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Bernoulli Equation - sign of gravitational acceleration

  1. Feb 29, 2016 #1
    1. The problem statement, all variables and given/known data
    Water flows from the faucet on the first floor of the building shown in the figure with a maximum velocity of 20 ft/s. For steady inviscid flow, determine the maximum water velocity from the basement faucet and from the faucet on the second floor. Assume each floor is 12 ft tall.
    fiAVcJJ.png

    2. Relevant equations
    Bernoulli:
    SygUNaj.gif

    3. The attempt at a solution
    Taking the north direction as the positive z-axis and assuming all pressures are 0 (free jet). Assuming the (1) is position is z = 0.
    zE3YFUJ.gif
    So, v1 = -20 ft/s, z1 = 0
    z2 = -12 ft, g= -32ft/s^2

    This gives a negative value for v2 squared, with no real solution. The correct answer is obtained by using g = 32ft/s instead of -32ft/s. I don't understand why. According to the reference frame I have chosen, the (2) position is negative, and so should be the gravitational acceleration since this is the direction the earth is pulling the water to. So if I take into account the direction for the elevation variable in Bernoulli's eq, it makes sense to also take it into account for the gravitational acceleration. Otherwise it makes no sense and it is inconsistent.

    What am I missing?
     
  2. jcsd
  3. Feb 29, 2016 #2
    In the Bernoulli equation, z is always measured upward and g is always taken as positive.
     
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