The correct string tension equation with M/u.l. expressed in either way

For clarity, I find it imperative to iterate that the 0.008 below is M, which is "mass per unit lenght" in kg/m of a chosen material of a certain density, not the total mass of an unbeknownst string:

Thus, for the fundamental tone A4=440Hz, the solution
to the above-given equation per string would be:

W= {4 (0.16 * 193 600) * 0.008} Newtons

W= {4 * 30.976 * 0.008} Newtons

W= 990 Newtons

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Thus, both

W (tension of the string) = 4 (L^2) * (F^2) * M

and

T = F^2 * L^2 * D^2 * Pi * Rho

equate to the same thing because of the relationship:

Pi * D^2 * Rho
M (mass per unit lenght) = ___________

4

I hope that this clears all misunderstandings.

Cordially,
Ozan