Typical Slurry Pump Calculation1.       First the user must enter design criteria or physical properties on the “Input Criteria” tap. Only values highlighted in blue need to be entered (NB: cells in blue font colour only).2.       The user must also enter the number of fittings in both the suction and the discharge side. If the fitting unique to your installation is not listed, just assign any fitting closest to yours in terms of head loss.3.       Then in the “CALCS” tab, the user must also enter design criteria only on the cell highlighted in blue.4.       In the “CALCS” tab, the user will need to determine and enter various factors (pipe friction factor, settling velocity factor, and slurry pump efficiency), in the cell shaded with dark blue fill by using the charts provided in various tabs.

First the user must enter design criteria or physical properties on the “Input Criteria” tap. Only values highlighted in blue need to be entered (NB: cells in blue font colour only).The user must also enter the number of fittings in both the suction and the discharge side. If the fitting unique to your installation is not listed, just assign any fitting closest to yours in terms of head loss.Then in the “CALCS” tab, the user must also enter design criteria only on the cell highlighted in blue.In the “CALCS” tab, the user will need to determine and enter various factors (pipe friction factor, settling velocity factor, and slurry pump efficiency), in the cell shaded with dark blue fill by using the charts provided in various tabs.

The user must also enter the number of fittings in both the suction and the discharge side. If the fitting unique to your installation is not listed, just assign any fitting closest to yours in terms of head loss.

In the “CALCS” tab, the user will need to determine and enter various factors (pipe friction factor, settling velocity factor, and slurry pump efficiency), in the cell shaded with dark blue fill by using the charts provided in various tabs.

Item Criteria Symbol Value Units

1 Ambiet Pressure 101,500 1015

2 Reference Pressure 100,000 1

3 Reference Temperature 54 Slurry Temperature T 305 Slurry Medium N/A Water N/A6 Slurry pH Level pH 7 N/A7 Desired Flowrate V 1060

8 Dry Solids Density 6800

9 Slurry Density 3200

10 Density of water at ambient conditions 994.7

11 Denisity of water at Reference conditions 1000

12 Volumetric temperature expansion coefficient b 0.00021413 Bulk modulus fluid elasticity e 2.15E+09

14 81% %15 Static Head, z z 30 m16 Pipe length, L L 41 m

17 Discharge Pipe Fittings 23.06 m

18 Suction Pipe Fittings 1.47 m19 Pipeline Material N/A HDPE N/A20 Pipeline Diameter (OD) OD 315 mm21 Pipeline Thickness t 17.5 mm22 Discharge Pipeline Diameter (ID/NB) ID 280 mm 78

23 Suction Pipe Length 1.5 m

23 Suction Pipe Diameter 250 mm24 Suction Pipe Material N/A Steel N/A25 # Pipeline fittings in Suction line N/A 2 N/A26 Types of pipe fittings N/A Knife Gate N/A27 Sump Design N/A Conical N/A

28 Operating Liquid level above CL 3.7 m29 Sump Agitation N/A Yes N/A

30 0.02 mm

P1 N/m2

P0 N/m2

T0oCoC

m3/h

rs kg/m3

rsl kg/m3

r1 kg/m3

r0 kg/m3

m3/m3 oCN/m2

Concentration of Solids, Cw CW

LD,F

LD,S

LS

Ds

CL

Slurry Particle size, d50 d50

# Fittings # FittingsID/NB (mm)

mb ID/NB Suction Discharge Suction Discharge 25 32

bar 0 3 0.00 17.29 0.52 0.73

0 0 0.00 0.00 0.7 0.910 0 0.00 0.00 0.26 0.370 3 0.00 5.76 0.17 0.24

Elbow 0 0 0.00 0.00 0.82 1.13Tee 0 0 0.00 0.00 1.77 2.38

Rubber hose 0 0 0.00 0.00 0.3 0.4

0 0 0.00 0.00 2.56 3.29

0 0 0.00 0.00

0 0 0.00 0.00 0.37 0.49

Taylor Valve Ball type 2 0 1.47 0.00

Enter number of pipe fittings

Equiv Length

Equiv Length

90o Long

90o Short45o Short30o Short

Diaphram Valve full Open

Full Bore Valve Round way

Plug-lub Valve Rec way

ID/NB (mm)

