I have used polar coordinates in a previous post. But that post contained mathematics that was more much difficult than is needed here. So, I am going to begin with a simple description of polar coordinates. Usually we describe the position of a point in space using Cartesian coordinates; in two dimensions the position of… Continue reading 21.3 Polar coordinates, circles and spirals

DNA is an example of a nucleic acid. Its name is an abbreviation for deoxyribonucleic acid. It was discovered in 1869 by a Swiss doctor called Friedrich Miescher (1844-1895). Most people know that DNA is responsible for coding genetic information but may not know much about its chemical composition, how it codes this information or… Continue reading 21.2 Nucleic acids

While I was compiling the index to this blog, I noticed that I had written several posts about mechanical simple harmonic oscillators but hadn’t written anything about electrical simple harmonic oscillators– the subject of this post. A simple harmonic oscillator is a system that oscillates indefinitely by exchanging potential and kinetic energy. In a real… Continue reading 21.1 An electrical simple harmonic oscillator

Before you read this, I suggest you read post 20.38. Cells (post 16.18) in plants are surrounded by a rigid wall made of the polysaccharide (post 20.38) cellulose that consists of repeating β-D-glucose residues (post 20.38) as shown above. In this picture, the second residue is identical to the first but I have shown it… Continue reading 20.40 Polysaccharides

Before you read this, I suggest you read post 20.7. For security reasons, there is a limit to the quantity of gels you can take on to an aeroplane. But do the passengers or security staff understand what a gel is? And what do the people responsible for the rules mean by the word “gel”?… Continue reading 20.39 Gels

Before you read this, I suggest you read post 20.32. In the English language the word “sugar” is often used to mean “sucrose” – the sugar extracted from sugar cane or sugar beet that is often used to sweeten foods and drinks. But sucrose is not the only type of sugar – other examples are… Continue reading 20.38 Sugars

Before you read this, I suggest you read posts 20.34 and 20.36. Poiseuille’s equation (highlighted in yellow above) enables us to calculate the rate of flow, R (volume divided by time), of a liquid of viscosity Ƞ in a narrow horizontal tube of radius a and length L, when there is a pressure difference, Δp,… Continue reading 20.37 Poiseuille’s equation

Before you read this, I suggest you read posts 17.15, 20.34 and 20.35. The equation highlighted in yellow, above, is the Navier-Stokes equation for incompressible flow of a fluid. A more complicated form of this equation can be used to explain the flow of compressible fluids. For more information on incompressible and compressible flow, see… Continue reading 20.36 The Navier-Stokes equation

In post 17.15, we saw how fluid flow could be explained by two equations – Bernoulli’s equation (conservation of mechanical energy) and a continuity equation (conservation of mass). But, conservation of mechanical energy assumes that the viscosity of the fluid is negligible because viscosity dissipates mechanical energy (post 17.17) and so is similar to friction… Continue reading 20.35 Incompressible and compressible fluid flow

Before you read this post, you should understand the dot product of vectors (appendix 2 post 17.13), the cross product of vectors (post 17.37) and partial differentiation (post 19.11). I have been asked to write a post on the Navier-Stokes equation that was briefly introduced in post 17.15. Before I write it, I need to… Continue reading 20.34 The operator ∇