Solving Riemann Sum for "Deformation of Water by Magnetic Field

In summary, the conversation is about someone trying to recreate an experiment on the deformation of water by a magnetic field. The paper with the experiment can be found on Google. The person is having trouble understanding how the values for Δh were obtained through a Riemann sum on the 2nd page of the paper. They have managed to obtain Δy values for their own experiment, but are unsure of how to proceed. They are asking for help to understand the equations and expressions used in the paper.
  • #1
subzero0137
91
4
I'm not sure if this is the right place to post this in, but I'm trying to recreate the "Deformation of water by a magnetic field" experiment by Chen et al. The PDF version of the paper can be accessed via Google (for some reason it won't let me provide a direct link).

On the 2nd page of the paper, they do a Riemann sum to calculate the value for the depression of the water surface as a function of position, but I can't figure out how they got those values for Δh. For my experiment I've managed to obtain the Δy values, but I don't know how to go from there. Any help would be appreciated.
 
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  • #2
subzero0137 said:
I'm not sure if this is the right place to post this in, but I'm trying to recreate the "Deformation of water by a magnetic field" experiment by Chen et al. The PDF version of the paper can be accessed via Google (for some reason it won't let me provide a direct link).

On the 2nd page of the paper, they do a Riemann sum to calculate the value for the depression of the water surface as a function of position, but I can't figure out how they got those values for Δh. For my experiment I've managed to obtain the Δy values, but I don't know how to go from there. Any help would be appreciated.

You should type out the few confusing equations/expressions.
 

Related to Solving Riemann Sum for "Deformation of Water by Magnetic Field

1. What is a Riemann Sum and how is it relevant to the deformation of water by a magnetic field?

A Riemann Sum is a method used in calculus to approximate the area under a curve by dividing it into smaller rectangles. In the context of the deformation of water by a magnetic field, the Riemann Sum is used to calculate the change in volume of water as it is exposed to a magnetic field.

2. How does a magnetic field cause water to deform?

A magnetic field is a region in space where magnetic forces can act on objects. In the case of water, the magnetic field causes the water molecules to align in a specific direction, resulting in a change in the overall shape and volume of the water.

3. What factors can affect the accuracy of the Riemann Sum calculation for the deformation of water by a magnetic field?

The accuracy of the Riemann Sum calculation can be affected by various factors such as the strength of the magnetic field, the temperature of the water, and the composition of the water (e.g. the presence of impurities or ions).

4. How can the results of the Riemann Sum calculation be applied in real-world situations?

The results of the Riemann Sum calculation can be applied in various fields, such as material science and engineering, to understand the impact of magnetic fields on the properties of water. This can be useful in the development of technologies that utilize magnetic fields for various purposes.

5. Are there any limitations to using the Riemann Sum for the deformation of water by a magnetic field?

Yes, there are limitations to using the Riemann Sum for this particular application. For instance, it assumes that the water is incompressible, which may not always be the case. Additionally, it does not take into account the effects of surface tension, which can also affect the deformation of water in a magnetic field.

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