40 50 65 80 90 100 115 125 150

0.85 1.07 1.28 1.55 1.83 2.13 2.41 2.71 3.35

1.1 1.4 1.65 2.07 2.44 2.77 3.05 3.66 4.270.43 0.54 0.64 0.78 0.92 1.07 1.21 1.36 1.680.28 0.36 0.43 0.52 0.61 0.71 0.80 0.90 1.121.31 1.68 1.98 2.47 2.9 3.35 3.66 4.27 4.882.74 3.35 4.27 5.18 5.79 6.71 7.32 8.23 10.06

0.49 0.55 0.7 0.85 1.01 1.16 1.28 1.43 1.55

3.44 3.66 4.6 4.88 7.62 13.11 18.29

1.19 1.43 1.52 1.92 2.19 3.05 3.11

0.58 0.73 0.85 1.04 1.22 1.4 1.58 1.77 2.13

0.2 0.23 0.3 0.37

ID/NB (mm)

200 250 300 350 400 450 500

4.27 5.18 6.1 7.01 8.23 9.14 10.36

5.49 6.71 7.92 9.45 10.67 12.19 13.112.14 2.59 3.05 3.51 4.12 4.57 5.181.42 1.73 2.03 2.34 2.74 3.05 3.456.4 7.92 9.75 10.97 12.8 14.02 15.85

13.11 17.07 20.12 23.16 26.52 30.48 33.53

2.41 2.99 3.35 4.27 4.88 5.49 6.1

19.81 21.34 28.96 28.96

7.92 10.67 15.85

2.74 3.47 4.08 4.88 5.49 6.22 7.32

0.82 0.61 0.76 0.91 1.04 1.16 1.25

Slurry Pump Calculations Q [%] Q=0% Q=10% Q=20% Q=30% Q=40% Q=50% Q=60% Q=70%DMS CM Pump Symbol Units Value Comments Q [l/s] 0.00 13.18 26.37 39.55 52.73 65.91 79.10 92.28

1 Normal Operating Temperature T 30 V [m/s] 0.00 0.21 0.43 0.64 0.86 1.07 1.28 1.502 Normal Operating Pressure mbar 1015 0.00 0.41 0.81 1.22 1.63 2.04 2.44 2.853 Normal Operating Pressure m 10.58 0.00 0.27 0.54 0.81 1.07 1.34 1.61 1.884 Vapour Pressure m 1.43 0.00 0.01 0.03 0.08 0.14 0.21 0.31 0.425 Specific Gravity of Solids S 6.8 0.00 0.00 0.00 0.01 0.02 0.03 0.04 0.056 Average Particle Size mm 0.02 0.00 0.00 0.00 0.01 0.02 0.02 0.04 0.057 Concentration of Solids by weight % 81% 0.00 0.00 0.01 0.02 0.04 0.06 0.08 0.118 Static Discharge Head m 30 0.000 0.002 0.007 0.017 0.029 0.046 0.066 0.0909 Suction Static Head m 3.7 26.30 26.31 26.36 26.43 26.54 26.67 26.83 27.02

10 Length of Pipeline L m 41 42.42 42.44 42.51 42.63 42.80 43.01 43.28 43.5911 Discharge Pipe Fittings Equiv. Length m 23.0612 Weight of solids in Slurry tons/h 1230 Solid dry tons to be transfered13 Weight of volume of Water equal to solids volume tons/h 18114 Weight of water in slurry tons/h 294 Q [%] Q=80% Q=90% Q=100% Q=110% Q=120% Q=130% Q=140% Q=150%15 Total weight of equal volume of water tons/h 475 Q [l/s] 105.46 118.65 131.83 145.01 158.20 171.38 184.56 197.7416 Total weigh of slurry mixture tons/h 1524 V [m/s] 1.71 1.93 2.14 2.35 2.57 2.78 3.00 3.2117 Specific gravity of slurry mixture 3.21 3.26 3.67 4.07 4.48 4.89 5.29 5.70 6.1118 Concentration of Solids by volume 38.1% 2.15 2.42 2.69 2.95 3.22 3.49 3.76 4.03

19 Quantity of Slury Q' 474.59 Equals 733.95 m3/h with the safety factor of 55% 0.55 0.69 0.85 1.03 1.23 1.44 1.68 1.9220 Quantity of Slury Q l/s 131.83 Equals 203.87 m3/h with the safety factor of 55% 0.07 0.08 0.10 0.13 0.15 0.18 0.21 0.2421 Pipeline size d mm 280 Desired pipe size 0.06 0.08 0.10 0.12 0.14 0.17 0.19 0.22

