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A hypodermic syringe contains a medicine with the density of water (figure below). The barrel of the syringe has a cross-sectional area of 2.44 10-5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force vector F of magnitude 1.91 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal.

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    The gauge pressure in the barrel of the syringe is
    1.91N/2.44*10^-5 m^2 = 7.83*10^4 Pa

    The gauge pressure at the opening of the needle is 0. (1.00 atm absolute)

    Use the Bernoulli equation for the velocity at the needle exit.

    deltaP(gauge) = 7.83*10^4 N/m^2
    = (1/2)(rho)*V^2

    rho is the medicine density, 1000 kg/m^3

    Solve for V.
    V = 12.5 m/s

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