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Volume Injected into Capillary

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    So for an experiment, we injected a small volume of fluid into a capillary (76 micrometer diameter) through a pressure difference and I'm trying to calculate exactly how much was injected.

    diameter of capillary = 76e-6 m
    height one end was raised above the other = 5.334 cm = 0.05334 m
    density of the fluid = .997 g/mL
    viscosity of the fluid = 1 g/(m*s) = 0.001 kg/(m*s)
    elapsed time during injection = 31 s
    capillary length = 78 cm = 0.78 m

    2. Relevant equations

    The formulas we are given are:
    pressure = (density) * (gravitational constant) * (change in height)
    volume injected = (pressure * pi * d^4 * t)/(128 * viscosity * capillary length) <-- Poiseuille's Law


    3. The attempt at a solution

    Based on my calculations, I'm getting:

    P = (997 kg/m^3)*(9.81 m/s^2)*(0.05334 m) = 521.7 Pa
    V = (521.7 Pa)(pi)(76e-6 m)(31s)/(128 * .001 kg/(m*s) * .780 m) = 37.676 m^3

    Clearly, we didn't inject anywhere close to that much into a tiny capillary, so where am I going wrong?

    Thanks in advance!
     
  2. jcsd
  3. Feb 27, 2013 #2

    haruspex

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    Is there something you forgot?
     
  4. Feb 27, 2013 #3
    Yes. My dignity.

    Thank you so much. I can't believe I didn't catch that.
     
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