Pump. Slurry Selection - Typical - Warman
Pump. Slurry Selection - Typical - Warman
Pump. Slurry Selection - Typical - Warman
20
25
2.2
2.8
3.5
1.9
2.3
1.8
2.9
4.4
1.8
2.0
2.5
2.9
3.5
4.2
4.8
2.3
2.9
3.6
4.3
5.1
6.3
7.1
3.7
4.6
5.8
6.8
8.2
10.0
11.4
5.5
6.9
8.6
10.3
12.3
15.1
17.1
32
2
3
40
50
63
75
90
110
125
1.8
1.9
2.2
2.7
3.1
1.8
2.0
2.3
2.8
3.4
3.9
140
3.5
4.3
5.4
8.0
12.7
19.2
12
160
180
200
225
250
280
315
355
400
4.0
4.4
4.9
5.5
6.2
6.9
7.7
8.7
9.8
4.9
5.5
6.2
6.9
7.7
8.6
9.7
10.9
12.3
6.2
6.9
7.7
8.6
9.6
10.7
12.1
13.6
15.3
9.1
10.2
11.4
12.8
14.2
15.9
17.9
20.1
22.7
14.6
16.4
18.2
20.5
22.7
25.4
28.6
32.2
36.3
21.9
24.6
27.4
30.8
34.2
38.3
43.1
48.5
54.7
13
450
11.0
13.8
17.2
25.5
40.9
61.5
22
500
560
630
710
800
900
1000
1100
1200
1400
1600
Dn [mm]
12.3
13.7
15.4
17.4
19.6
22.0
24.5
26.9
29.4
34.4
39.2
2 1/2
15.3
19.1
28.4
45.4
17.2
21.4
31.7
50.8
19.3
24.1
35.7
57.2
21.8
27.2
40.2
64.5
24.5
30.6
45.3
27.6
34.4
51.0
30.6
38.2
56.7
33.7
42.0
62.4
36.7
45.9
68.0
42.9
53.5
49.0
61.2
3.2
4
6
10
Presiones nominales PN [bar]
HDPE PE80 DIN 8074 / ISO 4427
Espesor [mm]
68.3
23
6
7
8
9
10
11
14
15
16
17
18
19
20
21
24
25
26
27
28
29
30
31
32
33
16
10
11
12
13
14
15
16
17
120
140
160
STD
XS
XXS
2.77
3.73
7.47
2.87
3.38
3.56
3.68
3.91
5.16
5.49
5.74
3.91
4.55
4.85
5.08
5.54
7.01
7.62
8.08
7.82
9.09
9.7
10.15
11.07
14.02
15.24
2
3
5
6
Size
dext
10
20
30
40
60
80
2.11
2.77
100
1/ 2
21.3
1.65
2.41
3.73
4.78
3/ 4
1
1 1/ 4
1 1/ 2
2
2 1/ 2
3
3 1/ 2
26.7
33.4
42.2
48.3
60.3
73
88.9
101.6
1.65
1.65
1.65
1.65
1.65
2.11
2.11
2.11
2.11
2.77
2.77
2.77
2.77
3.05
3.05
3.05
2.41
2.9
2.97
3.18
3.18
4.78
4.78
4.78
2.87
3.38
3.56
3.68
3.91
5.16
5.49
5.74
3.91
4.55
4.85
5.08
5.54
7.01
7.62
8.08
0
0
0
0
5.56
6.35
6.35
7.14
8.74
9.53
11.13
13.49 6.02
10
11
12
13
14
15
16
114.3
2.11
3.05
4.78
6.02
8.56
11.13
17
5
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
141.3
168.3
219.1
273
323.8
355.6
406.4
457
508
559
610
660
711
762
813
864
914
965
1016
2.77
2.77
2.77
3.4
3.96
3.96
4.19
4.19
4.78
4.78
5.54
6.35
-
3.4
3.4
3.76
4.19
4.57
6.35
6.35
6.35
6.35
6.35
6.35
7.92
7.92
7.92
7.92
7.92
7.92
-
6.35
6.35
6.35
7.92
7.92
7.92
9.53
9.53
9.53
12.7
12.7
12.7
12.7
12.7
12.7
-
7.04
7.8
8.38
9.53
9.53
11.13
12.7
12.7
14.27
15.88
15.88
15.88
15.88
15.88
-
6.55
7.11
8.18
