Question

Im having severe trouble understanding the concept of Dimensions. And with 300 other students in my physics class the Professor doens't have alot of time for individual students....

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

Q= (pi)R^n(P2-P1)/ 8nL

The length and radius of the needle are L and R, respectively, both of which have a dimension [L]. The pressures at opposite ends of the needle are P2 and P1 , both have the dimensions of [M]/{[L][T]^2}. The symbol n (On the bottom of the fraction) has the dimensions [M]/{[L][T]}. Pi, the number 8 and the exponent n (On the top) have no dimensions. Using dimensional analysis, determine the value of n in the expression for Q.

I have honestly spent an hour on this question with lettle or no understanding of what it means or how to go about solving it. Can someone please help?

Thanks.

Answer 1

somehow I see an error. Mass is in the pressure unit, but nowhere else. It wont cancel if that is so.

Answer 2

Q= (pi)R^n(P2-P1)/ 8nL

Just substitute the dimentsions for all the symbols:

Q = L^3 T^(-1)

R = L

P2 - P1 = M L^(-1)T^(-2)

n = M L^(-1)T^(-1)


L^3 T^(-1) =
L^n M L^(-1)T^(-2)M^(-1) L T =
L^n T^(-1) ---->

n = 3