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Homework Help: Fluid statics seems easy but can't figure it out please help.

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data

    A cylindrical tank of internal diameter 1.5m and length 2.0m is mounted on a trailer. When the tank is filled with water the combined weight is 55 kN. Find the weight of tank plus trailer with the tank full of methyl alcohol (relative density 0.789).

    2. Relevant equations

    density*volume=mass
    pi*r²*length= volume of cylindre


    3. The attempt at a solution

    total volume of methyl in tank= 3.53 m³
    using density of methyl (789 kg/m³)
    mass of methyl in tank= 2788.55 kg
    however, I don't see how this is gonna help finding the mass of water in the tank filled with water or the mass of the tank. Basically, if I don't find the volume of water in the tank filled but not fully with water I cannot find the mass of that water. Therefore, I cannot find the mass of the tank and trailer.
    if anybody could help that would be nice.
    thanks.
     
    Last edited: Apr 4, 2010
  2. jcsd
  3. Apr 4, 2010 #2

    Doc Al

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    Staff: Mentor

    How did you calculate that volume? (Is 1.5 m the radius or the diameter?)

    You can find the mass of the water just like you can find the mass of the methyl alcohol. You are given the total weight, so what's the total mass of truck plus water?
     
  4. Apr 4, 2010 #3
    no because the tank is not fully filled with water unless I know the volume I can't find it
     
  5. Apr 4, 2010 #4
    tried it with the corrected value of r it still doesn't work ( forgot to tell the answer should be around 47.7kN
     
  6. Apr 4, 2010 #5

    Doc Al

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    Staff: Mentor

    Answer these questions:

    What's the volume of the tank?

    What's the mass of the water?

    What's the total mass of the truck + water?

    What's the mass of the truck alone (empty tank)?

    What's the mass of the alcohol?
     
  7. Apr 4, 2010 #6
    1. 0.75²*pi*2=3.53m³
    2.mass of water:( 55kN-weight of tank)/9.81
    3. total mass of truck+water=55kN/9.81=5606.52 Kg
    4.mass of empty tank= 5606.52 Kg-mass of water
    5.mass of alcohol= 2785.17 Kg( in a tank full of alcohol)

    note 2 and 3 are the same equations which leads to 0=0.
    Moreover, I don't really see the point of the alcohol in this problem. In fact if we have a tank entirely filled with alcohol how is it related to the not entirely water filled tank?
     
  8. Apr 4, 2010 #7

    Doc Al

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    OK.
    Figure it out using density X volume. What's the density of water?
    OK.
    No. That's the total mass of truck + water. (See #3.) You'll need to combine the correct answer to #2 with #3 to solve for the mass of the empty truck.
    Good. (Figure out the answer to #2 in the same way.)
     
  9. Apr 5, 2010 #8
    ok here is what I did but did not get the right answer.

    mass of water = density of water x volume of water in the tank= 1000(kg/m³)*3.53(m³)
    =3530 kg note : I did this as if the tank was fully filled with water but it is not.
    mass of tank= total mass ( tank + water) minus mass of water. you have then 5606.52kg-3530kg=2076.52kg for the mass of the tank.
    In Newtons, you have 20.370 kN.
    the answer should be 47.7 kN
     
  10. Apr 5, 2010 #9
    Yes, the question says "when the tank is filled with water" so you now have the correct mass of water.

    This is also correct, now you have the mass of an empty container, but what does the question ask for?

    This is the correct weight of the container, but read my last statement.
     
  11. Apr 5, 2010 #10
    yeah the question says filled not "fully" filled and the question asks for the weight of the container. However, in this exercice I should find 47.7 kN for it's weight.
     
  12. Apr 5, 2010 #11
    fill - occupy: occupy the whole of; "The liquid fills the container"

    So when a question says 'filled you can assume it means to the containers capacity; after all I used this and got the correct answer(according to you).

    So you have to do a bit of extra working; otherwise what would be the use of even mentioning the methanol at all?
     
  13. Apr 5, 2010 #12

    Doc Al

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    Staff: Mentor

    Good.
    Sure it's full. You are told as much.
    Excellent.
    You forgot to add the mass of the methyl alcohol.
     
  14. Apr 5, 2010 #13
    thank you very much for your help I got it now. It is the way I read the question that was wrong. I'll try to be more focused next time. thanks again
     
  15. Apr 5, 2010 #14
    Finally :tongue:

    Glad we could help.
     
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