unit conversion coefficient?

Question

I've been stuck on this problem for a while. I need this equation for another question. here it is:
The unit conversion coefficient (u) for the equation R= u*C*I*A is 0.278. How do you calculate this number?
Units are :
R= m/s, C=unitless, I=mm/hr and A=km^2
I need help.

Answer 1

"u" converts hours to seconds and mm*km^2 to meters so

"u" must divide by 60^2 (1 hour = 60 minutes*60 seconds), divide by 1000 (1000mm = 1m) and multiply by 1,000,000(1000m^2 = 1km^2) to make R be in m/s. (By the way, this necessarily makes the units of "u" m^-2.)

1000^2/(60*60*1000) = 0.278m^-2

Answer 2

You don't. Something is wrong with your equation, or your units.

To convert all the variables to m/s you would multiply I by 1/1000/3600 (1 over mm/ meter over sec/hr, or meter hours per mm seconds), and A by 10^6 m/km. This gives you R = .278 CIA, but the units of R would be m^3/sec, not m/s. You are multiplying a velocity times an area. If C is unitless you can't get a velocity.

Answer 3

Are the units on R perhaps m³/s? If so, the conversion coef is

(1 mm/hr)(1 m/1000 mm)(1 hr/3600 s)(10^6 m²/km²)

= 5/18 ≈ 0.278

and the units on u (which I will denote [u]) come from

m³/s = [u] (mm/hr)(km²)

So

[u] = m³-hr/(s-mm-km²)