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__General Symbol__:-

Pi - - Value = 3.1415927

__Symbols for Heat / Chemical Equations__:-

A - area - m^{2} - metres
squared

ai,af – absorptivity m^2/s metres squared per second.

Bi – Biot number – dimensionless.

cv - specific heat capacity at constant volume - J/kg K

cp - specific heat capacity at constant pressure - J/kg K

c - specific heat capacity - J/kg K - Joules per (mass x temperature)

C - heat capacity - J/K - Joules per temperature

ci - concentration - g/cm^{3}

COP,cop – Coefficient of performance.

COPc – Coefficient of performance Carnot cycle.

D - density - Kg/m^3 - kilogram per metres cubed

D – Diffusion coefficient used for the Lewis Number

Fo – Fourier number – dimensionless.

H - enthalpy - J

h,h1,h2,hg,hf,hfg,h4,h3- specific enthalpy - kJ/kg - Kilo Joules per kilogram

h – heat transfer coefficient – W/m^2 C.

hd – Mass-transfer coefficient – metres per hour m/h

k - thermal conductivity - W/m k - watt per (metro x kelvin)

Kn – Knudsen number - dimensionless

l – length -

le – Lewis number – dimensionless.

L - latent heat - kJ/kg - kilo Joule per kilogram

M- mass flowrate- m/s- mass per second

M - relative molecular mass

Mv – lrradiation – total radiation incident upon a surface per unit time and per unit area.

Mf - mass flowrate- m/s- mass per second

m - mass - Kg - kilograms

n - mol - g - grams

Nu - Nusselts number, dimensionless

Pr - Prandlts number, dimensionless

P,P1,P2 - pressure - Pa - pascal

Q - heat - J - Joules

q - heat rate -J - Joules

R - universal gas constant - 8314 J/kg-mole - Jolues per kilogram-mole

Re - Reynolds number, dimensionless

Ref – Refrigeration effect, KJ/Kg

Sh – Sherwood number – dimensionless -

Sc – Schmidt number – dimensionless -

s – a characteristic dimension of the body

T1 - T2, Tc, Th - temperatures - K - kelvin

tf - time

vi - volume - cm^{3}

Vol - volumetric flowrate - m^3/s - metres cubed per second

V,V1,V2 - volume - m^3 - metres cubed

W, w – work – Joules, kilo joules etc. J, KJ

v – Kinematic viscosity.

vg - specific volume of gas, m^3/kg

x - distance - m - metres, used in the sherwood number as a coordinate., used in heat wet, steam equations as dryness fraction.

y – wave length

__SYMBOLS FOR ELECTRICAL
EQUATIONS__ :-

A - Area

B – Magnetic inductor

C - capacitor - F - Farad

R,R1,R2 - Resistance - ohm

E,E1,E2 - Voltage - volts

I,I1,I2 - Current - Amp- ampere

Tc - time constant capacitor - s - seconds

P - power - w -watts

L - inductor - Henry

q - Capacitor charge -

dE/dt - Voltage flux -

Xc - Reactance of capacitor

W – Electrical work

J – current density

@max,@ - magnetic flux

C - capactance

Uo,Eo – absolute permittivity

Ur,Er – relative permittivity

L – length of cylinders.

A – plate area, one side only.

A – thickness of dielectric

Iph – phase current, amp

Vph – phase voltage, volts

X - reactance

z - Impedance

s – Apparent power

Y – admittance.

B – refers to the induced flux

Vi – voltage due to self inductance.

w – omega symbol

N – number of turns of coil.

__d@/dt__ – rate of change
of flux.

Fl – refers to a transverse force

Fm – refers to the foce acting between two magnetic poles.

L – length of conductor.

