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Homework Help: Water pressure problem

  1. Jan 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Water flows through a hole at the bottom of a tank that is filled to a height h=3m. The radius of the hole is r1 = 1.5 cm.
    1. What is the speed of the water immediately after it leaves the hole?

    2. At what distance d below the bottom of the tank is the radius of the stream reduced to r2 = 1 cm?

    2. Relevant equations

    3. The attempt at a solution
    I managed to solve the speed for 7.7 m/s. However, I'm not sure what formula to use to address the atmospheric pressure that cause the stream to shrink.
  2. jcsd
  3. Jan 27, 2015 #2
    The stream shrinks because it is accelerating gravitationally. As it speeds up, for the flow rate to remain constant, the cross sectional area must decrease.

  4. Jan 27, 2015 #3
    Based on your clarification, I calculated the velocity at the bottom using the conservation of volumetric flow rate (R = Av = constant), v0 = 17.3. Then g = dv/dt -> dt = dv/g = 0.98 s. Then d = d0 + v0t + 0.5at2 = 12.3, which seems to be the correct result. What do you think?
  5. Jan 28, 2015 #4
    I haven't checked your arithmetic, but you seem to have the right idea.
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