installed gain as a control valve sizing criteria jon monsen, ph.d., p.e
TRANSCRIPT
![Page 1: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/1.jpg)
Installed Gain as a Control Valve Sizing
Criteria
Jon Monsen, Ph.D., P.E.
![Page 2: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/2.jpg)
Control Valve Characteristics
• Inherent• Installed
• Inherent• Installed
FL
OW
CA
PA
CIT
Y,
CV
VALVE TRAVEL
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FL
OW
CA
PA
CIT
Y,
CV
VALVE TRAVEL
FLOW
METER
P2P1
P
What you need to remember about the inherent characteristic:
1. It is the relationship between valve opening
and flow capacity (CV) of
the valve while the pressure drop is held constant. (No system effects.)
2. It is the characteristic that is published by the manufacturer.
Inherent Characteristic
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VALVE TRAVEL(PERCENT OF RATED TRAVEL)
40
10
20
50 1000 60 70
30
40
80 90
CV is linear with valve travel.
10 20 30
Linear
50
60
70
80
90
100
FL
OW
CP
AC
ITY
, C
V
What you need to remember about the linear characteristic:
1. Its graph is a straight line.
2. It is only used about 10% of the time.
Inherent Characteristic
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Equal changes in Valve Position produce equal percentage changes in flow capacity.
What you need to remember about the equal percentage characteristic:
1. The shape of the graph
2. It is used about 90% of the time.
Inherent Characteristic
VALVE TRAVEL(PERCENT OF RATED TRAVEL)
FL
OW
CP
AC
ITY
, C
V
40
10
20
50 1000 60 70
30
40
80 9010 20 30
50
60
70
80
90
100
Equal Percentage (=%)
+10 = 50%
+22.5 = 50%
+15 = 50%
45
67.5
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Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
280’ 1.5” pipe
0 50
050 0 gpm
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0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
FLOW (gpm) 10PIPE LOSS 1VALVE P 49
Pressure
source
50 psig
1 49
280’ 1.5” pipe049
10 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
Installed Characteristic
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0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
3.5 46.5
280’ 1.5” pipe
FLOW (gpm) 10 20PIPE LOSS 1 3.5VALVE P 49 46.5
46.5 020 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
Installed Characteristic
![Page 9: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/9.jpg)
Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
7.5 42.5
42.5280’ 1.5” pipe
FLOW (gpm) 10 20 30PIPE LOSS 1 3.5 7.5VALVE P 49 46.5 42.5
030 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
![Page 10: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/10.jpg)
Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
13 37
37280’ 1.5” pipe
FLOW (gpm) 10 20 30 40PIPE LOSS 1 3.5 7.5 13VALVE P 49 46.5 42.5 37
040 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
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Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
20 30
30280’ 1.5” pipe
FLOW (gpm) 10 20 30 40 50PIPE LOSS 1 3.5 7.5 13 20VALVE P 49 46.5 42.5 37 30
050 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
![Page 12: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/12.jpg)
Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
28 22
22280’ 1.5” pipe
FLOW (gpm) 10 20 30 40 50 60PIPE LOSS 1 3.5 7.5 13 20 28VALVE P 49 46.5 42.5 37 30 22
060 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
![Page 13: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/13.jpg)
Installed Characteristic
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
28 22
22280’ 1.5” pipe
FLOW (gpm) 10 20 30 40 50 60PIPE LOSS 1 3.5 7.5 13 20 28VALVE P 49 46.5 42.5 37 30 22
060 gpm
CraneTechnical Paper 410
(1942) www.tp410.com
![Page 14: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/14.jpg)
Installed CharacteristicF
LO
W
VALVE TRAVEL
=% V
ALVE
Pressure
source
50 psig
Rule of Thumb:
Lots of pipe, use Equal Percentage valve
Appr
ox. L
inea
r inst
alle
d
280’ 1.5” pipe
0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
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VALVE TRAVEL0
10
20
30
40
50
0 10 20 30 40 50 60
FLOW
VA
LV
E P
Pressure
source
50 psig
2.8’ 1.5” pipe
Linea
r inher
ent
Lin
ear i
nstal
led
0.28 psi drop @ 60 gpm
Rule of Thumb:
Very little pipe, use Linear valve
49.72
Installed CharacteristicF
LO
W
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Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Valve Travel, h
Gain = Output / Input
Installed Characteristic and Gain
Installed Characteristic
Flo
w,
q
![Page 17: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/17.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 18: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/18.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 19: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/19.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 20: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/20.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 21: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/21.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 22: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/22.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
q = h X Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 23: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/23.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
1%
1/4%
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
q = h X Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 24: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/24.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
1%
1/4%
4%
Gain = Output / Input
Gain = q / h = SLOPE
Installed Characteristic and Gain
q = h X Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 25: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/25.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 26: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/26.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 27: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/27.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 28: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/28.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 29: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/29.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 30: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/30.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 31: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/31.jpg)
Inst
alle
d G
ain
1.0
2.0
3.0
4.0
Gain = Output / Input
Gain = d q / d h = SLOPE
Installed Characteristic and Gain
Installed Characteristic
Valve Travel, h
Flo
w,
q
![Page 32: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/32.jpg)
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
Gain = Output / Input
Gain = q / h
q = h X Gain
Installed Gain Recommendations
Inst
alle
d G
ain 3.0
2.0
4.0
1.0
q min q maxFlow
![Page 33: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/33.jpg)
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
Gain = Output / Input
Gain = q / h
q = h X Gain
Installed Gain Recommendations
Loop Tuned here
Data courtesy of ExperTune, Inc.
