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

  1. Nov 4, 2012 #1
    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
    Am I reading correctly that:
    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. jcsd
  3. Nov 4, 2012 #2
    Wow, after typing that all out I was seeing what I was doing wrong. I've got it figured out now. :)
     
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