Peristaltic pump - theory vs reality, where is a problem?

I'm building a test system (experiment) for peristaltic pump to check if pump is able to pump according to specification. The pump data: 6,3ul liquid moved per stroke. 5 strokes per revolution. The tube used in the pump with 0,7mm diameter. The lenght of pump stroke ~17mm. Pump is designed to transport liquids, but I have to test it with air (becouse it shall be not contaminated when it's new). It means 0,7 tube from picture below contains air, but I'm trying to move liquid in glass tube with 3,15mm diameter. The test system looks like this:

Initially I'm pumping to reach “start level” to have initial “pressure” in channel to be able to move the liquid right away. Then I'm doing exact 10 full revolutions.
Theory:
Pump shall move: 5 strokes per revolution = 31,5ul. Multiply by 10, then I shall move 315ul.
Reality:
I measure 35mm of liquid transported thru glass tube (3,15 mm diameter) from starting point. So the result is: PI * R^2 * h=3,14 * (1,575)^2 * 35= 272,6ul.

My approach is probably too simple. Where to start? Do anybody know what I'm missing? Why I have differences in results? 272ul is far from 315ul :(

• Air is much more compressible than liquids… how do you account for that? Dec 3, 2021 at 10:39
• Yes, true. I thought It's compensated by initial pumping and building a start "vaccum" in the system. Of course I do not know if I shall continue to compansate that while pumping, and finally how to do it. I read about Hagen–Poiseuille equation, but I do not know how to apply this here yet. Dec 3, 2021 at 10:43
• The tubing is pinched by each roller and is not perfectly circular (more of a tapered pinch). What you can do is coorelate the number of rotations versus the volume delivered (includes partial rotations). If it takes 12.43 rotations to equate your desired volume, then there-you-go. Also you will see volume pulsations at slow rotation (fast too) as uncompression draws slight vacuum. Ultimately, as the tubing is "worked" (compressed, over and over) over a long time, it is likely to flatten some. Eventually the volume of each expression is likely to diminish. Dec 3, 2021 at 14:17
• Thank you Jim. The effect of "worked" over a long time tubing, I do not take into account in final solution, becouse I will test only once on a new pump with new tubing. Then I will judge if it's in the limits or not. New tubing will work for a short period of time in my situation. I have to perform a study and corelate reality vs theory, and compare the results with specification tolerances of tube. The peristaltic pumps rollers collapse the tube at the contact point,so I already include this into my calculations. Then theoretical value is much closer to measured one (diff around 2-3strokes). Dec 3, 2021 at 16:30
• Not only is the air compressible, but the peristalic tubing is deliberately elastic. Fill the system with representative liquid and run it at steady state at several RPM's. There will be a range of RPM's, not too high, not too low, where the flow-volume-per-revolution is pretty much constant -- at steady state. With peristalic pumps, it varies a fair amount over the life of the peristalic tube, and from specimen to specimen, and temperature, pressure, pressure difference, etc etc. You might need to collect a larger volume (like into cup, weigh with balance) to achieve steady state. Dec 3, 2021 at 20:35