SP
PV
Large gain change:Can’t maintain good control with stability throughout flow range.The “un-tunable” loop!
Inst
alle
d G
ain 3.0
2.0
4.0
1.0
q min q maxFlow
![Page 34: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/34.jpg)
Inst
alle
d G
ain 3.0
2.0
4.0
1.0
q min q max
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
Gain = Output / Input
Gain = q / h
q = h X Gain
Installed Gain Recommendations
Flow
Loop Tuned here
SP
PV
Data courtesy of ExperTune, Inc.
Small gain change:Good control with stability throughout flow range.
![Page 35: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/35.jpg)
Inst
alle
d G
ain 3.0
2.0
4.0
1.0
q maxq min
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
4. As constant as possible
5. As close to 1.0 as possible
Installed Gain Recommendations
Flow
Gain = Output / Input
Gain = q / h
q = h X Gain
Inst
alle
d G
ain 3.0
2.0
4.0
1.0
q min q maxFlow
![Page 36: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/36.jpg)
Cv
Valve Travel
Actual inherent flow characteristic Actual system characteristicFlow, gpm
Pre
ssu
re,
psi
g
3220
P1 = 42
P1 = 32
P2 = 10 P2 = 12
25
P1 = 36
P2 = 11
MinNorm
Max
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
Software Graphs Installed Characteristic & Gain
qf=766
![Page 37: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/37.jpg)
6” Sch. 40
580’(Equiv. pipe & fittings)
230’
70F Water
10P2P1PP
FC
=% Inherent characteristic
Flowgpm
PP
psigPipeLoss(up)
P1
psigPipeLoss
(down)
P2
psig P
80 42 0.1 42 0.05 10 32
550 37 5.0 32 2.00 12 20
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
Flow, gpm
Pre
ssu
re,
psi
g
32 20
P1 = 42
P1 = 32
P2 = 10 P2 = 12
Sizing Example
Cv QGP
![Page 38: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/38.jpg)
Sizing Example
![Page 39: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/39.jpg)
85 dBA for 6”32.8 fpsp < pT
Sizing Example
![Page 40: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/40.jpg)
80 dBA for 3”32.8 fps
Sizing Example
p < pT
![Page 41: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/41.jpg)
6” 3”
80
80
550
550
Sizing Example
![Page 42: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/42.jpg)
6” 3”
80
80
550
550
6”
3”
80 550
q maxq min
Inst
alle
d G
ain
3
2
4
1
q min q max
Inst
alle
d G
ain
3
2
4
1
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
4. As constant as possible
5. As close to 1.0 as possible
Sizing Example
4”
![Page 43: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/43.jpg)
What is the optimum control valve pressure drop to design into a system to ensure adequate control while avoiding the use of excessive pumping power?
Selecting the Right Pump
![Page 44: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/44.jpg)
TC
10
5 515
Pump head droops 5 psi from 100 gpm to 600 gpm
Pressure losses @600 gpm
6” Sch 40
70°F Water
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
P210
45
535
P1 (Pump A) 17 hp*35 2050
P1 (Pump B) 23 hp*6050
30
* At normal flow (400 gpm)
P1 P2
3565
P1 (Pump C) 29 hp*7565
Selecting the Right Pump
valve characteristic
Inhe
rrent
Inst
alle
d
Min. Norm. Max.
![Page 45: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/45.jpg)
PRESSURE DROP = 5 psi @ MAX. FLOWPump power = 17 hp @ 400 gpm
Selecting the Right Pump
![Page 46: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/46.jpg)
Selecting the Right PumpPRESSURE DROP = 5 psi @ MAX. FLOW
Pump power = 17 hp @ 400 gpm
![Page 47: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/47.jpg)
6”
Selecting the Right PumpPRESSURE DROP = 5 psi @ MAX. FLOW
Pump power = 17 hp @ 400 gpm
![Page 48: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/48.jpg)
3”
Selecting the Right PumpPRESSURE DROP = 20 psi @ MAX. FLOW
Pump power = 23 hp @ 400 gpm
![Page 49: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/49.jpg)
3”
Selecting the Right PumpPRESSURE DROP = 35 psi @ MAX. FLOW
Pump power = 29 hp @ 400 gpm
![Page 50: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/50.jpg)
5 psi, 17 hp
20 psi, 23 hp
35 psi, 29 hp
q maxq min
Inst
alle
d G
ain
3
2
4
1
q min q max
Inst
alle
d G
ain
3
2
4
1
Within the specified control range:
1. Gain 0.5
2. Gain 3.0
3. Gain (max) / Gain (min) 2.0
4. As constant as possible
5. As close to 1.0 as possible
3”
6”
Selecting the Right Pump
![Page 51: Installed Gain as a Control Valve Sizing Criteria Jon Monsen, Ph.D., P.E](https://reader036.vdocuments.site/reader036/viewer/2022062314/56649dc95503460f94abf0d8/html5/thumbnails/51.jpg)
20 psi, 23 hp
35 psi, 29 hp
3”
Maximum Calculated SPLTo avoid cavitation damage
UP TO 3” 80dBA4” TO 6” 85 dBA8” TO 14” 90 dBA16” AND UP 95 dBA
Selecting the Right Pump