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Evaluating a volume flow incremental sensor does not deliver expected results.

The pump of which the volume flow is to be measured has a hand-calculated flow rate of

$$Q = \dfrac{n}{ 60 \;\mathrm{s/min}} e \pi\left(\frac{d}{2}\right)^2 \approx 2 \;\mathrm{cm^3/s}$$

where $n$ is the rotational speed of $2000 \;\mathrm{1/min}$, $e$ the excentricity of the pump of $1.1 \;\mathrm{mm}$, and $\pi\left(\frac{d}{2}\right)^2$ is the area of the piston with $d = 8 \;\mathrm{mm}$.

Now the sensor (VSE, Type: VS 0,1) delivers 10000 impulses per liter.

The calculation counts the "Delta Impulses", call it dI, and divides by the time delta dt in milliseconds.

$$\dfrac{dI}{dt} = \text{impulses/ms}$$

Now I say that $10$ impulses mean $1 \;\mathrm{cm^3}$ as the spec says ($1 \;\mathrm{liter} = 1000 \;\mathrm{cm^3}$). So $$1 \;\text{impulse} = 0.1 \;\mathrm{cm^3/ms}$$

Further with $1000 \;\mathrm{ms} = 1\;\mathrm{s}$, it is $100 \;\mathrm{cm^3/s}$. I can multiply the $\frac{dI}{dt}$ with $100$ and get the flow in $\mathrm{cm^3/s}$.

$$1 \frac{dI}{dt} = 100 \;\mathrm{cm^3/s}$$

Is that correct?

Now this calculation is done within the program. The factor $100$ is given as a parameter that I have set to this value to translate the flow into $\mathrm{cm^3/s}$. The program always uses milliseconds (PLC-Control with $1\;\mathrm{ms}$ cycle, increments time ticker each time +1).

I don't know the values of the used impuls count, but the result in $\mathrm{cm^3/s}$ is about $10$ times higher than the hand-calculated flow rate. I can't find a logical mistake. Do you?

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The result looks right, though you've put "1 impulse = ...", when it should be "1 impulse/ms = ..." in the 3rd equation.

Have you access to the equipment to check how fast the fluid actually flows and/or how many milliseconds there are between pulses from the sensor?

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  • $\begingroup$ You are right, this was a typo - shame on me. I have access to the Beckhoff PLC and Systems Manager but did not set it up, though I think I understand how most of it works. Have to check if I may edit the PLC to give me interal values or figure out how to trace them. Right now I want to check how the incremental encoder (Beckhoff EL5151) in the PLC works in detail - may this be a good point to investigate? $\endgroup$ – user2366975 Dec 10 '14 at 15:05
  • $\begingroup$ I don't know anything about your experimental set-up. But at the moment, you have a pump where you have calculated the rate at which it should pump, but not checked that, and a flow meter where you think you have calibrated it, but haven't checked that. If possible, a good start would be to rig up something to test one or the other, even if only approximately. $\endgroup$ – Simon B Dec 10 '14 at 17:04

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