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.
2 answers
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
2 answers