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for a given patient it is determined that the blood vessel may rupture if its diameter increases faster than 200 um/s. The blood vessel starts with diameter 4mm and needs to expand to a diameter of 7mm. Is it safe to inflate the balloon at a constant rate of 30 mm^3/s? What about 60 mm^3/s.?

  • calculus -

    From the previous post, keeping all the measurements in mm,

    dV/dt = (4πr^2 + 60π) dr/dt

    so, if dV/dt = 30,

    30 = 4π(16 + 15) dr/dt
    dr/dt = .0770 mm/s = 77 um/s. That means that the diameter is increasing by 154um/s, so that's ok. As the diameter increases, the rate of expansion slows down.

    At 60mm^3/s, the inflation rate starts at 308um/s. Boom!

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