9.27
10.31
11.13
12.7
14.27
15.09
17.48
17.48
17.48
19.05
-
10.31
12.7
14.27
15.09
16.66
19.05
20.62
22.23
24.61
-
9.53
10.97
12.7
15.09
17.48
19.05
21.44
23.83
26.19
28.58
30.96
-
15.09
18.26
21.44
23.83
26.19
29.36
32.54
34.93
38.89
-
12.7
14.27
18.26
21.44
25.4
27.79
30.96
34.93
38.1
41.28
46.02
-
20.62
25.4
28.58
31.75
36.53
39.67
44.45
47.63
52.37
-
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
15.88
18.26
23.01
28.58
33.32
35.71
40.49
45.24
50.01
53.98
59.54
-
8.56 17.12
36
39
42
44
46
48
1067
1118
1168
1219
9.53
9.53
9.53
9.53
12.7
12.7
12.7
12.7
5.- Pump
Performance curve for Warman 6/4 D-AH pump
6.- Motors
Motors table CAN/CSA C391-1
7.- Belt
Drive efficiency
References
ms =
65
t/h
Ss =
2.65
Density of liquid
1000
L =
d50 =
211
kg/m
m
Solids concentration
Cw
30
Zd =
20
Suction head
Pipeline length
Suction equiv. lenght
Number of long rad. 90 elb.
Zs =
1
100
3
5
m
m
m
-
3.35
10
3
CS
m
C
bar
-
6
STD
0.1
in
mm
100
mm
5
6
7
8
9
10
11
12
13
14
L=
Leq_suc =
N=
Lelbow =
t=
P=
Mat =
dn =
17
18
sch =
Rabs =
dp =
Kexit =
21
Loss at entrance
Height above sea level
Kentr =
0.5
2700
22
transmission efficiency
15
16
19
20
HASL =
trans =
98
m.a.s.l.
(See sheet "7.- Belt")
Solution
1.- Pulp properties
Water absolute viscosity
Pulp density
P
w = SaturatedWaterAbsoluteViscosity_t
100
C w 100 Cw
s
L
p =
t=
10
w =
#VALUE!
C
Pa s
Cw =
30
s =
2.65
L =
Pulp viscosity
t/m
t/m
p/f=(1+2.5*Cv 10.05*Cv^2+0.00273*Exp(16.6*Cv))
p = S p
1.23
t/m
p =
1230
kg/m
Volumetric concentration
Cv
Cw
S s 1 C w C w
Cv =
0.1392
p / f =
1.57
p =
p / w * w
p / f =
1.57
w =
#VALUE!
Pa s
p =
#VALUE!
Pa s
Cv =
Cw =
0.30
Ss=
2.65
p =
p /p
L =
Cv =
t/m3
p =
#VALUE!
Pa s
p =
1229.7
kg/m
p =
#VALUE!
m/s
13.9
ms m P C w
mP =
ms =
ms / Cw
65
0.3
216.7
Cw =
mP =
1.23
176.2
48.9
t/h
t/h
Re =
#VALUE!
#VALUE!
#VALUE!
#VALUE!
Relative rugosity
Rabs =
0.1
di =
#VALUE!
Rrel =
#VALUE!
t/h
t/m3
m/h
l/s
m/s
m
m/s
mm
mm
-
Friction factor
f=
f(Rrel, Re)
Rrel =
#VALUE!
Re =
#VALUE!
f=
Pipe_Friction_Factor_Rrel_Re
f=
#VALUE!
-
VP / A
0.049
#VALUE!
#VALUE!
v*d/
m/s
m
m/s
mm
pipe diameter
di =
mm
Kinematic pressure
hv =
#VALUE!
mpc
#VALUE!
0.5
Pipe_Expansion_Theta30gr_beta
#VALUE!
mpc
#VALUE!
mpc
K2_ = 30 =
#VALUE!
#VALUE!
hv =
Pexp =
#VALUE!
mpc
#VALUE!
mpc
48.9
#VALUE!
function
l/s
HR =
m.p.c.