__SYMBOLS FOR PHYSICS EQUATIONS__
:-

a - acceleration- m/s^2 - metres per second squared, can also be used as an angle in projectile motion.

c - Speed of light - m/s - metres per second

E - energy - J - joule

f - focal length - m - metres

F - For lenses - Focus - m - metres

F - Force - N - newton

Fc - Centrifugal force - N - Newton’s

g - gravitational constant - 9.81 m/s^2 - metres per seconds squared

g - gravitational constant - 9.81 - N/kg - newton per kilogram

G - gravitational force

KE - kinetic energy - J - joules

l - length - m - metres

I - Image size - I

m -m1 -m2 - mass - Kg - kilograms

m, m1,m2 - For lenses - magnification factor

PE - potential energy - J - Joules

P - power - w -watts

h - vertical height - m - metres

T - torque - Nm- newton metro

T - For pendulum motion - Period of oscillation - s - second

t - time - s - seconds

r - radius - m - metres

s,s1 - displacement - m - metres

u - initial velocity- m/s - metres per second

v – initial velocity – m/s – metres per second.

v - velocity - m/s - metres per second

Ve - Velocity at point e - m/s - metres per second

w - angular velocity - rad/s - radians per seconds

W - work - J - Joules

x - distance - m - metres

Y – refers to Decay in lonizing radiation equations.

A – refers to activity in lonizing radiation equations. Number of atoms of aradioactive substance that diintegrates per unit time.

-dn/dt – rate of change of A

N – number of radioactive atoms.

He – radiant exposure, Ws/m^2

Ee – irradiance, W/m^2

Ye – refers to radiant power, W

A1, A2 – refers to the area of the surface

Le – refers to radiance, W/(sr m^2)

Ie – refers to the radiant intensity.

Qe – refers to the radiant energy, quantity of radiation, J

Om – Omega symbol

Hv – Light exposure

Ev – refers to the illuminance.

Yv – refers to Luminous flux

Lv – refers to Luminance

Qv – refers to the quantity of light, Luminous energy

__SYMBOLS FOR FLUID FLOW__

A - Cross sectional area of aperture at right angle to fluid flow

b Width of opening, - m - metres

u - Velocity at the outlet - m/s - metres per second

Cv - velocity coefficient- no unit

Cd - discharge coefficient - no unit

d - Density - kg/m^3 - kilogram per metres cubed

F - Reaction force

g - gravitational constant - 9.81 m/s^2 - metres per seconds squared

H , H1 , H2- Height- m- metres

h - Height- m- metres

Pex - External pressure in excess of atmospheric pressure - Pa - Pascal

V - Volume flow at outlet - m^3/s - metres cubed per second

s - Distance of discharge - m - metres

Ventrui , Orificeplate Symbols :

A - inlet area.

a - throat area.

A1 - pipe cross-sectional area.

A2 - Orifice cross-sectional area.

dm - density of fluid in manometer.

P1,P2 - refers to pressure at two points 1 and 2.

z - refers to the height difference in the manometer tubes.

Da - diameter of throat or Orifice.

Db - diameter of pipe.

Do - diameter of throat or Orifice.

Vb - outlet volume.

"Fluid Pressure Distribution, P1"

P1 – pressure at point 1

Po – external, surface pressure

g. . gavitation force due to gravity

d – density of the fluid

h1 – height between two points

"Fluid Pressure Distribution, P2"

P2– pressure at point 2

P1 – pressure at point

h1, h2– height between two points

"Buoyancy,Gas"

Fa - Buoyancy

V - volume

"Buoyancy,Fliuds"

d' - density

V' - volume

Float/Fliud Densities, Solid Body Greater

df – density of the fluid

F – equilibrium force required to balance the mass

M - mass

Float/Fliud Densities, Solid Body Smaller

Fh - equilibrium force required to balance the auxiliary mass

__SYMBOLS FOR GEOMETRY__

Line :

c – y intercept value for a straight line

m, m1,m2 – gradient values for 3 different lines.

@ - angle between line and x - axis

d – distance between two points.

xip – x intercept point between two lines.

y2,y1 – y axis co-ordinate points for two points.

x2,x1 – x axis co-ordinate points for two points.

Circle :

yc – y center point of the circle.

xc – x center point of the circle.

Hyperbola :

rv – vertex radius.

e – eccentricity.

