AP Physics

The volume of liquid flowing 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.

Q = pi * R^n (P2 - P1) /
8ηL

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]}. 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.

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  1. n=4

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