I'm aware of the hydrostatic paradox that water will exert same pressure from same height irrespective of the shape of container (mass of liquid). But is it true water in different shapes of container with upto same height and same base will weigh the same on weighing scale?
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$\begingroup$ Hi. Why do you think it's so? Or why do you think it isn't? You're expected to show some effort to work through the question. $\endgroup$– stafusaCommented Sep 27, 2017 at 16:54
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$\begingroup$ I'm sorry my first question 😅 $\endgroup$– sayed afzalCommented Sep 27, 2017 at 17:32
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$\begingroup$ @stafusa Sayed has explained his thoughts in his comment to the video. $\endgroup$– sammy gerbilCommented Sep 27, 2017 at 18:05
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1$\begingroup$ Sayed Afzal, that's a relevant question, and I think removing the link to the video (referenced to in the current answers) is only a good idea if you include in the question the information they contained. BTW, do you think your question is different from Pressure and weight? (hydrostatic paradox)? | @sammygerbil, it might be, but I think we prefer to have the questions more self-contained. $\endgroup$– stafusaCommented Sep 27, 2017 at 18:40
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3$\begingroup$ Possible duplicate of Pressure and weight? (hydrostatic paradox) $\endgroup$– sammy gerbilCommented Sep 27, 2017 at 20:07
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2 Answers
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But is it true water in different shapes of container with upto same height and same base will weigh the same on weighing scale?
No. The weight scale is not going to just measure the pressure at the bottom. The weight scale measures the force exerted by the cup down on the scale.
If two containers have an equal height of the same fluid, the pressure on the inside bottom of the cup will be the same, but that doesn't say anything specifically about the force at the outside bottom of the cup, which is what is measured by a weight scale.
The container will require a force equal to the weight of the fluid and the weight of the container to remain in equilibrium. By having different shaped containers of different volumes, you can have the same hydrostatic pressure at the bottom while having completely different weights.
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Your answer originally cited a video entitled The Hydrostatic Paradox which has now been removed by the author (Techila). It showed 3 vessels with equal base areas containing different volumes of water to the same depth and asked Which container weighs most?
The answer given by Techila was that the force on the base of each vessel is the same, and this is the force measured by the weight scale, therefore all 3 vessel weigh the same.
The explanation by Techila is not correct. The obvious answer is correct : the container with the most liquid weighs the most. It makes no difference whether the contents are liquid or solid.
In your comment to Techila's video you quoted another video, by Katerina Visnjic of Princeton University. This shows a different experiment.
In Dr Visnjic's video a cylinder (b) and funnel (c) are supported by clamp stands. The only force on the scale pan is that due to the pressure of liquid on the base of each vessel, which is the same in both cases. The contents of the funnel (c) obviously weigh more, but the extra weight is supported by the clamp stand, not the scale pan.
In Techila's video there are no clamp stands : each vessel is supported entirely by the weighing machine. If the clamp stand in Dr Visnjic's experiment was also placed on the scale pan, then this would be the same as Techila's experiment.
Techila's explanation omits the effect of the forces on the sides of the container $^*$. The sides of the cylindrical container are vertical so the force of liquid on these sides has no vertical component. The sides of the funnel-shaped container slope outwards so the liquid exerts a downward component of force on these sides, and this force is transmitted through the rigid container to the scale pan, causing the scale to read more than the force on the base. The sides of the conical container slope inwards so there is an upwards component of force on the sides of the container, which is transmitted through the rigid walls of the container to the scale pan, causing the scale to read less than the force on the base of the container.
If Dr Visnjic used a conical vessel (with a disconncted base), the clamp would have to supply a downward force to prevent the cone from being pushed upward by the liquid inside.
Hence the funnel weighs more than the cylinder and the cone weighs less - as you expect by comparing the total mass of liquid in each container.
- Actually Techila mentioned the forces from the sides of containers (a) and (c) on the water but omitted the effect of the paired forces of the water on the containers and how this affected the reading on the weight scale.
answered Sep 27, 2017 at 18:23
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$\begingroup$ Thanks for answering with respect to the videos. I wasn't able to watch them on my phone. I didn't know if they were spreading misconceptions or not. $\endgroup$– JMacCommented Sep 27, 2017 at 18:24
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$\begingroup$ Not sure it is right. Problem (a) will give the same pressure at the bottom and hence same weight as (b). Hence it is not the support as the clamp does not hold the thing so it does not float. $\endgroup$ Commented Jan 12 at 9:58