Handbook of Formulae and Constant by Afirk - HTML preview

_{Air (kg per kg of fuel) =} [( )]¹⁰⁰

38 23

 

Air Supplied from Analysis of Flue Gases

 

Air in kg per kg of fuel = ^N2 × C_{33 (CO2+CO)}

 

C is the percentage of carbon in fuel by mass

 

N₂ is the percentage of nitrogen in flue gas by volume CO₂ is the percentage of carbon dioxide in flue gas by volume CO is the percentage of carbon monoxide in flue gas by volume

 

Boiler Formulae

Equivalent evaporation =
m_s (h₁ -h₂) 2257 kJ/kg

Factor of evaporation =
(h₁ -h₂) 2257kJ/kg

m_s (h₁ -h₂ )^{Boiler efficiency =} m_f x calorificvalueof fuel

where m_s = mass flow rate of steam
h₁ = enthalpy of steam produced in boiler h₂ = enthalpy of feedwater to boiler m_f = mass flow rate of fuel

FLUID MECHANICS
Discharge from an Orifice

 

Let A = cross-sectional area of the orifice = (π/4)d²

 

and A

 

=

 

cross-sectional area of the jet at the vena conrtacta = (( π /4)

 

2 d

 

c

 

then A = C_cA

 

A

 

c

 

=

 

›

 

d

 

c

 

ž

 

2

 

or C_c = _{A œ d Ÿ} 

 

where Cc is the coefficient of contraction

 

At the vena contracta, the volumetric flow rate Q of the fluid is given by

 

Q = area of the jet at the vena contracta× actual velocity =A_cv

 

or Q = C_cAC_v 2gh

 

The coefficients of contraction and velocity are combined to give the coefficient of discharge, C_d

 

i.e. C_d=C_cC_v

 

and Q = C_dA2gh

 

Typically, values for C_d vary between 0.6 and 0.65

 

Circular orifice: Q = 0.62 A 2gh

 

Where Q = flow (m³/s) A = area (m²) h = head (m)

 

Rectangular notch: Q = 0.62 (B x H) 2_2gh3

 

Where B = breadth (m) H = head (m above sill)

 

Triangular Right Angled Notch: Q = 2.635 H^5/2

 

Where H = head (m above sill)

 

Bernoulli’s Theory

 

H =

 

h

+
P₊ v² w 2g

H = total head (metres)
h = height above datum level (metres) P = pressure (N/m² or Pa)
w = force of gravity on 1 m³ of fluid (N) v = velocity of water (metres per second)

Loss of Head in Pipes Due to Friction

 

Loss of head in metres = fL^v2

 

_d 2g

 

L = length in metres v = velocity of flow in metres per second d = diameter in metres f = constant value of 0.01 in large pipes to 0.02 in small pipes

 

Note: This equation is expressed in some textbooks as

 

Loss = 4fL^v2

 

_d 2g where the f values range from 0.0025 to 0.005

 

Actual Pipe Dimensions
ELECTRICITY
Ohm's Law

 

E

 

I =

 

R

 

or E = IR

where I = current (amperes) E = electromotive force (volts) R = resistance (ohms)

Conductor Resistivity

 

L

 

R =

 

a

where ρ = specific resistance (or resistivity) (ohm metres, &·m) L = length (metres)
a = area of cross-section (square metres)

Temperature correction

 

R_t = R_o (1 + αt)

 

where R_o = resistance at 0ºC (&)

 

R_t = resistance at tºC (&)

 

α = temperature coefficient which has an average value for copper of 0.004 28 (&/&ºC)

 

R

 

2

 

= R

 

1

 

(1+αt₂) (1+αt₁)

 

where R₁ = resistance at t₁ (&) R₂ = resistance at t₂ (&)

 

α Values &/&ºC

copper 0.00428
platinum 0.00385
nickel 0.00672
tungsten 0.0045 aluminum 0.0040

Dynamo Formulae

 

