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EQUATIONS HELP

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[(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.