SYMBOL HELP
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.
EQUATIONS FOR
FLUID FLOW
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.