MikeFerrara once bubbled...
We could all pitch in and have a FEA done. But..I suspect that we need to define "vibrate more". I think a curved structure will have different resonant frequencies (I think higher). Of course we would have to define the excitation spectrum and measure (or predict through FEA) the response spectrum in order to determin the transfer function. There may very well be transverse resonances that are not seen with excitation in only one direction. Therefore, It could be difficult to design a test that would simulate moving through the water. But...assuming the same material and demensions, will curves add stiffness? If so, I think the resonant frequency will be higher. Would you agree? I would expect the excitation (moving through water) to be a low frequency. Would you agree? If that is the case, I would expect a lower magnitude response in the snorkel When moving through water).
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A curved structure mainly shifts the nodal points. For example the frequency of a tuning fork, bent 180 degrees, remains the same as the straight bar (for the same harmonic mode). The nodal points shift to the bends and the stem is set at the anti-node where it produces the greater motion for power transfer to a resonator of some sort to enhance the sound. My reference is Kinsler and Frey, Ill give the full reference and correct spelling tomorrow when I have it in hand.
The curved snorkel adds a new torsional mode that does not exist in a straight tube producing additional vibrational modes. Have you taken that into consideration? It doesnt really matter because I believe you are on the wrong track from the start again. I dont believe that the simple vibration modes of a bar are what we are dealing with here. While snorkels are made out of a wide variety of plastic stiffnesses, if you rigidly support one out the water and strike it to excite vibrations, you will see they damp out in a fraction of a second. With the viscous damping of the water the vibrations will die out even more quickly. The frequencies we experience with a snorkel moving through the water are much much lower.
I believe that key factors in snorkel vibration are the elasticity of the connection between the snorkel and the mouth and the snorkel and the head/mask strap. The snorkel vibrations you feel are not bar mode vibrations as in a tuning fork. In all cases, except for possibly the very softest of bendable snorkels (and of course flexible scuba snorkels), it is a rigid bar and changes in stiffness are irrelevant. What matters are the hydrodynamic effects and fluctuations (such as vortex shedding) that cause the rigid bar of the snorkel to move, tensioning and releasing the elastic connections at the mouthpiece and the mask strap. While I dont believe curving the tube increases stiffness, I also do not believe the stiffness generally matters as long as it exceeds a minimum level. Curving does change the hydrodynamics and depending on the magnitude this might have some impact on vibrations. For example, the moment arm relative to the mouthpiece and mask strap obviously is reduced, which might act to reduce vibrations. Then again hydrodynamics between the tube and the head also change and I have no idea what the effect on vibrations would be here.
MikeFerrara once bubbled...
Actually drag is dependant on more than just frontal area. Shape (yes frontal area is part of this) will change drag. But we are not just concerned with the drag of the snorkel but the drag of the diver and the snorkel combined. Having the snorkel as close as possible to the head may very well be more hydrodynamic. In either case, I think it will alter flow in one way or the other, therefore changing drag.
Drag of a cylinder = (Cd)(A)(rho)(U^2)(0.5),
Where:
Cd coefficient of drag = 1.2 for a cylinder
A projected area in the plane normal to the flow
rho fluid density
U velocity
From: Streeter and Wylie,
Fluid Mechanics,McGraw-Hill, pg 281, 1975. (This equation will be found in virtually any fluids text.)
As you can see drag is directly proportional to projected area and proportional to velocity squared.
First, I of course assume we are talking about keeping the shape (cross section) of the tube unchanged and only changing the bend. This goes back to the old issue of only changing a single parameter at a time so that valid comparisons can be made. Unless youre once again seeking to obscure the answer? If the shape remains constant the frontal area remains constant and the major factor in drag should also remain constant.
Now its less clear what happens due to the close proximity of the top of the head. When the tube sticks straight up in the flow, the drag equation directly applies (at least for laminar flow). If the snorkel was shielded by the head, drag might be reduced. When the snorkel is positioned close to the top of the head, but not in direct contact, fluid must flow between the snorkel and the head. While I dont know what happens in this case, it is likely the forcing a viscous fluid to flow through the narrow area, increasing the velocity and disturbing the flow around the head, might actually increase the drag relative to the freestanding tube. I believe the effect will be relatively small either way
MikeFerrara once bubbled...
rcohn, do you ever provide references? I think in this case it could be done
I of course assumed anyone eager to discuss drag effects would be familiar with the elementary equation for drag in laminar flow, but if not you should be now. Do we have enough references or do you need more? I used the term moment arm, do you need a reference? We could look for some more elementary sources but they are limited, as these tend to be advanced (college level) topics.
I havent yet seen you support a single argument or supply a single reference. Oh, if you still want the FEA done there are a few experts here (not me) who would be quite happy to do it for you, I can get a job set up anytime. However, I guarantee you wont be happy with the price.
Ralph
