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mukushla
 3 years ago
how to choose repeating variables in Buckingham Pi Theorem...in particular
mukushla
 3 years ago
how to choose repeating variables in Buckingham Pi Theorem...in particular

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

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

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

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0we 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?

eashmore
 3 years ago
Best ResponseYou've already chosen the best response.1I 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

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

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0sorry 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

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

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

eashmore
 3 years ago
Best ResponseYou've already chosen the best response.1I'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?

akifersoylu
 2 years ago
Best ResponseYou've already chosen the best response.0ı think 3 repeating variables occur; u, d, ρ,
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