• Support PF! Buy your school textbooks, materials and every day products Here!

Basic Dimensional Analysis Question

  • Thread starter armolinasf
  • Start date
  • #1
196
0

Homework Statement



Porous rock through which groundwater can move is called an aquifer. The volume V of water that, in time t, moves through a cross section of area A of the aquifer is given by:

V/t=KA(H/L)

where H is the vertical drop of the aquifer over the horizontal distance L. The quantity K is the hydraulic conductivity of the aquifer. What are the SI units of K



The Attempt at a Solution



So since this is supposed to be a dimensional analysis question, I figured that I'd start by figuring out what the dimensions of the problem are and I came up with:

[V/t]=[K^a][A^b][(H/L)^c] ===> L^3*t^-1=[K^a][L^2b][L^c-c]

Since there is a time dimension on the left side of the equation I'm guessing that K has a time component but I'm not really too sure how to approach the problem...Thanks for the help
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Why are you writing [A]=[L^2b]? Area is just plain length squared, right? [A]=L^2. I don't know why you are writing [K^a] either. There's just a K in the formula. And H/L is dimensionless.
 
  • #3
196
0
Alright that clarifies some things for me...so then it would be L^3t^-1=K*L^2 (H/L is dimensionless because L/L is one right?) So for the dimensions to balance out K must be [L/T]? and that would be a speed right?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Alright that clarifies some things for me...so then it would be L^3t^-1=K*L^2 (H/L is dimensionless because L/L is one right?) So for the dimensions to balance out K must be [L/T]? and that would be a speed right?
Yes.
 

Related Threads on Basic Dimensional Analysis Question

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
6
Views
1K
Replies
2
Views
328
Replies
7
Views
3K
Replies
5
Views
2K
Top