5 variables F=f(L,U,p,u) F force MLT^-2 L length L U I think its potential energ

Question

                                 5 variables                             

                                F=f(L,U,p,u)                             

                                F force MLT^-2                             

                                L length L                             

                                U  I think its potential energy LT^-1                             

                                p density ML^-3                             

                                u viscosity ML^-1T^-1                             

                                 I understand that there are 2 PI groups but I dont understand why you use length (L) potential energy (U) and density (p)                             

                                to find the first PI group                             

Explanation / Answer

For findidng the PI group we have to select 3 repeating variables such that

1) they should have all basic dimensions

2)with in the repeating variables there should be no PI group by combining them

3)Don't choose the dependent variable as a PI group

Since F is the dependent variable it is better not to take in the repeating variable becuase in every PI groups it is present.SO calculation may be difficult

If you take L,u, U it voilates the second condition

you can take either p,L,U or p,L u as repeating variables

But if the problem if force is a function of viscosity (u) then we don't want it to be appear in every PI group so we will take p,L,U as our repeating variables

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