# Flow through a tube

1. Feb 20, 2015

### oceanspiral20

I have a setup where there is a source of air pressure, a tube through which the air flows, a connector through which air flows, and a flow meter which reads the flowrate of the air at the end.
The final goal is to use the readings from the flowmeter to determine the diameter of the tube through which the air is flowing (the diameter will be the unknown).

So, to get there, I wanted to create a calibration curve to relate diameter of the tube (the eventual unknown) to the flowrate (our measured variable) by using tubes of known diameter and reading the flowrate for each known diameter. So, the pressure at the air source is a constant and the flowrate would be read for each different diameter tube. From here, I would ideally have a calibration curve which I could use to determine diameter of the tube based on a flowrate.

However, by changing out the diameter of the tube through which air is flowing, I'm not getting any change in the readout of the flowrate from the flowmeter.

I'm wondering if the reason is the connector which connects the tube to the flowmeter. The connector shrinks to a much smaller diameter than the tube - is this effectively a limiting factor? I'm wondering if, for each diameter tube, since the connector is a much smaller diameter than the tube, the flowrate read by the flowmeter is the same (because input pressure is the same, output diameter is the same, and maybe what happens in the middle - whether it flows through a large diameter tube or a small diameter tube - doesn't matter)?

So, if my description is confusing, the setup (direction of air flow left to right) looks like this:
air source at a constant pressure -> constant diameter connector -> Variable diameter tubes (from 2-10 mm) -> constant tapered Connector which shrinks to 1 mm diameter -> Flowmeter

Do I need to find a way to use the flowmeter to measure directly at the end of the tube rather than through a smaller connector? Or is there something else I'm missing here?

Thanks!

2. Feb 20, 2015

### Quantum Defect

See p. 15 of this: https://indico.cern.ch/event/286275/contribution/149/material/slides/0.pdf or a book on basic experimental desing (e.g. Moore, Davis and Coplan, "Building Scientific Apparatus")

The total conductance of tubes in series are calculated like you would for resistances in parallel.

1/C_series = 1/C_1 + 1/C_2 + 1/C_3 + ...

Having a very small conductance tube on your flowmeter is going to be the limiting conductance of your system = 1/C_system = approx. 1/C_smallest