Physics project - Cylinder question

[c_m_wood]

Hi all. A part of my A2 physics research project is concerning cylinders. Im using a 15l cylinder as an example of how speed of filling can give a smaller quantity of air when allowed to cool than one filled slowly and also why not to leave a cylinder in a warm place. Fairly basic stuff. However I was wondering if anyone know how the 15l capacity is measured? In particular what temperature is it measured at? ATM im presuming 298K which is considered the international chemistry standard for standard conditions with 100 KPa which is pretty much 1ATM. Any thoughts would be much appreciated as a brief search through the archives here didnt turn up anything like this. Other areas Im researching include fin types, light under water, gps and sonar to find a dive sight, masks and regs. If anyone can think of a forumla to link viscosity of a medium, kinetic energy (half mass x velocity squared) and drag I would be very appreciative. Many thanks. Chris.

 

[donacheson]

Hi all. A part of my A2 physics research project is concerning cylinders. Im using a 15l cylinder as an example of how speed of filling can give a smaller quantity of air when allowed to cool than one filled slowly and also why not to leave a cylinder in a warm place. Fairly basic stuff. However I was wondering if anyone know how the 15l capacity is measured? In particular what temperature is it measured at? ATM im presuming 298K which is considered the international chemistry standard for standard conditions with 100 KPa which is pretty much 1ATM. Any thoughts would be much appreciated as a brief search through the archives here didnt turn up anything like this. Other areas Im researching include fin types, light under water, gps and sonar to find a dive sight, masks and regs. If anyone can think of a forumla to link viscosity of a medium, kinetic energy (half mass x velocity squared) and drag I would be very appreciative. Many thanks. Chris.

It's not important: 15 liters is 15 liters at any temperature. Of course, the relationship between the mass of gas contained in that volume, pressure, and temperature is defined by an equation of state such as the ideal gas law pv=mRT.

The conventional relationship between drag and velocity is D=CAv^2, where D is drag (a force); C, the drag coefficient; A, the frontal area; and v, the velocity. Mass, and thus kinetic energy is not a factor. The drag coefficient is emprical and depends on the fluid, the shape of the moving object, and its velocity; it's conventionally expressed as a function of the Reynolds number which includes viscosity.

As for the other things you asked about, you might find some help at www.howstuffworks.com and http://howthingswork.virginia.edu

 

[Rick Murchison]

The drag coefficient is emprical and depends on the fluid, the shape of the moving object, and its velocity; it's conventionally expressed as a function of the Reynolds number which includes viscosity.

Don't forget object orientation. For example, the drag coefficient for an aluminum tank is quite different if the tank is moving valve first than it is if it's moving bottom first, even though the crossectional area is the same.
And, of course, if you're dealing with movement through gasses we have compressibility and shock waves and area ruling and all that other stuff. Even in liquids things change if you get cavitation. (In other words, in the real world it is often easier to measure than to calculate. Or, as I advise, "The facts can shed a lot of light on the theory"
Rick

 

[Rick Murchison]

how the 15l capacity is measured?

First you have to understand that 15l is not exact. No two tanks are exactly the same. So while temperature will indeed effect the precise measurement of how much the interior volume of the tank is, it'll still be close to 15l, and each tank will have its own unique precise volume.
We like to come up with precise numbers, especially in the lab, but in the real world they rarely apply. For example, if you are at 100' on your depth gauge - and the depth gauge is precisely accurate - how deep are you? How deep is the tip of your left toe? Your heart? Your right thumb? Which one counts?
We tend to "measure with a micrometer, mark with chalk and cut with an ax" in the real world - and argue about the measurement to three decimal places
Don't get me wrong - you need to learn the physics and the formulae and the theory and the calculations. Then you can use those things to predict what will happen under certain circumstances, and to check results for reasonableness. Just realize that even the best theories can only approximate reality.
Rick

 

[oxyhacker]

You talking 15L euro or US medical?

15L (unless you are talking a very small med tank) is the actual water volume capacity - what it will hold if you pour it full of water. Temperature has little to do with it unless you are aiming for insane accuracy as long as you don't heat or cool it too much between dumping it out of the tank and measuring it.

