Calculating Effect of a Fluid Stream

How about a large, shallow tray with the discharge tube exiting horizontally into it. Start with the tube mouth just covered (with a known quantity of water in the tray. With a big enough tray the decrease in head due to the level in the tray rising would (probably) be negligible.

Maybe you could try it like that and compare the result with the stream dropping into a beaker as you've described. Could be that the effect you're fretting about is negligible anyway.

This is a self regulated level control with integral behaviour so that long time error is zero. As soon as the level opens the tube to the closed reservoir water flows and the level rises again till the tube is closed. The 300 mm tube must be horizontal in order to avoid the influences of gravity on the water column. The head errors will be very low in the range of 0.1 mm which means for 100 mm head around 1/1000. I hope this precision is enough for your demonstration. The collector has to be quite slim to offer a good precision in volume measuring.

Borrow Del the Cat's water dispenser, and adapt it just a little?

Simple solution is a small pitot tube (0.125 mm dia.) in the 2.00 mm pipe and a gage marked in flow rate values corresponding to the velocity determined by velocity pressure conversion.

Why would the coherent stream height affect the head? Where the stream leaves the tube, the pressure is atmospheric pressure and presumeably the reservoir has an open top so that is at atmospheric pressure also. Hence the head difference is simply the difference in physical level between the water surface level and the end of the tube. If I was using Bernouilli's equation I would just allow v^2/2g for the energy of the exiting flow. Can this work also with Poiseuille?

If I understand correctly, you are concerned about the height from the exit if the 2mm tube to the surface of the collector. Don't be!

As soon as the fluid forms a stream exiting the 2mm tube, the pressure is atmospheric, and remains so all the way down to the collection surface. None of this height affects the flow at all.

I did the same when i discovered viscosity and made a lot of measurements about at same than you, i had the problem of break in droplets in the check of a hose: You won't regret :do this fix a needle in the checkout count droplets, flux everything,try later to obtain the proper curve from which you will get at the same time in the same experience viscosity and surface tension coeficient.If you have problems i'llbe more detailed.(years later i found this procedure was correct).-

Have you thought about the demonstrator with VERTICAL outlet pipes of different length?

It could be very interesting considering the length effect which is valid only for laminar flows, the length has a different influence on flow if the pipe is horizontal.

Yes, thanks. (Also, thanks to all the other contributors - I'm still thinking about some answers and trying to rig a decent experimental setup to measure some things).

First, I think that the pressure at the exit is probably not atmospheric if there are streamlines. I doubt the effect is very large, but I can't really say what it is. So, that was the basis of my original question.

I have a good setup (as soon as the RTV dries) for a constant head source. I can make a constant exit head fixture that satisfies me, but it's clumsy and inelegant. I don't know if I can easily convince my audience.

Why does a horizontal tube differ? I've seen that a number of times, but without explanation. I will try it, but what's the theory? That must have been a factor in Poiseuille's original work on blood flow?

It has nothing to do with the original book but only with the basic theory and the equation which connects flow and pressure drop. If you write the equation with the flow proportional to dp/dx and not as Δp/L you will see the difference between horizontal and vertical laminar flows in tubes. Of course the level of water at entry to tube has to be maintained constant. I let you have a look if you do not find it let me know and I shall give the explanation.

The pressure at tube outlet IS atmospheric as soon as the fluid left the tube and is not any more "protected". It is this pressure which limits the pressure differential at the water column height. The velocity the fluid has at outlet is function of the head and internal friction losses at tube wall. I would be interested to know how you maintain the head constant. If you accept a slight error then a large surface in the reservoir (open to atmosphere) is enough. All depends on the accuracy you aim at.

It is also possible to use tubes up to 3mm internal diameter and still being in the laminar range (Re<100). It can be useful for a more precise measurement since flow is more important.

Thanks to all who have answered. I've not got a good response yet because I'm building a test rig. I'll post data when I get it. please stay tuned.