__SYMBOLS FOR INTEREST__

F - Future cash amount

P - Amount of initial cash

i - interest rate expressed in decimal form i.e. 0.06 represents 6% rate

n - Amount of years the money will be receiving the interest

__SYMBOLS FOR SERIES__

Tn - the nth term of the series

a - the initial term of the series

n - the term number

Sn - Sum of the n terms

Si - Sum to infinity terms

__SYMBOLS FOR PUMPS AND
COMPRESSORS__

atm - atmospheric pressure -

d - Density of gas - kg/m^3 - kilogram per metres cubed

D - Diameter of the impeller - m - meters

g - Gravity

H - Total dynamic head - Nm/kg - Newton metro per kilogram

hd - discharge head - m - metres

hs - total suction head - m - metres

hss - static suction head - m - metres

hv - velocity head - m/s - metres per second

hfs - suction friction head - m - metres

hgs - gauge reading suction side - m - metres

hvs - velocity head - m -metres

Had - adiabatic head - m - metres

N - speed of rotation of the compressor - rev/s - revolutions per second

p - vapor pressure

Q - quantity of flow - m^3/h - metres cubed per hour

u - viscosity of gas

V - velocity of gas - m/s - metres per second

__SYMBOLS FOR PUMPS AND NUMERICAL
EQUATIONS__

g – acceleration due to gravity m/s metres per second

L – Characteristic Length – m – metres

dp – Dispersed phase density – kg/m^3 – kilograms per metres cubed

d – Fluid density - kg/m^3 – kilograms per metres cubed

u – Fluid Viscosity – Pa s- pascal x second

ui – Infinite Shear Viscosity (Bingham plastics) - Pa s- pascal x second

V – Average fluid velocity – m/s – metres per second

V’ – System Volume – m^3 – metres cubed

s – Particle area/particle Volume – 1/m – 1 per metro

@ - Surface Tension – N/m – newton per metro

b – bulk modulus – Pa – pascal

D – Diameter of pipe – m – metres

Dc – Diameter of Curvature – m – metres

p’ – Average static pressure – Pa – pascal

q’ – Average Volumetric flow rate – m^3/s – metres per second

w – Characteristic frequency – 1/s- 1 per second

c – Sonic velocity – m/s- metres per second

a – wave speed - m/s- metres per second

dp – frictional pressure drop use in Hodgsen number – Pa – pascal

N – Rotational speed – 1/s – 1 per second

f’ – Vortex shedding frequency – 1/s – 1 per second

Fd – Drag force – N – newton

Y – Fluid relaxation time – s – second

e – void fraction – m^3 – metres cubed

dl, dg – Liquid, gas density - kg/m^3 – kilograms per metres cubed

__Manufacturing :__

MLT – manufacturing lead time

nm – number of separate machines, operations through which the product must be routed in order to produce the product.

Tsu – manufacturing setup time.

To – time per operation at a given machine, operation.

Tno – time of nonoperation with the machine.

Tp – average production time per unit of product for the given machine.

BT – batch time.

Q – number of units to be processed per batch.

Rp – rate of process a product, i.e. units of product per hour.

Tth – the, any, tool handling time per work piece.

Th – work piece handling time.

Tm – actual machining time.

PC – production capacity for a group of work centres.

W – number of work centres.

Sw – number of shifts per week

H – number of hours worked per shift.

Av – availability of the machine.

Mtbf – mean time between failures.

Mttr – mean time to repair.

Wip – work in progress

U – utilization, measure of the amount of output of a production facility relative to its capacity.

Cpc – production cost of an item, cost per piece

Cm – cost of material

Co – refers to the cost of each processing step on the part, production time x rate of cost of machine & labour

Cno – refers to the non-operational costs, inspection, material handling..……

SPPWF – single payment present worth factor

I – annual interest rate

n – term of interest in years.

CRF – capital recovery factor

USPWF – uniform series present worth factor.

SFF – sinking fund factor.

USCAF – uniform series compound amount factor.

Tc – ideal or theoretical cycle time.

F – refers to the frequency in which line stoppage occurs per cycle.

Td – average downtime to diagnose the problem within the process.

D – refers to the proportion of downtime on the production line.

Cl – refers to the cost per minute to operate the production line.

Ct – refers to the cost of disposable tooling, computed on a per workpiece basis.

E – proportion of time the production line is up and functioning

Twc – refers to total work content, is the sum of all work elements to be done on the production line.

