# Answer to Question #10507 in Electric Circuits for mohammed

Question #10507

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 = Rn(P2 - P1)/(8L)

The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at one end of the needle and the other end are P2 and P1, both of which have the dimensions of [M]/{[L][T]2}. The symbol represents the viscosity of the liquid and has the dimensions of [M]/{[L][T]}. The symbol 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 expressions for Q.

Q = Rn(P2 - P1)/(8L)

The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at one end of the needle and the other end are P2 and P1, both of which have the dimensions of [M]/{[L][T]2}. The symbol represents the viscosity of the liquid and has the dimensions of [M]/{[L][T]}. The symbol 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 expressions for Q.

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