Average e.m.f. generated in each conductor = 2

 

ΦNpZ 60c where Z = total number of armature conductors

 

c = number of parallel paths through winding between positive and negative brushes where c = 2 (wave winding), c = 2p (lap winding)

Φ = useful flux per pole (webers), entering or leaving the armature p = number of pairs of poles
N = speed (revolutions per minute)

Generator Terminal volts = E_G – I_aR_a

 

Motor Terminal volts = E_B + I_aR_a

 

where E = generated e.m.f. E_B = generated back e.m.f. I_a = armature current R_a = armature resistance

 

Alternating Current

 

R.M.S. value of sine curve = 0.707 maximum value Mean value of sine curve = 0.637 maximum value Form factor of sinusoidal = ^{R.M.S. value} =^0.707 =1.11_{Mean value 0.637}

 

Frequency of alternator = 60^{pN cycles per second}

 

Where p = number of pairs of poles N = rotational speed in r/min

 

Slip of Induction Motor

 

Slip speedof field-speed of rotor_{x 100Speedof field}

 

Inductive Reactance

 

Reactance of AC circuit (X) = 2πfL ohms

 

where L = inductance of circuit (henries)

 

Inductance of an iron cored solenoid = ^1.256T2µA henries_{L x 108}

where T = turns on coil
µ = magnetic permeablility of core A = area of core (square centimetres) L = length (centimetres)

Capacitance Reactance

 

Capacitance reactance of AC circuit = ¹ ohms _πfC

 

where C = capacitance (farads)

Total reactance =
^›2πfL -^{1 ž}_2πfCŸ ohms_œ

Impedence (Z) = (resistanc

 

^e)2 (reactance)²

 

+

 

= R

 

²+(2π fL-¹

 

_2πfC)² ohms

 

Current in AC Circuit

 

Current

=
impressedvolts impedance

Power Factor

p.f. =
truewatts volts x amperes

also p.f. = cos , where Φ is the angle of lag or lead

 

Three Phase Alternators

Star connected
Line voltage = 3 x phase voltage Line current = phase current

Delta connected
Line voltage = phase voltage Line current = 3 x phase current

Three phase power

 

P = cos Φ

E_L = line voltage I_L = line current cos = power factor

ION NAMES AND FORMULAE

MONATOMIC POLYATOMIC

Ag⁺ silver ion BO silver ion BO borate ion
Al³⁺ aluminum ion C₂H₃OO acetate ion
Au⁺ and Au²⁺ gold ion ClO^- hypochlorite ion Be²⁺ beryllium ion ClO beryllium ion ClO chlorite ion
Ca²⁺ calcium ion ClO calcium ion ClO chlorate ion
Co²⁺ and Co³⁺ cobalt ion ClOClO perchlorate ion
Cr²⁺ and Cr³⁺ chromium ion CN^- cyanide ion
Cu⁺ and Cu²⁺ copper ion CO copper ion CO carbonate ion
Fe²⁺ and Fe³⁺ iron ion C₂OO oxalate ion
K⁺ potassium ion CrO potassium ion CrO chromate ion
Li⁺ lithium ion Cr₂OO dichromate ion
Mg²⁺ magnesium ion HCO magnesium ion HCO hydrogen carbonate or bicarbonate ion Na⁺ sodium ion H₃O⁺ hydronium ion Zn²⁺ zinc ion HPO zinc ion HPO hydrogen phosphate ion

H₂POPO dihydrogen phosphate ion HSOHSO hydrogen sulphite or bisulphite ion HSOHSO hydrogen sulphate or bisulphate ion MnOMnO permanganate ion NN azide ion
NH4+ ammonium ion NONO nitrite ion
NONO nitrate ion
OO peroxide ion
OCN^- cyanate ion
OH^- hydroxide ion POPO phosphite ion
POPO phosphate ion
SCN^- thiocyanate ion SOSO sulphite ion
SOSO sulphate ion
S₂OO thiosulphate ion

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