S – refers to spindle speed, rev/min.

V – refers to cutting speed, sfpm.

fr – refers to the feed rate, in/rev.

f – refers to the feed, in/rev, (number of teeth on the cutter)(chip load).

MRR – material removal rate.

L – length of work piece in the direction of travel.

__SYMBOLS FOR DESIGN EQUATIONS__

Nt – number of tubes

K1 – constant for use in find number of tubes

Db – bundle diameter, mm

Do – tube outside diameter, mm

n - constant for use in find number of tubes

dTlm – Log mean temperature difference

T1 – inlet shell-side fluid temperature

t2 – outlet tube-side temperature

T2 – outlet shell-side fluid temperature

t1 – inlet tube-side temperature

Ft – temperature correction factor

R – number used to calculate Ft

S - number used to calculate Ft

Nu – Nusselt Number

Hi – inside heat coefficient, W/m^2 C

de – equivalent, hydralic diameter, m

Kf – fluid thermal conductivity, W/mC

Re – Reynolds Number

ut – water velocity, m/s

Pr – Prandtl Number

Cp – fluid specific heat, heat capacity, J/kgC

u – fluid viscosity at the bulk fluid temprature, Ns/m^2

C – a constant value , c= 0.021 for gases, c = 0.023 for non-viscous liquids, c = 0.027 for viscous liquids

uw – fluid viscosity at the wall

St – Stanton Number

E – Value used in the calculation of the Staton

L – Length of the tubes, m

Jh – Heat transfer factor

di – tube inside diameter, mm

(hc)s - Condensation inside horizontal tubes coefficient

kl – condensate thermal conductivity, W/mC

dl – condensate density, kg/m^3

dv – vapour density, kg/m^3

ul – condensate viscosity Ns/m^2

Z,Zv – the condensate rate per unit tube perimeter, kg/ms

Wc – total condensate flow

Rec – Reynolds number for the condensate film

(hc)l – mean condensation film coefficient, for a single tube, W/m^2C

Tsat – saturation temperature of the vapour

hcg – mean effective coefficient

hc – mean condensate film coefficient

Qg – total sensible-heat transfer from vapour

Qt – total heat transferred

Hg – mean effective coefficient

z2 height from datum to heavy liquid overflow, m

z1 – height from datum to light overflow, m

z3 – height from datum to interface, m

d1 – density of the light liquid, kg/m^3

d2 – density of the heavy liquid, kg/m^3

Ud – settling velocity of the dispersed phase droplets, m/s

dd – diameter of droplet , m

dp – dispersed phase density, kg/m^3

dc – continuous phase density, kg/m^3

Uc – continuous phase viscosity, Ns/m^2

w – interface width, m, for Interfacial Area - Horizontal Decanter equation

r – radius of cylinder, m, for Interfacial Area - Horizontal Decanter equation

z – interface height form base of vessel, m, for Interfacial Area - Horizontal Decanter equation

l – length of the cylinder, for Interfacial Area - Horizontal Decanter equation

t – pipe thickness, for pipes

P – internal pressure, for pipes equation

d – outside diameter, for pipes equation

Sd – design stress at working temperature

Sno – Schedule number

Ps – safe working pressure

Ss – safe working stress

T1

r2 - circumferential radius of curvature

r1 - meridional radius of curvature

S1=PD/4t

P - pressure

D – diameter of the cylinder

@ - angle to the axis

A – major axis for an ellipsoid

b – minor axis for an ellipsoid

Ro – outer edge radius

Rk – Knuckle radius

e – minimum thickness

Pi – internal pressure

Di – internal diameter

f – design stress

j – joint factor

Rc – crown radius

Cs – stress concentration factor for torispherical heads, equal to (1/4)(3 + (Rc/Rk)^0.5)

