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L-shaped tank problem; forces due to water pressure

  1. Oct 11, 2016 #1
    1. The problem statement, all variables and given/known data
    HELP!! L-shaped tank problem! figure: http://www.webassign.net/hrw/hrw7_14-33.gif

    The L-shaped tank shown below is filled with water and is open at the top.
    (a) If d = 7.0 m, what is the force on face A due to the water?
    (b) What is the force on face B due to the water?

    hrw7_14-33.gif

    2. Relevant equations

    F=PA
    P=pgh

    3. The attempt at a solution

    I've got the (a) part right: pgd*A = 1000*9.8*14*49 = 6722800.

    However, I don't have a clue how I can get pressure on face B!
     
  2. jcsd
  3. Oct 11, 2016 #2

    mfb

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    You should work with units.

    What is the pressure (not force) at the top of B? What is the pressure at the bottom? Optional: What is the pressure at a height x above the bottom? How can you combine this information?
     
  4. Oct 11, 2016 #3
    The tank is open from the top,dont you think atmospheric pressure should be added? Do you remember the law which states that fluids in closed systems transmit the same pressure at every surface of the closed vessel?
     
  5. Oct 11, 2016 #4

    gneill

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    If your course materials don't give you a "canned" formula for finding the net force on underwater vertical surfaces then presumably you'll be expected to derive them. What is your math background? Is a bit of calculus an option here?

    No for two reasons:
    1) The question specifically asks for the force due to the water.
    2) The force due to air pressure will exist on both sides of an external tank wall, cancelling out.
     
  6. Oct 11, 2016 #5
    Pressure at Bottom=ρgh
    =1000*9.81*21
    =206010 Pa
    Pressure at Top=137340 Pa

    Find the average and then substitute in P=F/A, face B's geometrical center is exactly at 3.5m so you can find the average force.

    DONT QUOTE ME!!!
     
    Last edited: Oct 11, 2016
  7. Oct 11, 2016 #6

    mfb

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    Providing full answers is against the forum rules, but your answer is wrong anyway. The pressure varies across the surface of B.
     
  8. Oct 11, 2016 #7
    I think calculus is not an option here as this is just high-school physics and sorry for my presumption, I thought that the question required the total force in one direction.( BTW for your second reason the resultant force is zero! Just 'Force' is a vector so you have to be specific otherwise the resultant force at B is 0 N if you know what I mean:wink:)
     
  9. Oct 11, 2016 #8
    Oh sorry then...BTW I know what you mean but the question asks for ''Average Force'' at B
    Edited: Now it doesn't give a full answer hope I helped!
     
    Last edited: Oct 11, 2016
  10. Oct 11, 2016 #9
    Zypheros_Knight mfb gneill
    can't we make an integral for force between 2d and 3d
    then F=integral(density.g.d.A) with boundaries from 2d to 3d
     
  11. Oct 11, 2016 #10

    gneill

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    You can. Although it might be more instructive to take a general case first. It's a standard result that you can then use whenever this sort of problem pops up.
     
  12. Oct 11, 2016 #11
    then it will be density.g.A.(9d^2-4d^2)/2=1000x9.8x49x245/2= 58824500N please check my answer if I'm solving it correctly
     
  13. Oct 11, 2016 #12
    Its wrong,BTW is this a high-school based question or a college based one because both will have different requirements? And please show your working (I haven't reached integration in my course!)
     
  14. Oct 11, 2016 #13

    gneill

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    Can you go into detail about how you arrived at your formula? I suspect that you've made a slip regarding how the wall area fits into your result.
     
  15. Oct 11, 2016 #14
    The wall area is 49 m2 but I cant figure out what integration method he used
     
  16. Oct 11, 2016 #15
    forget it, okay area =49 now what ??
     
  17. Oct 11, 2016 #16
  18. Oct 11, 2016 #17

    gneill

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    Your formula is pretty close to correct, but I believe you made a error when you introduced the area during your derivation. I really do suggest that you do the derivation for a general case, forgetting the multiples of d for the moment. Just assign a starting and ending depth to two variables. No numbers for now, just symbols.
     
  19. Oct 11, 2016 #18

    mfb

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    Two ways to check:

    - if you would have worked with units as I suggested in post #2 you would have noted your mistake directly at the point where you introduced it because the units stop matching there
    - while B is a bit deeper than A, the pressure there is not completely different, and A and B have the same area. The value for B should be a bit higher, but certainly not 10 times the result for A.
     
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