We've been doing the following experiment in our Physics Lab course and are coming up with some strange results which we're at a loss to explain.
The purpose of the experiment is to determine the conductance of various narrow pipes.
The outline of the experiment is as follows:
- Seal off a chamber from the atmosphere by closing tap 2 (See diagram below).
- Depressurise the chamber with a rotary vane pump.
- Seal off the chamber from the rotary vane pump by closing tap 1 and detach from the rotary pump.
- Open tap 2 and record how the pressure in the chamber varies as a function of time.
According to the theory we've been given, the flow through the narrow pipe will be viscous and thus the throughput will be given by:
$$Q = -V\frac{dP}{dt} = A(P+P_a)(P-P_a)$$
where $V$ is the volume of the chamber, $P$ is the pressure of the chamber, $P_a$ is the atmospheric pressure and $A$ is a constant which depends on the dimensions of the narrow pipe.
Solving this equation, one would expect that:
$$ P = P_a\mbox{Tanh}\left(\frac{AP_a}{V}t + C\right) $$
The following plot shows one of our actual results:
You won't be surprised to learn that fitting the above equation to this graph produces a terrible fit. What is really baffling us however is the way the pressure actually noticeably decreases a little after reaching the peak and then slowly starts to increase again. We've repeated the experiment with different equipment and the phenomena isn't going away so it doesn't appear to be a case of equipment failure. We've also noticed that the pressure decrease is more pronounced when the narrow pipe has a higher conductivity (i.e. wider or shorter pipes).
So what is causing this inexplicable pressure drop? Once the chamber has filled with air, why would its pressure drop to below atmospheric and then start to rise towards it again?
One possibility we've thought of is that our experiment involved turbulent flow as opposed to laminar flow (we've done the calculations and this is certain). The theory we've managed to find describes the difference but is ambiguous as to whether the equations for pipe conductivity are applicable to only laminar flow or also turbulent flow. Is this relevant or are we barking up the wrong tree? If it is relevant, how would this explain the pressure drop? You should bear in mind that we haven't taken any classes on fluid dynamics yet so we have very little knowledge to work with.
Thanks in advance.