The euros rate tanks by water volume. USA measures it by filled gas capacity, which does require specifying or compensating for temperature if you are trying to be accurate. Din/ISO usually uses 15 C as the standard temperature for measuring volume/pressure, USA 70 F

 

[c_m_wood]

It's not important: 15 liters is 15 liters at any temperature. Of course, the relationship between the mass of gas contained in that volume, pressure, and temperature is defined by an equation of state such as the ideal gas law pv=mRT.

The conventional relationship between drag and velocity is D=CAv^2, where D is drag (a force); C, the drag coefficient; A, the frontal area; and v, the velocity. Mass, and thus kinetic energy is not a factor. The drag coefficient is emprical and depends on the fluid, the shape of the moving object, and its velocity; it's conventionally expressed as a function of the Reynolds number which includes viscosity.

As for the other things you asked about, you might find some help at www.howstuffworks.com and http://howthingswork.virginia.edu

This is great thanks! When you say 15 L is 15 L though the number of moles of gas will vary depending on temperature. 1 mole will fill 21 litres i think under standard conditions.

That formula is exactly what I was looking for and I can certainately use it to show the benefits of horizontal motion. Just got to have a think about possibly the effort of swimming with different types of fins perhaps. Time for more research I think. Am glad I chose this topic - you guys are all very helpful! Many thanks

 

[c_m_wood]

Rick and oxyhacker. Thanks also for your replies. They definately helped to clarify things. I guess I was being a bit to accurate. Using a liquid at a set temperature to measure the volume of the cylinder certainately seems sensible. I'll take the 15L as an average value and use these explanations to justif a certain inaccuracy should one arise. I guess it would be stupid to be attempting to accurately calculate numbers of particles when they could vary so much from tank to tank. All decimal figures will be rounded and I shall look carefully at how many significant figures to use.

By the way I forgot to mention that Im from the UK so that would be metric litres or decimetres cubed.

Thanks again. Chris

 

[hdtran]

Actually, a calibrated volume using expansion of gas can be relatively accurate (on the order of 0.05% relative accuracy with 68% confidence). At the highest accuracies, pressure gauges are actually calibrated using weights acting on a piston. You measure the piston area; you weigh the weight, and you remember to correct for the effect of buoyancy in air of your weight (you can lose approx. 0.2 mg/cc buoyancy as you go from sea level, to, say, Denver). There's also a latitude correction for local gravity, but I don't remember how significant that is.

At very low speeds (very low reynolds numbers), drag is surface drag, and is proportional to velocity & area. The square term, which is related to dynamic pressure, goes away completely.

A fairly interesting study (not experiment, but study project) would be to determine if surface roughness/finish makes a difference in drag for typical scuba speeds; say the leg in a flutter kick. All the information you need is in the literature (encyclopedias, physics books, fluid mechanics books, etc. You don't say what level of physics you're doing; if its college/university, you should be able to find some elementary fluids books in the library. If it's high school/mid-school, you're going to have a harder time finding references). But anyway, you can calculate how fast the leg (a cylinder) moves in a flutter kick; you can measure the thigh diameter (ladies, don't go there, OK?), and look up water viscosity and density. In proper units, the reynolds number is (density*velocity*length)/(viscosity) (be sure to use absolute; not kinematic viscosity). You can then look up the typical flow patterns you'll see at those reynolds numbers. I highly recommend Milton Van Dyke's "An Album of Fluid Motion" (you can get this via interlibrary loan). This is why golf balls are roughened. At their high reynolds numbers, tripping the boundary flow from laminar to turbulent actually reduces drag (as you can see in Van Dyke's book). Van Dyke's book is accessible to everyone; it's not just for budding engineering PhD's.

 

[c_m_wood]

hdtran
Lots of great ideas here thanks. interesting way to model it with the legs as cylinders etc. Will definately give it a go.

As far as the level of the physics. I'm 18 - final year of secondary school (final year of A levels). So not quite university level but somewhere near it.

Thanks for your input and your time.
Chris.