Channel. 2.- Three Channel Types. Three_sizing_options. Constant_Manning_coefficient

8/12/2019 Channel. 2.- Three Channel Types. Three_sizing_options. Constant_Manning_coefficient

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Pulp flow in circular, semicircular or rectangular channels, with three

Reference drawing : M000-301Flow number : 302 Minimum flowReview: 0 Pulp density

Solids mass flow rate m s = 2200 t/h Volumetric conceRatio max. flow to nom. flow Q max / Q nom = 1.20 - Pulp kinematic vi

Ratio min. flow to nom. flow Q min / Q nom = 0.7 - Mc Elvain & CavSolids density r s = 2.66 t/m Friction factor Weight concentration Cw = 27.46% - Manning's coefficMedium value of the PSD (1) d50 = 60 mm Reynolds numbeLiquid density r L = 1000 kg/m Eq. 1Mannings' coefficient (2) N = 0.0130 - Eq. 2Slope S = 0.020 m/m Eq. 3

Lining thickness s Lining = 0 mm Eq. 4Froth factor FF = 1.0 - Eq. 5Design factor DF = 1.0 - Eq. 6

Temperature t = 18 C Eq. 7 Absolute rugosity of lining Rabs = 1.3 mm Eq. 8Chann height (if rectg or semicirc) Hchann = 1.5 m Eq. 9

Eq. 10

Channel type: Circular Selected dimensioning option:

Flow with froth Flow w. froth d or B h Am /s m m m

Minimum 1.29 1.200 0.395 0.3244Nominal 1.84 1.200 0.478 0.4201Maximum 2.21 1.200 0.529 0.4803

Note 1. PSD: Particle size distribution

Note 2. This input is a reference value. It does not consider the influence of the pipe rugosity (Rabs), the fluid vis

Note 3. If selected combination of nominal diameter and Schedule for carbon steel pipe does not exist, no soluti

Note 4. Annex A shows the steps required for the calculation of the Manning coefficient.

Flow rates:MinimumNominal Deposition:Maximum

Solution for circular channelManning coefficient N = 0.0130Slope S = 0.0200

Circular channel Flow w. froth d H AFlow with froth m /s m m m

Minimum 1.29 1.657 0.395 0.324Nominal 1.84 1.657 0.478 0.420

Nominal flow

Maximum flow

OK. v/vd >=1.1. No deposition will occur OK. v/vd >=1.1. No deposition will occur OK. v/vd >=1.1. No deposition will occur


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Maximum 2.21 1.657 0.529 0.480

Annex A. Manning coefficient calculation for a circularQ = 1.29 m 3/sd = 1.200 m

N = 0.013 -S = 0.01293 m/m

A = Channel_Circular_Area_Q_D_N_S A = 0.37981 mv = Q/AQ = 1.29 m 3/s A = 0.37981 mv = 3.40 m/s

Rh = Channel_Circular_Hydraulic_Radius_Q_D_N_SRh = 0.242 m

Rrel = Rabs / (4*Rh)Rabs = 1.3 mm

Rh = 242.2 mmRrel = 0.0013

n P = Slurry_Visc_Thomas_Cw_Ss_RhoL_t

n P = 1.30E-06 m/s

Carbon steel pipes


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dn Sc -in

1 1/2 52 3/4 103 1 204 1 1/2 305 2 406 3 60

7 4 808 5 1009 6 120

10 8 14011 10 16012 12 STD13 14 XS14 16 XXS15 18 6.3516 20 7.1417 22 7.9218 24 8.7419 26 9.5320 28 10.3121 30 11.1322 32 11.9123 34 12.724 36 14.2725 38 15.8826 40 16.6627 42 17.4828 44 19.0529 46 22.2330 48 25.431 5432 6033 66

34 7235 7836 8437 9038 9639 10240 10841 12042 144


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sizing options and constant Manning's coefficient (Channel 2)Qnom = 6,639 m

