The volume of liquid fl owing per second is called the

Chapter , Problem 60

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The volume of liquid fl owing per second is called the volume fl ow rate Q and has the dimensions of [L]3 /[T]. The fl ow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation: Q 5 pRn (P2 2 P1) 8hL 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.