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Fluid Mechanics - similarity

  1. May 1, 2009 #1
    1. The problem statement, all variables and given/known data
    A body when tested in air of density 1.18 kg/m3 and dynamic viscosity 1.52x10^-5 Pas at a velocity of 35 m/s was found to produce a resistance of 250 N. A similarly shaped body 10 times longer than the original was tested in water of dynamic viscosity 1x10^-3 Pas. Determine the resistance for the larger body.

    2. Relevant equations
    In the previous question I have obtained via the Pi-theorem:
    R / (rho x l^2 x v^2) = f ((rho x v x l)/μ)
    which is correct.

    3. The attempt at a solution
    1:
    rho air = 1.18 kg/m3
    μair = 1.52x10^-5 Pas
    v = 35 m/s
    R = 250N
    l

    2:
    rho water = 1000 kg/m3
    μwater = 1x10^-3 Pas
    v = ?
    R = ?
    10l

    For dynamic similarity:
    (rho1 x v1 x l1)/μ1 = (rho2 x v2 x l2)/μ2
    (1.18 x 35 x l)/1.25x10^-5 = (1000 x v2 x 10l)/1x10^-3
    (1.18 x 35)/1.25x10^-5 = (1000 x v2 x 10)/1x10^-3
    I get: v2 = 0.2717 m/s

    Complete similarity:
    R1 / (rho1 x (l^2)1 x (v^2)1) = R2 / (rho2 x (l^2)2 x (v^2)2)
    250 / (1.18 x l^2 x 35^2 = R2 / (1000 x 100l^2 x 0.2717^2)
    250 / (1.18 x 35^2 = R2 / (1000 x 100 x 0.2717^2)
    I get: R2 = 1276.8 N

    Though the answer should be:
    R2 = 1082063.71 N

    Does anyone know what I am doing wrong?

    Thanks in advance!
     
  2. jcsd
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