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Deriving Bernoulli's Equation from a Few Simple Concepts

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Among the classes I took as undergraduate was fluid mechanics, and among the most useful equations I learned, or at least to which I was reintroduced, was Bernoulli's equation. This equation is useful for understanding the flow of fluid in pipes, and as way of remembering the equation, I like to use a few concepts I easily remember to help derive the equations. The way I typically start is by thinking of the equation as a kind energy conversation equation. This ultimately leads to a kind of height conservation equation (this will become clearer as we reach our desired equation). To be more clear, all the terms in the equation have a set of units that evaluate to length. Additionally, there are three terms: one term for gravitational potential energy, another for kinetic energy, and one for pressure energy. Finally, each side of the equation will represent the energy (or height) state of the fluid a points A and B, respectively, and will have all three aforementioned terms (See the ...
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Obtaining the Fractional Form of a Repeating Decimal

I was out for a run recently, and I noticed I had forgotten how to convert a repeating decimal into a fraction; as a reminder, a repeating decimal is a decimal which has a set of digits that repeat infinitely. So I began by attempting to solve the simple repeating decimal of 0.333..., since I know what I'm working towards (1/3). Typically, such problems are presented in an academic environment where people are told exactly how to obtain it without experimenting. In daily problems we encounter, we typically do not have guidance as in a classroom, so we must experiment and observe while striving towards an answer. This is a common method of problem solving in the real world: We take a guess, try it, see if it works, and repeat if necessary until we arrive at an answer (exact or of varying precision). This is similar to a numerical methods approach, as when attempting to find the zeros of a function. It was this guess and test approach that I used to obtain a solution. I first began b...
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Introduction

I would like to start this blog by describing it's purpose. There are many blogs out there, but I hope to make this an interesting one that is worth your time. My aim is to provide my thoughts on various topics in mathematics, physics, philosophy, and the intersection of these subjects. So I may publish my reasoning on solving a problem in heat transfer or thermodynamics, or I may provide tips on approaching problem solving in various subjects. I also intend to publish some examples of programming in my ongoing efforts to self-learn. My interests involve things like computational applications and app development. I hope you find it useful, and feel free to add a respectful comment. Disagreement is welcomed, but not a disagreeable manner.
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