The volume of liquid flowing per second is call the volume flow rate Q and has the dimension of [L]^3/[T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation: Q=((pi)(R^n)(P2-P1))/8NL. The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the needle are P2 and P1, both of which have the dimensions of [M]/{[L][T]^2}. The symbol N represents the viscosity of liquid and has the dimensions of [M]/{[L][T]}. The symbol pi stands for pi and, like the number 8 and the exponent N, has no dimensions. Using dimensional analysis, determine the value of n in the expression for Q. :eek: please need help

If you simply substitute the dimensions that you are given into the equation you get this:


Q = \frac {\pi R^N (P_2 - P_1)} {8NL}\

=\frac {L^N \cdot \frac M {L T^2}} {\frac M {LT} \cdot L}\

= \frac {L ^{(N-1)}} T.


You are told that the units of Q are L^3/T -- can you take it from here to solve for N?