Dampener Calculations  Estimating Pulse Volume and Dampener Size
Estimating the Volume "V" of one movement of one displacer. "Displacer" means one vane, 1 gear tooth, 1 lobe, one cavity, one piston, plunger, or diaphragm. From this figure, & according to the pump type "F" number, a dampener volume may be estimated.
Note: These estimates ignore all of the dynamics, delta time / "dt" consideration, so are quasi static and do not take into consideration pipe system responses. The answers can be valid for residual acceleration head flow fluctuation purposes, but not for pressure pulsation system response, (for which flow through multi connection pressure pulsation dampeners are essential above 5 Hz.) 
EXAMPLES: Volume Of One Movement Of One Displacer or "One Flow Fluctuation." 

A centrifugal pump has 11 blades, at 725 RPM it Displacers 500 gpm,
500 gals x 231 in3 per Gallon / 11 blades x 725 rpm = 14.5 in3 displacement 
@ 133 Hz.
& use F=7


A gear pump has 17 teeth, @ 440 rpm it produces 2 Kg per second.
2 Kg per second x 60 secs per minute x 1000 gms per Kg / 17 teeth per rev x 440 rpm x SG 1.35 = 12 cm3 per tooth 
@ 125 Hz.
& Use F=3


A vane pump with 23 vanes, driven at 2,900 rpm, pumps 380 barrels per day
40 Liters x 1000 cm3 per Liter / 23 vanes x 2900 rpm = 0.6 ml displacement 
@ 111 Hz.
& Use F=5


A trilobe pump at 173 rmp, discharges 3 tons per hour
100 lbs per minute x 25 in3 per pound / 3 lobes per rev x 173 rpm = 4.8 in3 per lobe 
@ 8.7 Hz.
& Use F=1


A quintuplex plunger pump turned at 880 rpm, generates 60+ M3 per 8 Hr shift
2000 gls per hour x 3,800 ml per gallon/60 minutes per Hr. x 5 piston rev x 880 rpm = 28.8ml/stroke 
@ 73.5 Hz.
& Use F=0.6


F for duplex diaphragm heads also = 0.8
A simplex diaphragm head pump is pushed by a 100mm diam. piston with a 150mm stroke @ 205 spm
5 cm Piston Radius x 5 cm pist. rad,. x (Pi) 3.142 x 15 cm stroke = 1.18 Liters per stroke 
@ 3.4 Hz.
& Use F=0.8


The F figure assumes that the air supply to the A.O.D.D. is enough to ensure no return stroke delay.
An air operated double end diaphragm pump empties a 40gl drum in 4 mins., on a 2 second cycle.
10 gls per minute x 231 in3 per gallon/2 diaphragms per cycle x 30 cycles per min. = 38 in3 per end. 
@ 1.0 Hz.
& Use F=1.8


The F figure assumes that the size of the shoe or wheel is approx. one third of the volume between shoes or wheels.
A hose pump squelches out 150 liters or effluent sludge per minute, with 3 shoes revolving 15 times per minute.
150 liters/3 shoes x 15 revs = 3.33 Liters between shoes. 
@ 0.75 Hz.
& Use F=0.4

Additional "F" correction factors, for Progressive cavity, Screw, Packed Plunger, Dosing, and Intensifiers, please see Click Here 
Using the estimated volume of one pulse to find approx. Dampener volume 
= 
100 x Volume of One Movement of One Displacer 

No of displacers^{2} x F x The Percentage figure of allowable residual fluctuation 
Abbreviation 
100 ^{.} V 
N^{2} ^{.} F ^{.} % age fig. 
"F" is a correction Factor on the square of number of diplacers. Example, Centrifugals are intrinsically good  have a high F, Sandwich diaphragm metering pumps have a low F.
N: N Squared, N Exponent 2, means multiply the Number of displacers by that same number.
Example N2 : 1 Diaphragm head 1x1=1. 11 Blades 11x11=121, 2 Lobes 2x2=4, 3 Plungers 3X3=9
"%age figure" : 0.5% allowable residual fluctuation  use the figure 0.5 in the equation, for a residual fluctuation of say + &  3%, 3 positive plus 3 negative = 6  use 6 in the equation, +/ 5% total 10, use the figure 10. 
EXAMPLE

100 x 90 ml per stroke 
= 2,222 ml = 2.22 Litres = 0.59 US Gls.
Use a 135 in3 or greater Dampener 
__________________________________ 
[From a triplex] 9 x [plunger factor] 0.6 x 0.75 [for 3/4% residual] 

IT REALLY IS JUST THAT EASY TO OVERSIZE A DAMPENER BY IGNORING HOW MUCH PULSATION YOU WOULD HAVE WITHOUT ONE. 