Pc – critical pressure to cause buckling with reference to an open-ended cylinder

n – number of lobes formed at buckling

v – poisson’s ration

L – the effective length of the vessel, the supported length

Do – external diameter of the vessel

E – Young’s modulus

T – wall thickness

Fr – load per unit length on a ring

Pe – external pressure

Ls – spacing between the rings

Fc – critical load to cause buckling, with uniform radial load

Ir – second moment of area of the ring cross-section

Dr – diameter of the ring

Pc – critical buckling pressure

Rs – outside radius of the sphere

Vps – poisson’s ration

P - pressure loading

Sw – direct stress on the vessel

W – total weight of the supported by the vessel at the plane being considered

Di – internal diameter of the vessel

Sb – bending stress of the vessel

M – total bending moment at the plane in consideration

Iv – the second moment of area of the vessel about the plane of bending

ts – Torsional shear stress

T – the applied torque

Ip – polar moment of area for the vessel

S1 – circumferential stress

Sh – longitudinal stress

Sz – stress in the vertical plane

Wv – total weight of the shell, excluding internal fittings, i.e. plates, N

Cv – a factor to consider the weight of nozzles, manways, internal supports…….1.08 for vesels with only a few internal fittings, 1.15 for distillation columns or similar vessels, which contain serveral manways and plate support rings.

dm – density of the vessel material, kg/m^3

Dm – mean diameter of the vessel, m

G – acceleration due to gravity, 9.81 m/s^2

Hv length or height, between tangent lines , the length of the cylindrical section, m

Mx – bending moment of the vessel

W – load per unit length (Newtons per metre )

x - distance measured of the vessel from the free end

Pw – wind pressure, load per unit area

Cd – shape factor, drag coefficient

da – density of the air

uw – wind velocity

Fs – shear force on the vessel

ae – acceleration of the vessel due to the earthquake

W – total weight of the vessel

g – acceleration due to gravity

Me – Bending Moment

We – dead weight of the equipment.

Lo. – distance between the centre of gravity of the equipment and the column centre line.

Base openings :

v = Cv(2gH)^0.5

V = CdA(2gH)^0.5

Small side openings :

v = Cv(2gH)^0.5

s = s(Hh)^0.5

V = CdA(2gH)^0.5

F = dVv

Large side openings :

V = (2/3)Cdb(2g)^0.5(H2^(3/2) - H1^(3/2))

Excess pressure on surface of Liquid :

v = Cv(2(gH + Pex/d))^0.5

V = CdA((2(gH + Pex/d))^0.5

Excess pressure applied to an outlet point :

v = Cv(2(Pex/d))^0.5

V = CdA(2(Pex/d))^0.5

Note :-

Cd = CcCv

Cc = 0.62 for sharp edge openings

Cc = 0.97 for rounded openings

Cv = 0.97

Venturi :

Vb = (Cv/(1 - Db/Da)^4)^0.5)(2(P2 - P1)/d)^0.5

Q = (3.142/4)Do^2Vb

Qm = (1/A)(2(dm - d)gz/(d((A/a)^2 - 1)))^0.5

Orificemeter :

Uo = (Cv/(1 - Db/Da)^4)^0.5)(2(P2 - P1)/d)^0.5

Q = (3.142/4)Do^2Uo

Qa = (CdA2/(1 - A2/A1)^2)^0.5)(2(P2 - P1)/d)^0.5

Note :

Cd ~ 0.6 for Orificemeter, 0.99 for Venturi.

__GENERAL BATCH REACTOR HELP &
SYMBOLS__ :-

MATERIAL BALANCE:

Rate of reactant flow into element = Rate of reactant flow out of element + Rate of reactant loss due to

chemical reaction within the element. + Rate of accumulation of reactant in the element.

i.e. INPUT = OUTPUT + DISAPPEARANCE BY REACTION + ACCUMULATION.

