Calculate flow rate in a multi-cylinder positive displacement pump
Calculate flow rate in a multi-cylinder positive displacement pump
(OP)
I have been looking at a few technical articles and the image shown for the flow rate of a positive displacement pump doesn't match what I would expect. The image appears two have two 'humps' in the flow rate where I get regular peaks. can someone tell me if my understanding is correct.
The flow rate from one cylinder is :
ksin(wt)*(sin(wt)>=0)
where: k=some constant
w=angular velocity
t=time
And for two cylinders each one is shitfed by pi (180°)
flowrate = (ksin(wt)*(sin(wt)>=0))+(ksin(wt+pi)*(sin(wt+pi)>=0))
And for three cylinders each one is shifted by 2/3 pi (120°)
flowrate = (ksin(wt)*(sin(wt)>=0))+(ksin(wt+(2/3*pi))*(sin(wt+(2/3*pi))>=0))+(ksin(wt+(4/3*pi))*(sin(wt+(4/3*pi))>=0))
Is this theory correct or am I missing something glaringly obvious?
The flow rate from one cylinder is :
ksin(wt)*(sin(wt)>=0)
where: k=some constant
w=angular velocity
t=time
And for two cylinders each one is shitfed by pi (180°)
flowrate = (ksin(wt)*(sin(wt)>=0))+(ksin(wt+pi)*(sin(wt+pi)>=0))
And for three cylinders each one is shifted by 2/3 pi (120°)
flowrate = (ksin(wt)*(sin(wt)>=0))+(ksin(wt+(2/3*pi))*(sin(wt+(2/3*pi))>=0))+(ksin(wt+(4/3*pi))*(sin(wt+(4/3*pi))>=0))
Is this theory correct or am I missing something glaringly obvious?





RE: Calculate flow rate in a multi-cylinder positive displacement pump
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RE: Calculate flow rate in a multi-cylinder positive displacement pump
RE: Calculate flow rate in a multi-cylinder positive displacement pump
I presume that the chart is correct because it isn't the first time I've seen the same plot.
RE: Calculate flow rate in a multi-cylinder positive displacement pump
What I forgot to consider was the interaction of the connecting rod.
If y=crank throw(r)/connecting rod centres(l) then
If P=y.sin(wt).cos(wt)
And Q=1-(y^2).((sin(wt))^2))
Velocity V(w,t)=w.r.(cos(wt)+(P/(Q^(1/2))))
If you consider flow only occuring when the velocity is positive then
Flowrate Q(w,t)=A.V(w,t).(V(w,t)>0)
Where A is the area of the piston face.
This gives different curves dependant upon the crank throw and the distance between the connecting rod centres for the same angular velocity.
If there a n cyclinders this gives the following:
Total Flowrate=flowrate(wt) + flowrate(wt+z).(z>=n) + flowrate(wt+2z).(z>=n)....
where z is the phase shift between each cylinder.
.........I think