22 Gravitational Acceleration g 9.81 0.15 0.19 0.23 0.28 0.34 0.39 0.46 0.5323 Limiting Settling Velocity Factor 0.76 0.1176 0.1488 0.1837 0.2223 0.2646 0.3105 0.3601 0.413424 Settling Velocity m/s 1.88 27.24 27.49 27.77 28.08 28.42 28.79 29.19 29.6225 Slurry Velocity V m/s 2.14 43.94 44.35 44.80 45.30 45.85 46.44 47.08 47.7726 Total Equivalent length of a Discharge pipe m 64.0627 Darcay Friction Factor f 0.01628 Discharge Pipeline Friction Head Loss 0.85 FLOW Velocity PIPE HEAD MP CURVE RECOMMENDED VEL.29 Pump Discharge Diameter mm 203 As specified on the Pump Q [l/s] V [m/s] H [m] H [m] 25NB 1.4 m/s

30 Pump Nozzle Upstream Velocity m/s 4.07 0.00 0 0.00 42.42 44.5 40NB 1.6 m/s31 Pump nozzle size - Pipe size ratio 0.73 13.18 47 0.21 42.44 44.5 50NB32 Loss in pipe enlargement (Ke*(V-V1)/2g) m 0.10 26.37 95 0.43 42.51 44.5 80NB 1.9 m/s

33 m 0.10 39.55 142 0.64 42.63 44.3 100NB 2.0 m/s34 Loss at pipe discharge m 0.23 52.73 190 0.86 42.80 44.1 150NB 2.2 m/s35 Pump Suction diameter mm 250 As specified on the Pump 65.91 237 1.07 43.01 44.0 200NB 2.4 m/s36 Slurry Velocity at Suction m/s 2.69 79.10 285 1.28 43.28 43.8 300NB 2.6 m/s37 Loss of head at entrance to suction pipe m 0.18 92.28 332 1.50 43.59 43.538 Suction Pipe Lenth Ls m 2.00 105.46 380 1.71 43.94 42.939 Suction pipe fittigs length Equiv. Length m 1.47 118.65 427 1.93 44.35 42.640 Total Equivalent length of a Suction pipe m 3.47 131.83 475 2.14 44.80 42.541 Suction Pipeline Friction Head Loss m 0.08 145.01 522 2.35 45.30 42.142 Total dynamic head on the pump m 27.86 158.20 570 2.57 45.85 42.043 Slurry Pump Derating Efficiency ( = HR*ER) ER*HR 0.62 171.38 617 2.78 46.44 41.544 Equivalent water total head dynamic m 44.93 184.56 664 3.00 47.08 41.045 Pump Efficiency em 62.04% From Manufacturers Curve 197.74 712 3.21 47.77 40.0 from the pump cure46 Required Power P kW 300.51 Calculated47 Installed power P kW 400.00 From Manufacturers Curve48 Installed Pump Speed n r/min 703.94 From Manufacturers Curve 6 65 3049 Nett Positive Suction Head NPSHa m 3.43 Calculated 0.14 1.15 0.5549 Nett Positive Suction Head NPSHr m 3.32 From Manufacturers Curve K 0.42 0.0660849249 Nett Positive Suction Head Difference NPSHa -NPSHr m 0.11 Installation Fine

oCHatm Vp [m/s]Hatm Vi [m/s]Hvap Hf [---]

Lc [m] d50 HL [m]Cw Le [m]Zd Li [m]Zs Hm [m]

Hw [m]

Sm Vp [m/s]Cv Vi [m/s]

m3/h Hf [---]Lc [m]HL [m]

m/s2 Le [m]FL Particle size d50 = 20mm Li [m]VL Hm [m]

Hw [m]LD

Hf,D

Dpump Q [m3/hr]

Vpump

D1/D2

Le

Loss in pipe contraction (hL = K*V22/2g) hL

Ld

Dsuction

Hi

Li

LS

Hf,S

Hm

Hw

Intrapolation of Ke Factor

0.00 50.00 100.00 150.00 200.00 250.0036.00

38.00

40.00

42.00

44.00

46.00

48.00

50.00

Circulating Medium Pump (140-PCB-42)PUMP SELECTION GRAPH : (10/8 F/G AH Metal)