__Symbols Used:-__

Fao - molar flow of a into the reactor

-ra - rate of disappearance of a by reaction, (moles of a reacted)/(volume)(time)

V - volume of fluid in the reactor

Vo - volumetric feed rate to the reactor - m^3/s - metres cubed per second

Cao - feed concentration of a - kmol/m^3 - kilo mol per second

Xa - conversion of a

Ea - fractional change in volume on complete reaction

Na - moles of a present in the element at time t. i.e. Nao refers to moles present at time t=0

__GENERAL PUMP &
COMPRESSOR HELP & SYMBOLS__

Total discharge head :

H = hd - hs

Total suction head:

hs = hgs + atm + hss

Total discharge head :

hd = hgd + atm + hvd

Velocity Head :

hv = v^2/2g

Power output:

P = HQ/3.599 x 10^6

Net Positive Suction Head:

(NPSH),new = hss - hfs - p

Net Positive Suction Head:

(NPSH),existing = atm + hgs - p + hvs

Specific speed, Ns (centrifugal pumps)

Ns = NQ^0.5/(gh)^0.75

Q = flow - m^/s - metres cubed per second

h = head - m - metres

g = gravitational acceleration - m/s^2 - metres per second

Reynolds Number, Nre

Nre = dVD/u

Specific speed :Ns (compressor)

Ns = N(Q)^0.5/(Had)^314

Specific Diameter, Ds

Ds = D(H)^0.25/(Q)^0.5

__GENERAL Equations used for
the Design Equations (SYMBOLS for Notation) __

Triangular & Square Patterns, tube count" ' Nt = K1(Db/do)^n

Bundle Diameter" ' Db = do(Nt/K1)^1/n

Mean Temperature Difference" ' dTlm = ((T1 - t2) - (T2 - t1))/(ln((T1 - t2)/(T2 - t1)))

True Temperature Difference" ' dTm = FtdTlm

R Value" ' S = (T1 - T2)/(t2 - t1)

S Value" ' S = (t2 - t1)/(T1 - t1)

Ft Value" ' Ft = Sqr(R^2 + 1)ln[(1 -s)/(1 - RS)]/((R - 1)ln[(2-s[r + 1 - sqr(r^2 + 1)]/(2-s[r + 1 + sqr(r^2 + 1)]]

Prandtl Number" ' Pr = CpU/kf

Heat Transfer Data correlation, 1" ' Nu = CRe^0.8Pr^0.33(U/Uw)^0.14

Heat Transfer Data correlation, 2" ' St = ERe^-0.205Pr^-0.505

Stanton Number" ' St = Nu/(RePr)

E Value" ' E = 0.0225exp(-0.0225(lnPr)^2)

Flim heat-transfer coefficient, Nu" ' Nu = 1.86(RePr)^0.33(de/L)^0.33(U/Uw)^0.14

jh" ' jh = StPr^0.67(U/Uw)^-0.14

Condensation inside and outside vertical tubes, (hc)v" '0.0.926*kl[(dl(dl - dv)g)/(UlZv)]^1/3

Condensation inside and outside vertical tubes, Zv" ' Zv = Wc/(Nt*Pi*di)

Reynolds number for the condensate film, Rec" ' Rec = 4Zv/Ul

Prandtl number for the condensate film, Prc" ' Prc = CpUl/Kl

Condensation outside horizontal tubes, (hc)l" '0.95*kl[(dl(dl - dv)g)/(UlZ)]^1/3

Condensation inside horizontal tubes, (hc)s" ' 0.76*kl[(dl(dl - dv)g)/(UlZh)]^1/3

Mean Temperature Difference, dTlm" ' dTlm = (t2 - t1)/(ln[(Tsat - t1)/(Tsat - t2)]

Partial Condensers, hcg" ' 1/hcg = 1/hc + Qg/(Qt*hg)

Heavy Liquid Overflow, Z2" ' z2 = (z1 - z3)d1/d2 + z3

Settling Velocity, Ud" ' Ud = ((dd)^2g(dp - dc))/(18Uc)

Interfacial Area - Horizontal Decanter, w" ' w = 2(2rz - z^2)^0.5

Pipe Thickness, t" ' t = Pd/(20Sd + P)

Schedule Number, Sno" ' Sno = Ps*1000/Ss

Maximum Shear Stress" ' s1 = +- (S1 - S2)/2

Shear Stress 1" ' s1 = +- (S1 - S2)/2

Shear Stress 2" ' s2 = +- (S2 - S3)/2

Shear Stress 3" ' s3 = +- (S1 - S2)/2

Meridional Stress" s1 = Pr2/2t

Cylinder, Shear Stress 1" ' S1=PD/4t

Cylinder, Shear Stress 2" ' S2=PD/2t

Sphere, Shear Stress 1 = 2" ' S1=S2 = PD/4t

Cone, Shear Stress 1" ' S1 = Pr/(2tcos@)

