I just made some quick numbers. Assuming hand-sanitizer has the following properties inside the 1/2" pipe
- 0.0127m = D = pipe ID
- 890kg/m**3 = ρ = fluid density
- 8000mPa s = 8 kg m**-1 s**-1 = μ = fluid viscosity
Then Reynolds number Re = DVρ/μ = 1.4 V, where V is speed of the fluid in the pipe (mean speed, IIRC). Say we fill a 5gal pail in one minute, the volume flow would be
5gal x 231 in**3 gal**-1 x 0.0254**3 m**3 in**-3 / 60s
= 0.000315 m3/s
The cross-sectional area of the pipe is π D**2 / 4 = π 0.0127**2 / 4 = 0.000127 m**2
So the mean speed is 2.5m/s.
That puts Re at 3.5, ouch. Even if we filled the bucket in a second Re would only go as high as 210, so it's going to be laminar flow. Maybe I missed a few powers of 10?
I'm not sure my suggestion to do this using an analog of the Beebe Lake gravity feed system is going to work unless the driving head is somewhere near the ceiling or maybe the third floor, eh?
Also, I wonder if the Keyence flowmeter calibration assumes laminar flow (velocity profile is a parabola (1-(r/R)**2) across the pipe), IIRC) or turbulent flow (velocity profile approximated by (1-(r/R)**7) across the pipe), the latter being more or less plug flow.
Oh dear, I just calculated the pressure drop per meter of pipe using Darcy-Weisbach: 641220 Pa/m or 93psi/m. So we will use some of that 60psi, depending on the length of the pipe.
19psi for 20cm (0.2m ~ 8") or 9.3psi for 10cm (4"). At 890kg/m**3 that would be over 40' or 20' of head.
That pressure drop is inversely proportional to V, I think (doing a bunch of stuff in my head here), so increasing the 5gal fill time to two minutes reduces the pressure drop to 23psi/m, so only 10' or 5' of head for 8" and 4" drain pipes into the buckets. Also at those short lengths (L/D ~ 16), Darcy-Weisbach may not be valid.
I think Beebe Lake is a pipe dream