Slurry_HR_factor_Ss_Cw_d50
Validity
Ss :
1-6
Cw :
1- 70%
d50 :
20 - 10000
Ss =
2.7
Cw =
30
d50 =
211
%
m
HR =
0.89
Q l S p Hw m.w.c.
PkW
(7)
1.02 w _ %
Pmotor =
P / trans
P=
#VALUE!
kW
trans =
98
Pmotor =
#VALUE!
kW
Pump power
P=
Qp =
L/s
Sp =
1.23
Hw =
#VALUE!
m.w.c.
w_% =
66
#VALUE!
kW
P=
kW
11.- Resume
Data for pump enquiry
Pulp temperature
Pulp flow rate
Total dynamic head
Calculated data
t=
QP =
TDH =
s =
10
48.9
l/s
###
mpc
2650
kg/m
1000
kg/m
L =
Cw =
Ss =
2.65
d50 =
FVF =
NPSHa =
211
0
###
Solids density
Liquid density
30
%
m
m.p.c.
2. Pipe
Carbon steel pipeinterior diamweter
dn =
6
in
sch =
STD
di =
Pipe_Imp_CS_Dint_dn_sch
di =
#VALUE!
mm
di =
#VALUE!
Pipe area
100
A=
di =
(pi()/4) * di^2
#VALUE!
A=
#VALUE!
N=
Lelbow =
5
3.35
LN-elbows =
16.75
L=
LN-elbows =
100
16.75
Leq =
116.8
Validity ranges
d50 >= 200 m
5% <= Cv <= 40%
m
mpc
mpc/ m
116.75
#VALUE!
#VALUE!
d50 =
Cv =
d=
SS =
VL =
VL=Slurry_Limit_Deposition_Velocity_JRI_Imp_d50_Cv_dn_Ss
211
13.9
6
2.65
#VALUE!
#VALUE!
m
%
in
m/s
m
mpc/m
mpc
Kinematic pressure
hv =
#VALUE!
mpc
Pentr =
#VALUE!
mpc
Pexp =
#VALUE!
mpc
Pexit =
#VALUE!
mpc
Hsing =
hv =
Pexit =
#VALUE!
mpc
#VALUE!
mpc
#VALUE!
mpc
20
m.p.c.
Zs =
m.p.c.
Hfric =
#VALUE!
m.p.c.
Hsing =
#VALUE!
m.p.c.
Hp =
#VALUE!
m.p.c
g=
9.80665
m/s
The correctionfactor HR is
HR =
0.89
#VALUE!
m.p.c.
Hp / HR
48.9
Hw =
#VALUE!
l/s
m.w.c.
one obtains
Hp =
#VALUE!
m.p.c.
HR =
Hw =
0.89
#VALUE!
m.w.c.
Ew =
Pump velocity
66
N=
1130
%
rpm
6.04
m.p.c.
m.p.c.
3
#VALUE!
m
mpc/m
#VALUE!
mpc
#VALUE!
mpc
#VALUE!
mpc
Psuc=
#VALUE!
mpc
alculated data
Sp =
1.23
Cv =
13.9
p =
#VALUE!
HR =
0.89
HE =
Hw =
0.89
#VALUE!
mwc
N=
Ew =
Ep =
P=
P=
NPSHr =
AH 6/4
1130
66
58.8
#VALUE!
30
#VALUE!
rpm
%
%
kW
kW
m.p.c.
m/s
otor velocity
ficiency on water
ficiency on pulp
ump power requirement
tk =
283.2
ca =
cb =
-5800.2
-5.5
cc =
-0.05
cd =
4.2E-05
ce =
-1.4E-08
cf =
Pw_vap =
6.5
1.228
kPa
Pw_vap =
1228
Pa
Pw_vap =
0.102
m.p.c.
NPSHa =
10
Pf =
t=
#VALUE!
m.p.c.
Page 2 of 7
Page 3 of 7
Page 4 of 7
Page 5 of 7
Page 6 of 7
K ^ 3 + cf * Ln(tK))
Page 7 of 7
Pump power
Q m TDH Pa
P
3
m
s
m3
s
m3
s
m3
s
Q m TDH Pa
PW
m N
Pa
s m
N m
Pa
s
J
Pa
s
Q m g TDHmm. w. c .
