A number of Fluid Flow/heat/chemical/Electrical/ Physics/Batch
Reactor/Distillation, Design, Stress, manufacturing and Dimensionless
number 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.
In the above example, the Electrical field between two charge
plates, V=Ed, has been selected. The variable V is to be solved for,
as a Question Mark (?) has been placed in the text box entry, the
remaining variables in the equation have numerical values. Once all
values have been entered click the an>CALCULATE button and
the solution to the variable V is displayed. Generally Any variable
in the equation can be solved for.
Equations and symbols used :
SEE also :- SYMBOLS HELP for an explanation of all
the symbols used in the equations.
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.