The volume of liquid fl owing per second is called the volume flow rate Q and has the dimensions of [L]3 / [T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation:

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 h represents the viscosity of the liquid and has the dimensions of [M] / {[L] [T]}. The symbol p 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?

Transcribed Image Text:

TR"(P2 – P;) 8nL