MHB Find an Equivalent Law for Dimensionless Quantities

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The discussion focuses on finding an equivalent law for a physical system described by the equation f(E,P,A)=0, where E, P, and A represent energy, pressure, and area, respectively. The user initially believes that the number of fundamental units is equal to the number of dimensional quantities, suggesting that Buckingham's π theorem cannot be applied. However, other participants clarify that the chosen units are correct and interdependent, indicating that Buckingham's theorem can still be utilized. The conversation emphasizes the need to explore the application of dimensionless quantities despite initial doubts. Overall, the thread highlights the importance of understanding dimensional analysis in physical laws.
evinda
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Hello! (Wave)

A physical system is described by a law of the form $f(E,P,A)=0$ where $E,P,A$ represent, respectively, enery, pressure and area of surface. Find an equivalent law that relates suitable dimensionless quantities.

I have tried the following:

The fundamental units are:

Mass: $M$, Length: $L$, Time: $T$.

Thus:
$$[E]=ML^{2}T^{-2} \\ [P]=ML^{-1}T^{-2} \\ [A]=L^2$$

In this case, the number of fundamental units is equal to the number of the quantities with dimensions, so we cannot apply Buckingham $\pi$ theorem , right?

But how else can we find an equivalent law that relates suitable dimensionless quantities? (Thinking)

Or have I done something wrong at the choice of the fundamental units? :confused:
 
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Hey! (Blush)

Those units are correct and they are dependent on each other.
I think that means that we can still apply Buckingham's theorem.
Did you try? (Wondering)
 
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