The drag force (FD) on a body of a given shape (such as a sphere) will be influenced by the variables listed below having dimensions indicated. The drag force is the main dependent variable in this...

The drag force (FD) on a body of a given shape (such as a sphere) will be influenced by the variables listed below having dimensions indicated.

The drag force is the main dependent variable in this case, and there will be three dimensionally independent quantities involving F, L, and T. These may be taken to be S, ρ, and V.

a) Show that S, ρ, and V are dimensionally independent.

b) How many nondimensional quantities (π₁,π₂,π₃...) will there be, in this case?

c) Perform a dimensional analysis and express π1 involving FD as a function of the other π quantities; i.e., find π1 = ψ (π₂, …).