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Time rate of change of air pressure

  1. Oct 9, 2014 #1
    Air pressure decreases at a rate of 2.5 pascals per kilometer in the eastward direction. In addition, the air pressure is increasing at a constant rate with respect to time everywhere. A ship sailing eastward at 10 km/hour past an island takes barometer readings and records a pressure drop of 30 pascals in 2 hours. Estimate the time rate of change of air pressure on the island. (A pascal is a unit of air pressure.)

    What is time rate of change of air pressure?

    Attempt:

    Basically tried everything possible

    10 x 2 = 20 km

    30 Pa / 2 hrs = 15 Pa / hr

    2.5 Pa x 20 km = 50 Pa
     
  2. jcsd
  3. Oct 9, 2014 #2

    pasmith

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    This is an exercise in using the multivariate chain rule in the form [tex]\frac{dp}{dt} = \frac{\partial p}{\partial t} + \frac{\partial p}{\partial x}\frac{dx}{dt}[/tex] where [itex]x(t)[/itex] is the position of the ship. You are trying to find [itex]\frac{\partial p}{\partial t}[/itex] which is stated to be constant.
     
  4. Oct 9, 2014 #3
    -15 = ∂p/∂t + (-2.5)(10) ?
    Is the unit for the answer Pa/hr?
     
  5. Oct 10, 2014 #4
    Yes
     
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