PW
PW
Q m TDH Pa
Q m g 1000 S p TDHm. p. c .
PW
PkW
PkW
1000
1
1000
PkW
PkW
PkW
1
Q l g S p TDHm. p .c .
1000 s
1000
Q l S p TDHm. p. c.
s
PkW
Q l S p TDHm. p. c.
PkW
%
100
Q l S p TDHm. p. c.
PkW
102
1.02 %
102
Q l S p TDHm. p. c.
Q m g 1000 S p TDHm. p. c.
Q l S p TDHm.
g
1
1000 102
Q l S p TDHm. p. c.
PkW s
102
Q m g S p TDHm. p .c .
Pa W
s
PW
Head on pulp
Head on water
Hp
HR
Hw
and
Hp Hw HR
(3)
HR
g
000
Q l S p TDHm. p . c.
s
Q l S p TDHm. p . c .
PkW
PkW
102
PkW
Q l S p TDHm. p. c.
s
102
1.02 %
%
100
Q l S p TDHm. p. c.
PkW
1000
Q m S p TDHm. p . c .
3600
h
1.02 %
3.67 %
3600
1.02 %
1000
3600
1.02 3.67
1000
Q m S p TDHm. p . c.
PkW h
3.67 %
102
(1)
Pump p ower
From equation
Q l S p TDHm. p. c.
PkW
1.02 %
(1)
(2)
one gets
PkW
PkW
1.02 %
(6)
1.02 w _ % ER
HR ER
Q l S p Hw m.w.c.
Q l S p Hw m.w.c. HR
(5)
(5)
Q l S p Hw m.w.c. HR
Considerin g that
(1)
Q m S p TDHm. p .c.
1.02 %
PkW
1.02 %
PkW
Q m S p TDHm. p . c.
Q l S p TDHm. p. c.
1.02 %
Q l S p TDHm. p. c .
(1)
1000 Q m S p TDHm. p . c.
1
102
Q l S p TDHm. p. c.
s
PkW
1.02 w _ %
(7)
(2)
Q l S p Hw m.w.c.
Q l S p Hw m.w.c. HR
PkW
(5)
1.02 %
(4)
or
% w _ % ER
(4a)
PkW
1.02 w _ %
(7)
w:% transm
DHm. p . c .
(1)
DHm. p . c.
(2)
Page 2 of 2
Slurry parameters
[2]
Slurry density
100
Cw 100 C w
s
L
[2] (1-4)
P =
100
Cw 100 C w
s
L
100 / (Cw/s +(100-Cw)/L )
di =
154.08
mm
di =
0.15408
Cw =
30
s =
2.65
t/m3
Pipe area
L =
t/m
P =
1.23
t/m3
A=
di =
A=
%
3
(pi()/4) * di^2
0.15408
0.0186
m
m
ms m P C w
mP
ms
Cw
mP =
m s / Cw
ms =
65
t/h
Cw =
mP =
0.3
216.7
t/h
Slurry velocity
vP =
VP / A
VP =
0.049
m/s
A=
vP =
0.0186
2.6
m/s
Cv =
13.9
d=
SS =
in
2.65
mP =
216.7
t/h
P =
VP =
1.23
t/m
176.2
m/h
VP =
48.9
l/s
Volumetric concentration
VL=Slurry_Limit_Deposition_Velocity_JRI_Imp_d50_Cv_dn_Ss
Cw
Cv
S s 1 C w C w
Cv =
VL =
#VALUE!
