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Math Help - How to form equations for these two statements, please give explanations?

  1. #1
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    How to form equations for these two statements, please give explanations?

    1. The pressure of a liquid varies as depth, when the density is constant.
    2. The pressure of a liquid varies as density when the depth is constant.

    Here is my try
    1. pressure=k(depth)+density.
    2.pressure=k(density)+depth
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  2. #2
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    Re: How to form equations for these two statements, please give explanations?

    Quote Originally Posted by hisajesh View Post
    1. The pressure of a liquid varies as depth, when the density is constant.
    2. The pressure of a liquid varies as density when the depth is constant.

    Here is my try
    1. pressure=k(depth)+density.
    2.pressure=k(density)+depth
    I am not sure what "varies as depth" means. If it means that pressure is proportional to depth, then the equation pressure = k * depth + density does not work. Indeed, if depth is doubled, then pressure = 2k * depth + pressure, which is not 2(k * depth + pressure) unless pressure = 0.

    I think pressure = k * density * depth.
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  3. #3
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    Re: How to form equations for these two statements, please give explanations?

    "The pressure of a liquid varies as density when the depth is constant"

    Is it Pressure = k* density*depth or Pressure=k*density+depth? Kindly give explanation on your choice.
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  4. #4
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    Re: How to form equations for these two statements, please give explanations?

    Quote Originally Posted by hisajesh View Post
    Is it Pressure = k* density*depth or Pressure=k*density+depth? Kindly give explanation on your choice.
    The first one. I explained in post #2 why I think that the second variant does not work.
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  5. #5
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    Re: How to form equations for these two statements, please give explanations?

    Can you help soloving this problem, steps are appreciated.
    The pressure of a liquid varies as depth, when the density is constant and its varies as density, when the depth is constant. The pressure is 1, when the depth is 32 and the density is 1. Find the depth at which the pressure is 2, when density is 16.
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  6. #6
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    Re: How to form equations for these two statements, please give explanations?

    Quote Originally Posted by hisajesh View Post
    The pressure of a liquid varies as depth, when the density is constant and its varies as density, when the depth is constant. The pressure is 1, when the depth is 32 and the density is 1. Find the depth at which the pressure is 2, when density is 16.
    Multiplying density by 16 in

    depth = 32, density = 1 => pressure = 1

    we get

    depth = 32, density = 16 => pressure = 16.

    We need pressure = 2, so we divide depth by 8 to get

    depth = 4, density = 16 => pressure = 2.

    Another way is to substitute depth = 32, density = 1 and pressure = 1 into the equation in post #2 and find k. Then you can find any of depth, density or pressure knowing the other two.
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