Please help. Consider the case of a system made up of:
The blower has already been running while the valve was closed. The valve is then suddenly opened to enable flow through the pipe to the blower. For the purposes of applying Steady Flow Equations, when (a time in seconds measured from the moment the valve is opened and expressed in terms of the parameters above) can it be considered that Steady Flow has developed?
Thanks in anticipation of the help.
Raymond,
I've been using Simflow with fair success on vaguely similar problems.
What you're asking for lies somewhat outside the realm of 'steady flow equations'. This is a transient - no matter how you look at it.
It's somewhat complicated as the air source is not a simple (easily modelled) volume at a given pressure - it takes a few revs for the blower blades to exit from a stalled regime, and start delivering flow. It's quite unlike opening the valve on a pressurized tank.
Are you looking for a heuristic equation?
(it strikes me that this would be a lovely 1st year practical experiment for engineer/physicists - develop a transient flow equation using a variety of conduits!)
@ Zoubair: Thanks. Posted it to the forum.
@James: Thanks. Yes I am looking for a heuristic equation. I want to have an idea of the time lapse after which one can assume Steady Flow (the time lapse for Transient Flow to pass and give way to reasonably approximate Steady Flow) to apply the Steady Flow Equations. A heuristic equation of a form such as: "t = constant * L/(Q/A)" would be most helpful.
@ James: Would the situation be any easier if the fluid were reasonably incompressible such as water (101Kpa and 288K)? Is a heuristic equation available?
Raymond,
A little digging reveals that this topic was attacked in the 1930s for Newtonian fluids.
http://webx.ubi.pt/~pjpo/ri62.pdf - first paragraph, and the equations are at least dimensionally correct - that much I can tell. But it assumes an instantaneously applied pressure - which isn't a bad approximation.
I think that a significant part of the lag in establishing equilibrium, for a reasonable length of duct, is the need for the fan to re-engage with the air, and come up to full speed.
However.
For non-Newtonian (viscoelastic) fluids such as air, equation 23 seems to be the outcome.
Not the simplest to evaluate, and I still reckon that this would be a marvellous experiment for a small lab.
If the fluid is water, then there is the chance of cavitation - which is an equally fascinating topic.
http://repository.tue.nl/682840
@James: Thanks a lot. I reviewed the equation on the first paragraph. The values seemed quite off from what one would expect (required about 9 hours?). I do not know if it is because of the 1% limit they used (e.g. if the time would have been within a fraction of a second if they had used a 10% limit?) or if the equation itself is problematic. I looked at equation 23 and I am wondering if there's a readily accessible weblink at which I can find the needed relaxation and retardation times of air and water in order to compute the values. Please do you know of any link?
Thanks in anticipation of the help. I appreciate it.
Raymond,
Indeed, that (puzzlingly simple) equation in the first paragraph is, I think, purely a dimensional relationship (the denominator of viscosity indeed yields a maddeningly large timescale for settling).
I will make some investigations - this is a topic not too far from a project that I am addressing.
Thanks James. I really appreciate this. I will wait for the outcome of your investigations.
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