# Homework Help: Continuity Equation: Relationship between vA and vB in terms of d and D

1. Nov 4, 2012

### bcalkins

1. The problem statement, all variables and given/known data
The continuity equation provides a second relation between the vA and vB, this time in terms of the diameters d and D. Numerical check: If the diameters are d = 1 cm and D = 10 cm, what is the ratio of the speeds, vB/vA?

2. Relevant equations
To clarify, is both d and D diameters, just one's capitalized to show the difference between the two?
The continuity equation is: Δm=ρV=ρAvΔt
my notes show: ρ2A2v2 = ρ1A1v1
ρ=density
A= cross-sectional area (equal to ∏(Diameter^2/4))?
v= velocity/speed

3. The attempt at a solution
A1v1=A2v2 ===> v2=v1(A1/A2) ====> v2=v1(d1^2/d2^2) ===>
Plugging this into the above given information:
v2= v1(10cm^2/1cm^2) = v1(100cm)
v1 = v2 (1cm^2/10cm^2) = v2(.01cm)
So the ratio of speeds would be .01cm/100cm = .0001
I know I'm doing something wrong, but this is all I have in my notes that looks somewhat useable. Please help! Thank you!

2. Nov 4, 2012

### bcalkins

Wow, after typing that all out I was seeing what I was doing wrong. I've got it figured out now. :)