weber)

mWb (Microweber)

Previous unit: M = Maxwell

1 Wb = 1 Tm

1 Wb = 10

mWb = 10

1 mWb = 10

–6

Wb = 100 M

1 M = 10

–8

Wb = 0.01 mWb

SI unit: T (Tesla)

mT (Millitesla)

Previous unit: G = Gauss

1 T = 1 Wb/m

1 T = 10

mT = 10

1 mT = 10

–3

T = 10 G

1 G = 0.1

–3

T = 0.1 mT