MHB Find an Equivalent Law for Dimensionless Quantities

[evinda]

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?

 

[I like Serena]

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)