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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

H = hd - hs

hs = hgs + atm + hss

hd = hgd + atm + hvd

hv = v^2/2g

Power output:

P = HQ/3.599 x 10^6

(NPSH),new = hss - hfs - p

(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)

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

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.