Cone, Shear Stress 2" ' S2 = Pr/(tcos@)

Ellipsoid, at Crown, Shear Stress 1 = 2" ' S1=S2= Pa^2/(2tb)

Ellipsoid, at Equator, Shear Stress 1" ' s1 = Pa/2t

Ellipsoid, at Equator, Shear Stress 2" ' s2 = (Pa/t)[(1 - 0.5(a^2/b^2))]

Torus, Shear Stress 1" ' s1 = Pr2/2t

Torus, Shear Stress 2" ' s2 = (Pr2/t)[(1 - (r2sin@)/(2(Ro + r2sin@)))]

Torus, at centre line , Shear Stress 2" ' s2 = Pr2/t

Torus, at outer edge , Shear Stress 2" ' s2 = (Pr2/2t)[(2Ro + r2)/(Ro + r2)]

Torus, at inner edge , Shear Stress 2" ' s2 = (Pr2/2t)[(2Ro - r2)/(Ro - r2)]

Torisherical Heads, Shear Stress 1 = 2" ' S1=S2= PRc/2t

Torisherical Heads, for Torus , Shear Stress 1" ' S1 = PRk/2t

Cylindrical shell, Minimum Thickness" ' e = (PiDi)/(2f - Pi)

Sphere shell, Minimum Thickness" ' e = (PiDi)/(4f - Pi)

Ellipsoidal Heads, Minimum Thickness" ' e = (PiDi)/(2fj - 0.2Pi)

Torispherical Heads, Minimum Thickness" ' e = (PiRcCs)/(2fj + Pi(Cs - 0.2))

Open-ended Cylinder, Critical Pressure to cause buckling" ' pc = (1/3)*[n^2 - 1 + (2n^2 - 1 v)/(n^2(2l/(piDo)^2)-1)](2e/(1-v^2))(t/Do)^3 + (2Et/Do)/((n^2 - 1)(n^2(2L/piDo)^2 + 1)^2)

Stiffening Rings, Critical Load to cause buckling" ' Fc = 24EIr/Dr^3

Vessel Heads, Sphere" ' Pc = 2Et^2/(Rs^2 SQR(3*(1 - Vps^2)))

Primary Stress, Longitudinal" ' Sh = PDi/2t

Primary Stress, Circumferential" ' Sl = PDi/4t

Direct Stress, Weight" ' Sw = W/(pi(Di + t)t

Bending Stress" ' Sb = M/Iv(Di/2 + t)

Bending Moment" ' Iv = pi/64(Do^4 - Di^4)

Torsional Shear Stress" ' ts = T/Ip(Di/2 + t)

Principal Stress 1" ' S1 = 0.5(Sh + Sz + SQR((Sh - Sz)^2 + 4t^2))

Principal Stress 2" ' S2 = 0.5(Sh + Sz - SQR((Sh - Sz)^2 + 4t^2))

Principal Stress 3" ' S = 0.5P

Weight Loads" ' Wv = CvpidmDmg(Hv + 0.8Dm)tx10^-3

Weight Loads, for steel Vessel" ' Wv = 240CvDm(Hv + 0.8Dm)t

Wind Loads, tall vessels" ' Mx = wx^2/2

Dynamic Wind Pressure" ' Pw = 0.5CdDaUw^2

Earthquake Loading ' Fs = ae(W/g)

Eccentric Loads, tall vessels ' Me = WeLo

__DISTILLATION SYMBOLS USED IN THE EQUATIONS__

V1= vapor flow from the stage 1

D = flow of distillate

xd = mole fraction of component in liquid.

hd = specific enthalpy of liquid

yn+1 = mol fraction of component

Vn+1 = vapor flow into the stage from the stage below

Hn+1 = specific enthalpy vapor phase.

Qc = heat across the condenser.

yn = mol fraction of component in vapor.

vn = vapor flow from the stage.

B = bottoms flow.

xb = mol fraction in the bottoms.

Qb = heat across the bottoms.