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Fluids problem

  1. Dec 25, 2006 #1
    I don't have a diagram for this, so I'm going to do my best to describe it.

    A glass tube lying horizontally has three different cross-sectional areas, A, B and C. Area A is 12 cm^2, B is 5.6 cm^2, and C is 6.0 cm^2. Mercury (density = 13,600 kg/m^3) is being pushed through the tube by a piston open to the atmosphere at the end of area A. The mercury flows through area B and leaves the tube at area C with a velocity of 8.0 m/s.

    a) What is the total pressure at point A in area A?
    b) What is the total pressure at point B in area B?

    Relevant equations:

    Pressure = Force/Area
    Density = mass/volume
    A(1)v(1) = A(2)v(2)
    P(1) + (1/2)pv(1)^2 = P(2) + (1/2)pv(2)^2 } part of Bernoulli's equation

    ^all that comes to mind

    My attempt at a solution:

    To calculate the velocity of mercury through area A:
    A(1)v(1) = A(2)v(2)
    .12 m^2 * v(1) = .06 m^2 * 8 m/s
    v(1) = 4 m/s

    To calculate the velocity of mercury through area B:
    A(1)v(1) = A(2)v(2)
    .12 m^2 * 4 m/s = .056 m^2 * v(2)
    v(2) = 8.57 m/s

    I think that the total pressure at point A is just atmospheric pressure (1.013 * 10^5 Pa), but I'm not sure. When I use this value in Bernoulli's equation to calculate the pressure in area B, I get a negative number, which makes me think that my assumption is wrong.
    Last edited: Dec 25, 2006
  2. jcsd
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