#VALUE!
m/s
Cw =
0.30
Ss=
2.65
t/m3
L =
Cv =
t/m3
13.9
Slurry density
=
1230
Kinematic viscosity
=
/
=
2.0E-03
=
1229.7
=
1.7E-06
kg/m
Pa s
kg/m
m/s
Reynolds
Re =
v=
v*d/
2.62
m/s
d=
0.15408
LN-elbows =
16.75
Total eqivalent length
L + LN-elbows
Leq =
L=
100
LN-elbows =
16.75
Leq =
116.75
Slurry properties
t=
P=
10
3
w =
m
m
C
bar
SaturatedWaterAbsoluteViscosity_t
1.3E-03
1.7E-06
244,021
m/s
0.1
154.08
0.0006
mm
mm
-
Relative rugosity
w =
=
Re =
Pa s
Pulp viscosity
Ratio of viscosities (Thomas)
p / f = (1+2.5*Cv 10.05*Cv^2+0.00273*Exp(16.6*Cv))
Rabs =
di =
Rrel =
Friction factor
f=
f(Rrel, Re)
Rrel =
0.0006
Re =
244,021
f=
Pipe_Friction_Factor_Rrel_Re
f=
0.0192
Kinematic pressure
(/2) * v^2
hv =
=
1229.70
kg/m
Cv =
0.1392
v=
2.62
m/s
p / f =
hv =
4236.3
Pa
p =
1.57
p / w * w
p / f =
1.57
w =
1.3E-03
Pa s
p =
2E-03
Pa s
Kinematic pressure
hv =
v^2 / (2*g)
v=
2.62
g=
9.81
hv =
0.351
Pa/m
Pressure loss in expansion
K2_ = 30 * hv
Pexp =
Pressure loss
Hf =
Leq =
J=
Hf =
Hf =
Hf =
m/s
m/s
msc
Leq * J
116.75
528.8
61,736
6295
6.30
K2_ = 30 =
m
Pa /m
Pa
mmwc
mwc
hv =
Pexp =
#VALUE!
0.351
msc
#VALUE!
msc
Kinematic pressure
hv =
0.351
msc
154.08
mm
Kexit =
hv =
Pexit =
0.351
msc
0.35
msc
mm
Pipe_Expansion_Theta30gr_beta
K2_ = 30 =
#VALUE!
HR factor
Validity
Ss :
-
Kinematic pressure
hv =
0.351
hv =
Pentr =
1- 70%
d50 :
20 - 10000
msc
1-6
Cw :
Ss =
2.7
Cw =
30
d50 =
211
%
m
0.5
0.351
msc
HR =
0.18
msc
HR =
Slurry_HR_factor_Ss_Cw_d50
0.891
Zs =
Hf =
Pexp =
-1
5.12
msc
#VALUE!
msc
Pexit =
0.35
msc
Pentr =
0.18
msc
Hm =
#VALUE!
msc
Hm =
HR =
Hw =
Let
Hw =
#VALUE!
0.891
#VALUE!
28.2
mwc equiv.
mwc
Pump selection
Select a pump with following results
VP =
48.9
l/s
Hw =
28.2
mwc
Ss =
2.65
l
S P TDH msc
s
1.02 m %
with
TDH =
kW
P=
Q=
SP =
Hm
and
=
l
S P Hw msc
s
1.02 w %
Hw =
w =
P=
l
S P Hm msc
s
1.02 m %
kW
(1/1.02) * Q * Ss * Hw / w
48.9
l/s
1.23
28.2
66
25.2
mwc
kW
with
l
S P TDH msc
s
1.02 ER w %
kW
Hm =
Hw * HR
m =
w * ER
and
l
S P Hw HR msc
s
1.02 w E R %
kW
as HR is assumed equal to HR
kW
l
S P Hw HR msc
s
1.02 w H R %
l
S P Hw msc
s
1.02 w %
kW
kW
Power
m3
Q
TDH Pa
s
P
P
m3 N
Q TDH
s m 2
P
P
P
m3
TDH Pa
s
P
m
N
s
P
Q TDH
Nm
s
P
Q TDH
J
Q TDH
s
P
P
Q TDH
P
W
P
________________
m3
TDH mmwc
s
P
l
S P TDH msc
s
1.02 %
Q
P g
m3
TDH mwc
s
P
g 100
3600
Q
P g 1000
m3
S P TDH msc
s
P
Q
P g 1000
g 1000
1000
m3
S P TDH msc
s
m3
S P TDH msc
s
P
Q
P g
W
kW
kW
m3
S P TDH msc
s
P %
Q
P g 100
g 100
P
1000
g
P
10
g
P
10
kW
l
S P TDH msc
s
P %
kW
l
S P TDH msc
s
P %
kW
l
S P TDH msc
s
1.02 P %
kW
l
S P TDH msc
s
P %
1
P
10
g
P
l
S P TDH msc
s
P %
kW
kW
36
m3
S P TD
h
%
m3
S P TDH m
h
%
m3
S P TDH msc
h
3.67 %
1
Solids flow rate
ms =
65
t/h
Ss =
2.65
d50 =
211
Solids concentration
Cw
30
Zd =
20
Suction head
Pipeline length
Number of long rad. 90 elb.
