- freely available
Methods Protoc. 2019, 2(1), 14; https://doi.org/10.3390/mps2010014
2. Materials and Methods
2.1. Automated Flow Rate Measurements
2.2. Intra-Tube Pressure Dynamics
3.1. What’s Really Happening within the Tube
3.2. The “Electronic–Hydraulic Analogy” Model of Pressure, Flow, and Resistance to Flow
- If the resistance of 1 foot of tubing is R1foot, the resistance of 10 feet of tubing will be approximately the sum of 10 such resistances, or 10R1foot;
- Doubling the resistance at a given pressure should approximately halve the flow rate;
- Doubling the pressure should approximately double the flow rate.
- A single coupler such as a plastic reducing adapter is comparably resistive to a foot of 1/16″ i.d. tubing;
- A single foot of 1/16″ i.d. tubing is comparably resistive to 40 feet of 1/8″ i.d. tubing;
- The solenoid and tank outlet contribute to the resistance significantly in and of themselves.
- Resistance among solenoids that appear similar can vary by more than one order of magnitude, so choice of solenoid can greatly influence exactly what PSI will be required to achieve a desired strength of puff. Note: the 2V025-06 is included as a high-flow-rate example only; it is not designed for quiet operation.
3.3. “Puff” Geometry
- There is a near-field region in which the flow remains somewhat collimated, and square in velocity profile, for a short distance (~10 times the aperture diameter).
- The flow then diverges with a half-angle of approximately 12°, gradually adopting a Gaussian velocity profile.
- The peak (axial) velocity drops off monotonically toward zero with distance from the aperture as the velocity profile broadens laterally.
- The flow profile shape, half-width, and peak velocity all vary with distance;
- This variation is particularly interesting at precisely the separation distances typically chosen by experimenters (i.e., “close to the eye”, where the flow is transitioning from the near- to far-field region);
- Where this interesting transition happens depends upon the diameter of the exit orifice of the system.
4.1. What Flow Rate Should One Choose?
- 100 mL/s is too strong by far;
- 10 mL/s is rather strong but not obviously unacceptable;
- 1 mL/s is perceptible but subtle.
4.2. Measuring Flow Rate at Your Workbench
- The make and model of the solenoid or off-the-shelf system used;
- the length and inner diameter of the tubing used;
- the exit aperture diameter, if different from that of the tubing;
- the tubing-eye separation distance.
- A direct measurement of the flow rate of the system, as the experimenter, with system in hand, is uniquely positioned to best determine this number.
Conflicts of Interest
Appendix A. Error Analysis
Appendix A.1. Adiabatic Expansion and Subsequent Temperature Equilibration
Appendix A.2. Varying Height within Water Column
Appendix A.3. Reynolds Number
Appendix A.4. Calibration
Appendix A.5. Steady-State Approximation of Transient Puffs
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