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Homework Help: Question dealing with density and pressure

  1. Jan 18, 2009 #1
    I haven't taken physics in a while, and most of this is physics related. My professor's lectures have not helped me understand the material, so I have questions on my homework. I would like to learn how to approach this problem and solve it.


    The figure shows a vertical dam holding back a reservoir of depth h. The lower half of the reservoir consists of a sludge whose density is twice that of water, and the upper half of the reservoir's volume consists of pure water.

    a. Determine how pressure depends on altitude z in the water and sludge.
    b. Let w be the dam's width, and determine the horizontal component of force on the dam.


    Thank you in advance.
     

    Attached Files:

  2. jcsd
  3. Jan 18, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi tophat22! Welcome to PF! :smile:
    a. The pressure is basically the weight of the fluid above (per area). :smile:

    b. Pressure = force per area, so the force on the dam is the integral of pressure times area. :wink:
     
  4. Jan 19, 2009 #3
    for part a, what am I supposed to do with vector z? will I have to deal with an integral?
     
  5. Jan 19, 2009 #4

    tiny-tim

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    Hi tophat22! :smile:
    No, you'd only need an integral if the density was varying continuously

    but here, it's constant to a certain height, and then a different constant, so you can just multiply instead of integrating. :smile:
     
  6. Jan 20, 2009 #5

    stewartcs

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    Since the pressure varies with depth there will be a different force on the dam at different depths. So integration would be needed.

    CS
     
  7. Jan 20, 2009 #6

    tiny-tim

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    Hi stewartcs! :smile:

    Not for part a. :wink:
     
  8. Jan 20, 2009 #7

    stewartcs

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    Sorry I missed the "part a" there! :blushing: Silly me...I should not post until my morning tea!

    CS
     
  9. Jan 20, 2009 #8

    tiny-tim

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    It's afternoon here in London! :biggrin:

    'll soon be proper tea-time

    … and time for "Countdown" on telly. :tongue2:​
     
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