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EQUATIONS HELP
Equation solvers in the fields of Fluid Flow/heat/chemical/Electrical/ Physics/Batch Reactor/Distillation, Design, Stress, manufacturing, Dimensionless number, more equations can be solved for. Equations are displayed in the List Box in sub sections. The variables of each equation can be solved for individually.
Method of Operation : (The method of use is the same for each Equation section.)
Change a variable field forces a recalculation of the variables in the equation.
Equations and symbols used :
SEE also : SYMBOLS HELP for an explanation of all the symbols used in the equations.


Notes about the bit map image information not in the images :
R refers to any Alkyl group
R’ refers to any Alkyl group which may be different then R
RX refers to a Alkyl Halide group.
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
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
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[(2s[r + 1  sqr(r^2 + 1)]/(2s[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 heattransfer 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))
Openended Cylinder, Critical Pressure to cause buckling" '
pc = (1/3)*[n^2  1 + (2n^2  1
v)/(n^2(2l/(piDo)^2)1)](2e/(1v^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.