Zs =
1
100
5
m
m
L=
N=
4
Kinematic pressure
hv =
v^2 / (2*g)
v=
2.62
g=
9.81
hv =
0.351
m/s
m/s
msc
f * (1/d) * hv
f=
d=
0.019
0.154
hv =
J=
0.4
0.044
mwc
mwc/ m
Pressure loss
Hf =
Leq =
J=
Hf =
Leq * J
116.75
0.044
5.12
m
msc/m
msc
0.41
l
S P TDH msc
s
1.02 %
g 100
P
3600
36
kW
m3
S P TDH msc
h
%
m3
S P TDH msc
h
%
m3
S P TDH msc
h
3.67 %
kW
kW
kW
Hw
Hm
HR
Q
P
(Eq. a)
l
S P H w mpc
s
1.02 w %
Cw :
1- 70%
d50 :
20 - 10000
kW
(Eq. f)
Cw =
30
d50 =
211
HR =
HR =
Slurry_HR_factor_Ss_Cw_d50
0.891
Let, as an example
TDH =
25.1
and with
HR =
0.891
the water equivalent head is
Hw =
28.17
48.9
following data
%
m
urry_HR_factor_Ss_Cw_d50
mpc
Q=
Assume
SP =
48.9
l/s
1.23
Hw =
28.17
mwc
w =
P=
66
25.17
%
kW
ent head is
mwc
flow rate be
l/s
and
Hp Hw HR
(3)
H (m)
50
40
1200 rpm
30
20
10
0
0
#VALUE!
mwc
At this point,
N=
Ew =
NPSHr =
1130
66
#VALUE!
rpm
%
m
1350 rpm
60%
65%
70%
77.5% 70%
1300 rpm
66 %
1200 rpm
1130 rpm
1100 rpm
1000 rpm
28.2 mwc
2.5 m 3.0m
NPSH 4.5
m
48.9 l/s
20
40
60
80
100
Q (L/s)
120
http://oee.nrcan.gc.ca/regulations/products/14297
Item
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Power (HP)
1
1.5
2
3
4
5
5.5
7.5
10
15
20
25
30
40
50
60
75
100
125
150
175
200
250
300
350
400
450
500
Power (kW)
0.75
1.1
1.5
2.2
3
3.7
4
5.5
7.5
11
15
19
22
30
37
45
55
75
90
110
132
150
185
225
260
300
335
375
N/CSA C390-1
fficiency Standard (Percentage)
2 Pole
75.5
82.5
84
85.5
85.5
87.5
87.5
88.5
89.5
90.2
90.2
91
91
91.7
92.4
93
93
93.6
94.5
94.5
95
95
95.4
95.4
95.4
95.4
95.4
95.4
Enclosed
4 Pole
6 Pole
82.5
80
84
85.5
84
86.5
87.5
87.5
87.5
87.5
87.5
87.5
87.5
87.5
89.5
89.5
89.5
89.5
91
90.2
91
90.2
92.4
91.7
92.4
91.7
93
93
93
93
93.6
93.6
94.1
93.6
94.5
94.1
94.5
94.1
95
95
95
95
95
95
95
95
95.4
95
95.4
95
95.4 95.4 95.8 -
N/CSA C391-1
http://www.vanmeterinc.com/assets/files/pdf/3.20VBeltsSynchronicBelts.EdHubble.pdf
Hubble.pdf
3 V Narrow
d
=
B Classical
d
=
4
95
in
%
4
94
in
%
in
%
[1]
http://www.pumpfundamentals.com/slurry/Warman_slurry_pumping.pdf
[2]