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!

Water pressure in a tank

  1. Aug 2, 2017 #1
    1. The problem statement, all variables and given/known data

    on a flat desk is an aquarium with a volume of 640 cm3 ,t's not full of water. The pressure to the bottom of the aquarium is 3 times bigger than to one side of it, how much water is in the tank?
    2. Relevant equations
    [​IMG]
    [​IMG] is the pressure,
    [​IMG] is the normal force,
    [​IMG] is the area of the surface on contact.


    3. The attempt at a solution
    I think this mainly requires crunching of crude formulas, I don't even know how to calculate the pressure to the side of a tank even if I have more variables. Thanks for even reading so far, any help is appreciated.
     
  2. jcsd
  3. Aug 2, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I'm not sure what the question means. Have you stated it exactly as given to you?
    The pressure at the side is not uniform on the sides. It could mean the average pressure there.
    Or, if, you knew the shape of the aquarium, it could mean the force, not the pressure.

    If the water has depth h, what is the average pressure on the side?
     
  4. Aug 2, 2017 #3

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    This question is bonkers - is that the actual wording of the problem as given to you ?
     
  5. Aug 2, 2017 #4
    Sorry I missed to mention that the tank is an cube, I forgot to mention it since I had to translate the whole question.
     
  6. Aug 2, 2017 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Then I would interpret it as saying the force is the same on the bottom as on each side.... particularly if it is a translation.
    If the depth is h, can you calculate the force on each side?

    Edit: correction.... Since we know the depth is less than the length and width, the total force on a side must be less than that on the base, so the right interpretation must be that the average pressures are equal.
     
    Last edited: Aug 5, 2017
  7. Aug 2, 2017 #6
    does that mean you would use the same formula as for the bottom? (ro)mg?
     
  8. Aug 2, 2017 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No. The pressure varies according to depth.
    Consider a horizontal strip of width dx at depth x. What is the pressure there? What is the total force on that strip?
     
  9. Aug 2, 2017 #8
    so any idea how to find out the h? I'm trying to understand other branches of physics, not just the ones I'm fairly good at.
     
  10. Aug 2, 2017 #9

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    We'll get to that. Please try to answer my question.
     
  11. Aug 2, 2017 #10
    ok so using a formula to find the F on a strip I used F=(ro)gLh*1/2 . I can put in all the numbers but what about depth?
     
  12. Aug 2, 2017 #11
    You need to solve for h using the information you have been given. Do you have another relationship involving h?
     
  13. Aug 3, 2017 #12
    This is the part that I get stuck at, if I knew the exerted force on the side or bottom I could just rearrange the variables and be done with it, but all I know is that the force to the bottom is 3 times stronger than to one side.
     
  14. Aug 3, 2017 #13
    What is the force to one side as a function of h (algebraically)?
     
  15. Aug 3, 2017 #14

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I specified a strip width dx at depth x, i.e. from depth x to depth x+dx. Where are those in your formula for the force?
     
  16. Aug 3, 2017 #15
    let's say the pressure on that strip is dF which is equal to the pressure at that depth P which we multiply by the area of the strip dA
    dF=PdA dA=Ldx
    dF=PLdx P=(ro)gx
    dF=(ro)gxLdx
    something like this?
     
  17. Aug 3, 2017 #16

    jbriggs444

    User Avatar
    Science Advisor

    Yes. The force on an incremental strip at depth x is ##\rho g x L\ dx##

    Now if you integrate that incremental force from top strip (x=0) to bottom strip (x=h), what do you get?
     
  18. Aug 3, 2017 #17
    I get the force applied to the whole wall of the aquarium, but we don't know the x or h
     
  19. Aug 3, 2017 #18

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    x is the variable of integration. After doing the integration and applying the bounds you will have a function of h.
    The force on the base of the tank is also a function of h.
    Find both functions.
     
  20. Aug 3, 2017 #19
    that makes some sense, I'll try that tomorrow. Thanks.
     
  21. Aug 4, 2017 #20
    I've got the formula for the base of the tank bF=(ro)gxL2
    but I'm quite lost on how to find a function, we worked a bit with them last year, but we didn't find new functions we just solved given ones.(which is stupid to be honest)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Water pressure in a tank
  1. Pressure of water tank (Replies: 1)

  2. Pressure at water tank (Replies: 3)

Loading...