- #1
evinda
Gold Member
MHB
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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?
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?