Pressure required to inflate a balloon
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- Опубликовано: 30 сен 2024
- Why does it become easier to inflate a balloon once it grows beyond a certain size? Here we develop a simple model to find the excess pressure required to inflate the balloon to an arbitrary radius r, and use the result to gain some understanding of this effect.
Deriving the equation Δp = 2γ/r: • Laplace pressure in a ...
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About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.
My website: benyelverton.com/
#physics #mathematics #pressure #balloon #elastic #elasticity #youngsmodulus #stress #strain #materials #extension #arc #surfacearea #volume #crosssection #equilibrium #forces #balance #laplacepressure #physicsproblems #maths #math #science #education
That's very cool, but to be honest i don't really understand how tension force per unit lenght work, it doesn't feel intuitive why there's a tension force at every lenght of the segment, (per area is understandable). maybe you can give us introduction on that?
Maybe I'll do a quick video on surface tension to try and clarify that!
thank you for this content dr Ben, great job!
Indeed , he has all kind of unique content in physics .If he were to include relativistic(special) type of problems it will be pretty cool
@@shrivatsa8604 that will actually be interesting
Thanks for this, your explanation was very clear! I have two questions:
1. Does the graph imply that the balloon's pressure actually goes down as the balloon's radius increases past that tipping point?
2. If you were to tie off the balloon after filling it to a given pressure/radius, and then increase the external pressure (say, in a pressure chamber), the balloon should shrink, right? What equation governs the decrease in radius? How does it interact with the ideal gas law?
Very unique problem, thanks for posting, as always. More continuum mechanics please! Also, could you perhaps do a concept video on Young's modulus, strain, stress and all that? Similar to how you treated the D and E fields. That would be great! I encountered differential equations in continuum mechanics in applied mathematics texts but they don't offer much physical explanation on the physical meanings of those quantities so often I felt the need of a 'sanity check'.
Thanks for the suggestion, will put that on my list of ideas.
Thank you so much this was unbelievably helpful.
Solution seems pretty interesting. However I encountered some discrepancy in your solution and mine (I get proportionality 1/r⁴). I consider directly that pressure acting on a small element of a balloon is equal to four tensions projected onto vertical axis(which should give some solid angle ) divided by the surface dS. The rest is just like you did,and at the end I got different formula (dimensions are ok!!). Is my method correct or there's something I miss?
That should get you the same result! I have used a similar method in another video, maybe compare your working against this: ruclips.net/video/CtUetjUX-yY/видео.html
Hello. For a project, we performed an experiment of inflating a balloon and we measured the differential pressure which I assume would be the same as the delta P here. However, for the equation derived in this video, the asymptote is at the x-axis (0) and it falls quite sharply too. But in our experiments although the relative shape of our graph was the same, the asymptote would not be at 0 but a little bit above atmosopheric pressure. Is there a subtle detail I'm missing here? Is delta P here differential pressure (P_inside - P_outside)?
Interesting! Is the excess pressure you mentioned too large to be explained by experimental uncertainties? Although the model in the video is very simple, I'd definitely expect the pressure to tend to zero at large radii because as the radius becomes very large, the walls of the balloon become essentially flat so that no excess pressure is needed to balance the inward pull of the rubber surface. Also, are you sure you measured the pressures at sufficiently large radii to conclude that the pressure doesn't asymptote to zero? I'd imagine the balloon would probably burst before that point!
Hi Ben, amazing videos as usual! Just wanted to ask with what platform or app, iPad, computer, etc. are you using in these videos?
Thanks! I use Xournal++ with a One by Wacom graphics tablet connected to my PC.
Hi Dr Ben,
thanks for your videos. I was wondering if would mind if I used some of your examples as inspiration for my own physics videos here in Brazil, which will be posted in Portuguese. I always wanted to share interesting physics and engineering problems on youtube in a similar fashion that you do. If I do use one of your exercises as inspiration, I would most certainly link your channel in the description in the video and mention (in portuguese) that you were the inspiration. Would that be ok for you? I totally understand if not, but I wanted to ask for your permission nonetheless.
Thanks for asking - as long as you're adding something unique and explaining things in your own way, please feel free!
so many arnolds
could we calculate the youngs modulus with respect to the thickness t? Y = (pressure)/(t-t0)/t0, i cant figure out whats wrong with it, and its getting me a different relation
Sir please solve jee advanced physics problem and their concept
Are there any particular concepts you'd like to see more of?
@@DrBenYelverton yes sir angular momentum conservation
Thanks for the suggestion. You might be interested in the following video that covers an interesting problem involving angular momentum: ruclips.net/video/nyu01GgBURI/видео.html
your vid doent show the good thumbnail graph is very disappointing