IMPELLER SIZE : (686) MM SPEED : 703 (REV/MIN) RPM

Q [l/s]

Head

[m]

Imperial Units - BG SI Units VAPOUR PRESSURES [kPa]

TEMPAcetone 1.34 0.92 5

Carbon Tetrachloride 1.91 1.32 10Ethyl Alcohol 1.54 1.06 15

Gasoline 1.9 1.3 20Glycerin 6.31 4.35 25Mercury 41.4 28.5 30

Paraffin Oil 2.41 1.66 35Petrol 1.55 - 2.16 1.07 - 1.49 40

SAE 30 Oil 2.2 1.5 45Seawater 3.39 2.34 50

Water 3.12 2.15 60Liquid 70

80Acetic acid 0.0011 0.00061 90

Acetone 0.00143 0.00079 100Ethyl (ethanol) 0.00109 0.00061

Methyl (methanol) 0.00118 0.00066Ammonia 0.00245 0.00136

Aniline 0.00085 0.00047Benzene 0.00125 0.00069Bromine 0.0011 0.00061

Carbon disulfide 0.00119 0.00066Carbon tetrachloride 0.00122 0.00068

Chloroform 0.00127 0.00071Ether 0.0016 0.00089

Ethyl acetate 0.00138 0.00077Ethylene glycol 0.00057 0.00032

Freon refrigerant R-12 0.0026 0.00144n-Heptane 0.00124 0.00069

Isobutyl alcohol 0.00094 0.00052Gasoline 0.001 0.00056

Glycerine (glycerol) 0.0005 0.00028Kerosene 0.001 0.00056Mercury 0.00018 0.0001

Methyl alcohol 0.00119 0.00066Methyl iodide 0.0012 0.00067

n-Octane 0.00114 0.00063Oil (unused engine oil) 0.0007 0.00039

Olive oil 0.0007Paraffin oil 0.000764 0.00042Petroleum 0.001 0.00056

Bulk Modulus - E

(105 psi, lbf/in2) (109 Pa, N/m2)

Volumetric Coefficient of Expansion, b

(m3/m3K, m3/m3oC) (1/oF)

n-Pentane 0.00158 0.00088Phenol 0.0009 0.0005

Sulphuric acid 0.00055 0.00031Toluene 0.00108 0.0006

Trichloroethylene 0.00117 0.00065Turpentine 0.001 0.00056

Water 0.000214 0.00012

VAPOUR PRESSURES [kPa] LIQUID DENSITY @ 1bar

H2O TEMP SO2 H2SO4 TEMP H2O H2SO40.87 -50 11.57 5 1000.01.23 -40 21.57 10 999.71.70 -30 38.05 15 999.22.34 -20 63.55 0.001 20 998.3 1840.03.17 -10 101.4 25 997.14.24 0 155.4 30 995.75.62 10 230.2 35 994.07.38 20 330.5 40 992.39.58 30 416.9 45 990.2

12.34 40 841.7 50 988.019.92 50 60 983.231.16 70 977.7

47.36 80 971.670.11 90 965.2

101.33 100 958.1

Surface (feet)Copper, Lead, Brass, Aluminum (new) 0.001 - 0.002

PVC and Plastic Pipes 0.0015 - 0.007Epoxy, Vinyl Ester and Isophthalic pipe 0.005

Stainless steel 0.015Steel commercial pipe 0.045 - 0.09

Stretched steel 0.015Weld steel 0.045

Galvanized steel 0.15Rusted steel (corrosion) 0.15 - 4

New cast iron 0.25 - 0.8Worn cast iron 0.8 - 1.5Rusty cast iron 1.5 - 2.5

Sheet or asphalted cast iron 0.01 - 0.015Smoothed cement 0.3Ordinary concrete 0.3 - 1Coarse concrete 0.3 - 5Well planed wood 0.18 - 0.9

Ordinary wood 5

Absolute Roughness - k10-3 (m)

3.33 - 6.7 10-6

0.5 - 2.33 10-5

1.7 10-5

5 10-5

1.5 - 3 10-4

5 10-5

1.5 10-4

5 10-4

5 - 133 10-4

8 - 27 10-4

2.7 - 5 10-3

5 - 8.3 10-3

3.33 - 5 10-5

1 10-3

1 - 3.33 10-3

1 - 16.7 10-3

6 - 30 10-4

16.7 10-3

0.001562

2.419355E-05