anonymous
  • anonymous
An ideal liquid with density ρ is poured into a cylindrical vessel with cross section A1 to a level of height h from the bottom, which has an opening of cross section A2. Find the time it takes for the liquid to flow out
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1324391218466:dw| Ok you have this problem
anonymous
  • anonymous
quick analysis reveals that time is independent on the density rho, so thats one down
anonymous
  • anonymous
We can translate the units into units/m2 -rho*v*g => -rho*h*g m*g => rho*g 1/2*rho*v^2 = p*g + p*g*h So that's initially, but in the end h=0. We are gonna view this as a linear problem (not 100% true, but ok. A better assumption would be to take an integral over it). So at the end the formula is: 1/2*rho*v^2 = p*g To get the average velocity, solve this problem. Because you know the volume of the total box (A1*h) and now know the liquid flow (in m/s which multiplied by A2 becomes volume/s)

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anonymous
  • anonymous
The average velocity can be found by combining both formulas: rho*v^2 = 2*p*g + p*g*h
anonymous
  • anonymous
Wher I say p, I mean rho ;P ... I mix em up sometimes
anonymous
  • anonymous
after we solve for v, what can we do to obtain ttime?
anonymous
  • anonymous
You translate V (m/s) into cuubs per second (by multiplying with outlet surface A2). Now you have a box with a fixed volume, that decrease with that rate over time
anonymous
  • anonymous
I don't usually work with inviscid flow, so maybe your teacher wants a more complicated solution, idk that.. this gives at least a relatively accurate solution
anonymous
  • anonymous
http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/units-and-dimensional-analysis/MIT8_01SC_problems01.pdf
anonymous
  • anonymous
im stuck on the very first problem :(
anonymous
  • anonymous
Always draw before you start your analysis... It makes the problem a lot easier.. I think my solution is the one your teacher is searching for... But you might want to open your book to see if it's done there differently.
anonymous
  • anonymous
it was done quite differently :( http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/units-and-dimensional-analysis/MIT8_01SC_problems01_soln.pdf
anonymous
  • anonymous
They've made more assumptions than I did. Haha, dimensional analysis, I've had that a long while back. I don't think I'll be to good at that. I only use it as a check, not as a way to work ;P
anonymous
  • anonymous
Yeah I don't even understand how they could pull out those assumptions.

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