1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Hydrostatic forces

  1. Dec 20, 2009 #1
    I need to find the hydrostatic force exerted on a plane submerged vertically in water. I attached a diagram of the problem.

    Here are the basic definitions:
    ---------------------------
    d=distance from surface, p=density, P=pressure

    [tex]p=\frac{m}{V}[/tex]

    [tex]P=pgd=\delta d[/tex]

    [tex]F=mg=pgAd[/tex]

    ---------------------------

    The area of the ith strip is [tex]A_i=6\Delta y[/tex] so the pressure exerted on the ith strip is [tex]\delta d_i=pgd_i=pg(6-y_i^*)[/tex]

    The hydrostatic force on the ith strip is [tex]F_i=\delta_iA_i=6pg(6-y_i)\Deltay[/tex]

    The approximate force along the entire surface is therefore:

    [tex]F_{net}=\lim_{n-\infty}\Sigma_{i=1}^n6pg(6-y_i)\Delta y[/tex]

    [tex]=6pg\int_0^4(6-y)dy[/tex]

    Am I setting this up correctly?
     

    Attached Files:

  2. jcsd
  3. Dec 20, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    It looks like you are doing it correctly from first principles, but I think this line should be (not sure on notation but this is how I saw a similar summation in a math book)


    [tex]F_{net}=\lim_{\Delta y \rightarrow 0} \sum_{y=0} ^{y=4} 6pg(6-y_i)\Delta y[/tex]
     
  4. Dec 20, 2009 #3
    I was writing out the limit of the Riemann sum. There are [tex]n[/tex] subdivisions and [tex]\Delta y=\frac{4-0}{n}[/tex]. So I think what you wrote was equivalent to the Riemann sum.
     
  5. Dec 20, 2009 #4

    rock.freak667

    User Avatar
    Homework Helper

    It probably is, I was never taught the Riemann Sum, but you are correct though.
     
  6. Dec 20, 2009 #5

    ideasrule

    User Avatar
    Homework Helper

    You don't need to write out the Riemann sum; that just makes things unnecessarily complicated. I find that going directly to Fnet[itex]=6pg\int_0^4(6-y)dy[/itex] is much easier and more intuitive. (BTW, that integral gives the exact force on the plate, not the approximate force.)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook