Question

Thelength and radius of the needle are L and R,respectively, both of which have the dimension [L]. Thepressures at opposite ends of the needle are P₂and P₁, both of which have the dimensions of[M]/{[L][T]²}. The symbolη represents theviscosity of the liquid and has the dimensions of[M]/{[L][T]}. The symbol π stands for pi and, likethe number 8 and the exponent n, has no dimensions. Usingdimensional analysis, determine the value of n in theexpression for Q.

Q= πRn (P2-P1)/8ηL