3/h Eq. 1

Q max = 7,967 m3/h Eq. 2 Circular and semiciercular c

Q min = 4,647 m3/h Eq. 3 Nominal diameter, CS. pipe

r P = 1.21 t/m Eq. 4 Schedule

ntration Cv : 12.46 % Eq. 5 Rectangular channels: scosity n P = 1.33E-06 m/s Eq. 6 Interior channel width

factor FL = 0.795 - Eq. 7f = f(Rrel, Re) - Eq. 8 Selected dimension option:

ient N = f(Rh, Rabs, Re) - Eq. 9 r Re = f/Rrel,Re) - Eq. 10

Qnom = (m p /( r P *Cw )) * FF * DF Selected dataQmax = Q nom * Qmax / Qnom * FF * DF Qmin = Q nom * Qmin / Qnom * FF * DF

r P = (1/1000) * ( r L*Ss)/(C w+(1-C w)*S s)

Cv = C w /(C w + (1-C w) * S s)

n P = Slurry_Visc_Thomas_Cw_Ss_RhoL_t

FL = Slurry_Fl_McElvain_d50_Cv Available channel types:f = Pipe_Friction_Factor_Rrel_Re Selected cha

N = Pipe_Manning_coefficient_Channel_Rh_Rabs_Re

Re = v * (4 * Rh) / n

Option1 Table uses single functions

v E Froude P Rh T H/Dm/s m - m m m %

3.98 1.202 2.37 1.467 0.221 1.13 0.3294.39 1.460 2.34 1.639 0.256 1.18 0.3984.61 1.611 2.32 1.742 0.276 1.19 0.441

osity ( n P), nor the degree of fullness of the pipe (Rh). For a more accurate result, this input value can be repalced by the respectiv

n will be available (and no messages will be given).

HtoD ratio, for circular channels and Hn/D = 0.33 %Freeboard "FB" for semicircular and Hn/D = 0.40 %rectangular channels. FB = H chann - H Hn/D = 0.44 %

s using the matrix function Channel_Circular_Matrix_Q_D_N_S = Array(H, A, v, E, F-

m/m

v E Fr P Rh T HtoDm/s m - m m m %3.98 1.202 2.369 1.467 0.221 1.128 0.3294.39 1.460 2.344 1.639 0.256 1.175 0.398

Dimension options fo


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4.61 1.611 2.318 1.742 0.276 1.192 0.441

hannelRe = v * (4*Rh) / nv = 3.40 m/s

Rh = 0.242 mn P = 1.30E-06 m/s

Re = 2.54E+06 -

f = Pipe_Friction_Factor_Rrel_Re

Rrel = 0.0013 -Re = 2.54E+06 -

f = 0.0212 -

N = (f * Rh ^ (1 / 3) / (8 * g)) ^ 0.5f = 0.0212

Rh = 0.242N = 0.01297

N = Pipe_Manning_coefficient_Channel_Rh_Rabs_ReRh = 0.242 m

Rabs = 1.3 mmRe = 2.54E+06 -N = 0.01297 -

DataN = 0.01300


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Rev. cjc. 30.01.2014

Modules inclu

hannels: Option1 Option2 Option3dn (in) = 48 60 66Sch (-) = STD STD STD

Bint (mm) = 1300 1400 1500 Data sheets i

Option1

dn (in) = 48 inSch (-) = STD -

Bint (mm) = 1300 mm

Circular Semicircular Rectangular nel type: Circular

fi Qmax Re N (4) f vd v/vdrad m /s - - -. m/s -

Eq. 10 v / v d1.92 5.933 2.7E+06 0.0129 0.0217 2.86 1.391.78 5.933 3.4E+06 0.0130 0.0209 3.14 1.401.69 5.933 3.8E+06 0.0130 0.0205 3.31 1.39

e calculated values.

g = 9.80665 m/s

, P, Rh, t, HtoD, fi, Qmax)

fi Qmaxrad m /s

1.92 5.9331.78 5.933

OK. hn/D


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1.69 5.933


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ded

cluded

hvm

v/(2*g)0.810.981.08

Channel. 2.- Three Channel Types. Three_sizing_options. Constant_Manning_coefficient

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