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mukushla
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how to choose repeating variables in Buckingham Pi Theorem...in particular
 2 years ago
 2 years ago
mukushla Group Title
how to choose repeating variables in Buckingham Pi Theorem...in particular
 2 years ago
 2 years ago

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mukushla Group TitleBest ResponseYou've already chosen the best response.0
nondimensional groups for heat transfer in a pipe...effective parameters : \[h : Mt^{3}T^{1}\]\[u : Lt^{1}\]\[k : MLt^{3}T^{1}\]\[c_p : L^2t^{2}T^{1}\]\[\mu : ML^{1}T^{1}\]\[\rho : ML^{3}\]\[d : L\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
we have 74=3 nondimensional group and 4 repeating variables..how to choose them considering the dimensions i gave u
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
and sorry \[\mu : ML^{1}t^{1}\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
@experimentX
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
we have a rule that No repeating parameter should have dimensions that are a power of the dimensions of another repeating parameter. why ...and how apply it here?
 2 years ago

eashmore Group TitleBest ResponseYou've already chosen the best response.1
I seem to have forgotten this from fluids (or maybe I never really learned it). You might find this helpful: http://www.eng.wayne.edu/legacy/forms/4/Buckinghamforlect1.pdf
 2 years ago

eashmore Group TitleBest ResponseYou've already chosen the best response.1
It says that the repeating variables that you choose cannot be manipulated into dimensionless groups. Define the above parameters for me please.
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
sorry i was out h: heat transfer coefficient u: flow mean velocity k: heat conductivity coefficient cp: specific heat capacity \(\mu\): viscousity \(\rho\) : density d: diameter of pipe
 2 years ago

eashmore Group TitleBest ResponseYou've already chosen the best response.1
Oh. Those are the units after each parameter. Let's see. We need 3 recurring variables. Choose d, u, and \(\rho\) Those should work.
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
emm...we need 4 if im not wrong
 2 years ago

eashmore Group TitleBest ResponseYou've already chosen the best response.1
I'm working out of that document I linked and it's ringing some bells. It looks like we have 7 variables\[f(h, u, k, c_p, \mu, \rho, d) \] Between these 7 variables, we have 4 different dimensions. Mass (M), time (t), temperature (T), and length (L). n = 7; m = 4 nm gives 3 dimensionless groups. We then need to choose 3 variables (these three cannot be formed into dimensionless groups themselves. That is to say that we cannot manipulate these three independently to create a dimensionless group. For example, if we had length and diameter, we couldn't choose these are two of our three. ) Once we choose three variables, we rewrite the four dimensions in terms of the three variables we chose. Does this follow?
 2 years ago

akifersoylu Group TitleBest ResponseYou've already chosen the best response.0
ı think 3 repeating variables occur; u, d, ρ,
 11 months ago
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