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Thread: Height of Water in Tipping Glass

  1. #1
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    Height of Water in Tipping Glass

    So this is an interesting trig problem, and one I'm having trouble with. You have a glass filled with water, and you're given the width of the glass (W) and the initial height of the water(H0). As the glass tips over, what is the height of the water from the table (before it spills) in terms of W, H0, and θ? A diagram below is attached to help explain it better.
    Attached Thumbnails Attached Thumbnails Height of Water in Tipping Glass-img_0329.jpg  
    Last edited by bbk001; Jul 15th 2018 at 07:26 PM. Reason: Image upload failure
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  2. #2
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    Re: Height of Water in Tipping Glass

    When it is a trapezoidal cross-section, I think the height is:

    $$\dfrac{2WH_0+W^2\tan \theta}{2W^2\tan \theta}$$

    When it is a triangular cross-section, the height is:

    $$\sqrt{\dfrac{2WH_0}{\tan \theta}}\sin \theta$$
    Last edited by SlipEternal; Jul 16th 2018 at 08:01 AM.
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